├── OpenMP Version ├── .Rhistory ├── .DS_Store ├── LT_Simulations_OpenMP.R ├── Simulations_OpenMP.R ├── MAPIT_OpenMP.R └── MAPIT_OpenMP.cpp ├── .DS_Store ├── QQPlot.R ├── README.md ├── Standard Version ├── LT_Simulations.R ├── Simulations.R ├── MAPIT.R └── MAPIT.cpp └── License.md /OpenMP Version/.Rhistory: -------------------------------------------------------------------------------- 1 | 1e5*1e2 2 | 1e5*1e-2 3 | -------------------------------------------------------------------------------- /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lorinanthony/MAPIT/HEAD/.DS_Store -------------------------------------------------------------------------------- /OpenMP Version/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lorinanthony/MAPIT/HEAD/OpenMP Version/.DS_Store -------------------------------------------------------------------------------- /QQPlot.R: -------------------------------------------------------------------------------- 1 | ggd.qqplot = function(pvector, main=NULL, ...){ 2 | o = -log10(sort(pvector,decreasing=F)) 3 | e = -log10( 1:length(o)/length(o) ) 4 | plot(e,o,pch=19,cex=1, main=main, ..., 5 | xlab=expression(Expected~~-log[10](italic(p))), 6 | ylab=expression(Observed~~-log[10](italic(p))), 7 | xlim=c(0,max(e)), ylim=c(0,max(o))) 8 | lines(e,e,col="red") 9 | } -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # The MArginal ePIstasis Test (MAPIT) 2 | 3 | ### Important Note on Repository 4 | A generalization of this software is now maintained in the [**multivariate MArginal ePIstasis Test (mvMAPIT)** GitHub repository](https://github.com/lcrawlab/mvMAPIT) which generalizes the univariate MAPIT framework to any number of traits. Full documentation of the mvMAPIT R package, including examples and articles, can be found [here](https://lcrawlab.github.io/mvMAPIT/). 5 | 6 | ### Introduction 7 | Epistasis, commonly defined as the interaction between multiple genes, is an important genetic component underlying phenotypic variation. Many statistical methods have been developed to model and identify epistatic interactions between genetic variants. However, because of the large combinatorial search space of interactions, most epistasis mapping methods face enormous computational challenges and often suffer from low statistical power. In [Crawford et al. (2017)](http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1006869) and [Crawford and Zhou (2018)](https://www.biorxiv.org/content/early/2018/07/23/374983), we present a novel, alternative strategy for mapping epistasis: the MArginal ePIstasis Test (MAPIT). Our method examines one variant at a time, and estimates and tests its "marginal epistatic effects" --- the combined pairwise interaction effects between a given variant and all other variants. By avoiding explicitly searching for interactions, our method avoids the large combinatorial search space and improves power. Our method is novel and relies on a recently developed variance component estimation method for efficient and robust parameter inference and p-value computation. 8 | 9 | MAPIT is implemented as a set of R and C++ routines, which can be carried out within an R environment. 10 | 11 | 12 | ### The R Environment 13 | R is a widely used, free, and open source software environment for statistical computing and graphics. The most recent version of R can be downloaded from the [Comprehensive R Archive Network (CRAN)](http://cran.r-project.org/). CRAN provides precompiled binary versions of R for Windows, MacOS, and select Linux distributions that are likely sufficient for many users' needs. Users can also install R from source code; however, this may require a significant amount of effort. For specific details on how to compile, install, and manage R-packages, refer to the manual [R Installation and Administration](http://cran.r-project.org/doc/manuals/r-release/R-admin.html). 14 | 15 | In its current construction, we recommend against running MAPIT while using R Studio. 16 | 17 | 18 | ### R Packages Required for MAPIT 19 | MAPIT requires the installation of the following R libraries: 20 | 21 | * [doParallel](https://cran.r-project.org/web/packages/doParallel/index.html) 22 | 23 | * [Rcpp](https://cran.r-project.org/web/packages/Rcpp/index.html) 24 | 25 | * [RcppArmadillo](https://cran.r-project.org/web/packages/RcppArmadillo/index.html) 26 | 27 | * [RcppParallel](https://cran.r-project.org/web/packages/RcppParallel/index.html) 28 | 29 | * [CompQuadForm](https://cran.r-project.org/web/packages/CompQuadForm/index.html) 30 | 31 | * [truncnorm](https://cran.r-project.org/web/packages/truncnorm/index.html) 32 | 33 | The easiest method to install these packages is with the following example command entered in an R shell: 34 | 35 | install.packages("doParallel", dependecies = TRUE) 36 | 37 | Alternatively, one can also [install R packages from the command line](http://cran.r-project.org/doc/manuals/r-release/R-admin.html#Installing-packages). 38 | 39 | ### C++ Functions Required for MAPIT 40 | The code in this repository assumes that basic C++ functions and applications are already set up on the running personal computer or cluster. If not, the MAPIT functions and necessary Rcpp packages will not work properly. A simple option is to use [gcc](https://gcc.gnu.org/). macOS users may use this collection by installing the [Homebrew package manager](http://brew.sh/index.html) and then typing the following into the terminal: 41 | 42 | brew install gcc 43 | 44 | For extra tips on how to run C++ on macOS, please visit [here](http://seananderson.ca/2013/11/18/rcpp-mavericks.html). For tips on how to avoid errors dealing with "-lgfortran" or "-lquadmath", please visit [here](http://thecoatlessprofessor.com/programming/rcpp-rcpparmadillo-and-os-x-mavericks-lgfortran-and-lquadmath-error/). 45 | 46 | Note that there are two available versions of MAPIT, one of which takes advantage of [OpenMP](http://openmp.org/wp/), an API for multi-platform shared-memory parallel programming in C/C++. This is to speed up the computational time of the modeling algorithm. Unfortunately, OS X does not currently support OpenMP under the default compiler. A work around to use OpenMP in R on OS X can be found [here](http://thecoatlessprofessor.com/programming/openmp-in-r-on-os-x/). If after following these directions, the compiler of the C++ functions with 'omp.h' still does not work, we offer a standard version of MAPIT without the option of parallelization. If it is at all possible to get the OpenMP of MAPIT up and running, then we highly recommend it because this version of the code can drastically decrease computational time --- especially for larger data sets. 47 | 48 | 49 | ### Tutorial for Running MAPIT 50 | For the simulation tutorial provided here, we generate simulated genotypes for 10,000 unrelated variants. We show in our example R code how to implement MAPIT (for quantitative traits) and LT-MAPIT (for case-control studies) to perform a marginal epistatic association mapping test in order to find interacting causal variants of interest. 51 | 52 | ### Relevant Citations 53 | L. Crawford, P. Zeng, S. Mukherjee, and X. Zhou (2017). Detecting epistasis with the marginal epistasis test in genetic mapping studies of quantitative traits. *PLoS Genet*. **13**(7): e1006869. 54 | 55 | L. Crawford and X. Zhou (2018). Genome-wide marginal epistatic association mapping in case-control studies. *bioRxiv*. 374983. 56 | 57 | ### Questions and Feedback 58 | For questions or concerns with the MAPIT functions, please contact 59 | [Lorin Crawford](mailto:lorin_crawford@brown.edu) or 60 | [Xiang Zhou](mailto:xzhousph@umich.edu). 61 | 62 | We appreciate any feedback you may have with our repository and instructions. 63 | -------------------------------------------------------------------------------- /Standard Version/LT_Simulations.R: -------------------------------------------------------------------------------- 1 | ### Illustrating the Liability Threshold MArginal ePIstasis Test (LT-MAPIT) with Simulations ### 2 | 3 | ### Clear Console ### 4 | cat("\014") 5 | 6 | ### Clear Environment ### 7 | rm(list = ls(all = TRUE)) 8 | 9 | ### Load in the R libraries ### 10 | library(doParallel) 11 | library(Rcpp) 12 | library(RcppArmadillo) 13 | library(RcppParallel) 14 | library(CompQuadForm) 15 | library(truncnorm) 16 | 17 | ### Load in functions to make QQ-plot plots ### 18 | source("QQplot.R") 19 | 20 | #NOTE: This code assumes that the basic C++ functions are set up on the computer in use. If not, the MAPIT functions and Rcpp packages will not work properly. Mac users please refer to the homebrew applications and install the gcc commands listed in the README.md file before running the rest of the code [Warning: This step may take about an hour...]. 21 | 22 | ### Load in the C++ MAPIT wrapper functions ### 23 | source("MAPIT.R"); sourceCpp("MAPIT.cpp") 24 | 25 | ###################################################################################### 26 | ###################################################################################### 27 | ###################################################################################### 28 | 29 | ### Set the Seed for the analysis ### 30 | #set.seed(11151990) 31 | 32 | # Data are p single nucleotide polymorphisms (SNPs) with simulated genotypes. 33 | # Simulation Parameters: 34 | # (1) ind = # of samples in the population 35 | # (2) nsnp = number of SNPs or variants 36 | # (3) PVE = phenotypic variance explained/broad-sense heritability (H^2) 37 | # (4) rho = measures the portion of H^2 that is contributed by the marignal (additive) effects 38 | # (5) k = assumed disease prevelance in the population 39 | # (6) samp = # of samples to analyze 40 | 41 | ind = 1e6; nsnp = 1e4; pve=0.6; rho=0.5; k = 0.001; samp = 500 42 | 43 | ### Simulate the genotypes such that all variants have minor allele frequency (MAF) > 0.05 ### 44 | # NOTE: As in the paper, we center and scale each genotypic vector such that every SNP has mean 0 and standard deviation 1. 45 | maf <- 0.05 + 0.45*runif(nsnp) 46 | Geno <- (runif(ind*nsnp) < maf) + (runif(ind*nsnp) < maf) 47 | Geno <- matrix(as.double(Geno),ind,nsnp,byrow = TRUE) 48 | Xmean=apply(Geno, 2, mean); Xsd=apply(Geno, 2, sd); Geno=t((t(Geno)-Xmean)/Xsd) 49 | 50 | ### Set the size of causal SNP groups ### 51 | ncausal1= 10 # Set 1 of causal SNPs 52 | ncausal2 = 10 # Set 2 of Causal SNPs 53 | ncausal3 = 1e3-ncausal1-ncausal2 # Set 3 of Causal SNPs with only marginal effects 54 | 55 | # NOTE: As in the paper, we randomly choose causal variants that classify into three groups: (i) a small set of interaction SNPs, (ii) a larger set of interaction SNPs, and (iii) a large set of additive SNPs. In the simulations carried out in this study, SNPs interact between sets, so that SNPs in the first group interact with SNPs in the second group, but do not interact with variants in their own group (the same applies to the second group). One may view the SNPs in the first set as the “hubs” in an interaction map. We are reminded that interaction (epistatic) effects are different from additive effects. All causal SNPs in both the first and second groups have additive effects and are involved in pairwise interactions, while causal SNPs in the third set only have additive effects. 56 | 57 | #Select Causal SNPs 58 | s = 1:nsnp 59 | s1=sample(s, ncausal1, replace=F) 60 | s2=sample(s[s%in%s1==FALSE], ncausal2, replace=F) 61 | s3=sample(s[s%in%c(s1,s2)==FALSE], ncausal3, replace=F) 62 | 63 | #Create Causal Epistatic Matrix 64 | Xcausal1=Geno[,s1]; Xcausal2=Geno[,s2]; Xcausal3=Geno[,s3] 65 | Xepi=c() 66 | for(i in 1:ncausal1){ 67 | Xepi=cbind(Xepi,Xcausal1[,i]*Xcausal2) 68 | } 69 | dim(Xepi) 70 | 71 | #Marginal effects only 72 | Xmarginal=cbind(Xcausal1,Xcausal2,Xcausal3) 73 | beta=rnorm(dim(Xmarginal)[2]) 74 | z_marginal=c(Xmarginal%*%beta) 75 | beta=beta*sqrt(pve*rho/var(z_marginal)) 76 | z_marginal=Xmarginal%*%beta 77 | 78 | #Epistatic effects 79 | beta=rnorm(dim(Xepi)[2]) 80 | z_epi=c(Xepi%*%beta) 81 | beta=beta*sqrt(pve*(1-rho)/var(z_epi)) 82 | z_epi=Xepi%*%beta 83 | 84 | # NOTE: Each effect size for the marginal, epistatic, and random error effects are drawn from a standard normal distribution. Meaning beta ~ MVN(0,I), alpha ~ MVN(0,I), and epsilon ~ MVN(0,I). We then scale both the additive and pairwise genetic effects so that collectively they explain a fixed proportion of genetic variance. Namely, the additive effects make up rho%, while the pairwise interactions make up the remaining (1 − rho)%. Once we obtain the final effect sizes for all causal SNPs, we draw errors to achieve the target H^2. 85 | 86 | #Error 87 | z_err=rnorm(ind) 88 | z_err=z_err*sqrt((1-pve)/var(z_err)) 89 | 90 | #Latent Variables 91 | z=z_marginal+z_epi+z_err 92 | 93 | # NOTE: Now that we have the liabilities, we can assign case-control labels according to the disease prevelance parameter. We will treat this like the LT-MAPIT paper and take an equal number of cases and controls. 94 | 95 | ### Set the Threshold ### 96 | thresh=qnorm(1-k,mean=0,sd=1) 97 | 98 | ### Find the Number of Cases and Controls ### 99 | Pheno=rep(0,ind) 100 | Pheno[z>thresh] = 1 101 | 102 | ### Subsample a particular number of cases and controls ### 103 | cases = sample(which(z>thresh),samp/2,replace = FALSE) 104 | controls = sample(which(z<=thresh),samp/2,replace = FALSE) 105 | y = Pheno[c(cases,controls)] 106 | X = Geno[c(cases,controls),] 107 | 108 | ### Remove the variables that are not being used ### 109 | rm(z); rm(z_marginal); rm(z_epi); rm(Xmarginal); rm(Xepi) 110 | rm(Xcausal1); rm(Xcausal2); rm(Xcausal3) 111 | 112 | ### Check dimensions and add SNP names ### 113 | dim(X); length(y) 114 | colnames(X) = paste("SNP",1:ncol(X),sep="") 115 | 116 | ### Save the names of the causal SNPs ### 117 | SNPs = colnames(X)[c(s1,s2)] 118 | 119 | ###################################################################################### 120 | ###################################################################################### 121 | ###################################################################################### 122 | 123 | ### Running LT-MAPIT using Davies Method ### 124 | 125 | ### Set the number of cores ### 126 | cores = detectCores() 127 | 128 | ### Run LT-MAPIT ### 129 | ptm <- proc.time() #Start clock 130 | mapit = MAPIT(t(X),y,hybrid=FALSE,test="davies",k=k,cores=cores) 131 | proc.time() - ptm #Stop clock 132 | 133 | davies.pvals = mapit$pvalues 134 | names(davies.pvals) = colnames(X) 135 | 136 | ### NOTE: The first set of p-values will be deflated (as mentioned in Crawford and Zhou (2018)). To fix this issues we next run the test statistic readjustment procedure ### 137 | pvals = davies.pvals[davies.pvals>=0]; summary(pvals) 138 | q = qchisq(pvals,df=1,lower.tail = FALSE); summary(q) 139 | gs = median(q); m = 0.4549; summary((q/gs)*m) 140 | pvals = pchisq((q/gs)*m,df=1,lower.tail = FALSE) 141 | summary(pvals) 142 | 143 | ### Plot observed the p-values on a QQ-plot ### 144 | ggd.qqplot(pvals) 145 | 146 | ### Look at the causal SNPs in group 1 and 2 ### 147 | pvals[s1]; pvals[s2] 148 | 149 | ###################################################################################### 150 | ###################################################################################### 151 | ###################################################################################### 152 | 153 | ### Running an Informed Exhaustive Search ### 154 | 155 | #NOTE: Now we may take only the significant SNPs according to their marginal epistatic effects and run a simple exhaustive search between them 156 | 157 | thresh = 0.05/length(pvals) #Set a significance threshold 158 | v = pvals[pvals<=thresh] #Call only marginally significant SNPs 159 | pwise = c() 160 | for(k in 1:length(v)){ 161 | fit = c(); m = 1:length(v) 162 | for(w in m[-k]){ 163 | pt = lm(y~X[,names(v)[k]]:X[,names(v)[w]]) 164 | fit[w] = coefficients(summary(pt))[8] 165 | names(fit)[w] = paste(names(v)[k],names(v)[w],sep = "-") 166 | } 167 | pwise = c(pwise,fit) 168 | } 169 | 170 | ### Look at the exhaustive search results ### 171 | vc.pwise = sort(pwise[!is.na(pwise)]) #Get rid of the NAs 172 | vc.pwise = vc.pwise[seq(1,length(vc.pwise),2)] #Only keep the unique pairs 173 | sort(vc.pwise)[1:150] #Sort the pairs in order of significance -------------------------------------------------------------------------------- /OpenMP Version/LT_Simulations_OpenMP.R: -------------------------------------------------------------------------------- 1 | ### Illustrating the Liability Threshold MArginal ePIstasis Test (LT-MAPIT) with Simulations ### 2 | 3 | ### Clear Console ### 4 | cat("\014") 5 | 6 | ### Clear Environment ### 7 | rm(list = ls(all = TRUE)) 8 | 9 | ### Load in the R libraries ### 10 | library(doParallel) 11 | library(Rcpp) 12 | library(RcppArmadillo) 13 | library(RcppParallel) 14 | library(CompQuadForm) 15 | library(truncnorm) 16 | 17 | ### Load in functions to make QQ-plot plots ### 18 | source("QQplot.R") 19 | 20 | #NOTE: This code assumes that the basic C++ functions are set up on the computer in use. If not, the MAPIT functions and Rcpp packages will not work properly. Mac users please refer to the homebrew applications and install the gcc commands listed in the README.md file before running the rest of the code [Warning: This step may take about an hour...]. 21 | 22 | ### Load in the C++ MAPIT wrapper functions ### 23 | source("MAPIT_OpenMP.R"); sourceCpp("MAPIT_OpenMP.cpp") 24 | 25 | ###################################################################################### 26 | ###################################################################################### 27 | ###################################################################################### 28 | 29 | ### Set the Seed for the analysis ### 30 | #set.seed(11151990) 31 | 32 | # Data are p single nucleotide polymorphisms (SNPs) with simulated genotypes. 33 | # Simulation Parameters: 34 | # (1) ind = # of samples in the population 35 | # (2) nsnp = number of SNPs or variants 36 | # (3) PVE = phenotypic variance explained/broad-sense heritability (H^2) 37 | # (4) rho = measures the portion of H^2 that is contributed by the marignal (additive) effects 38 | # (5) k = assumed disease prevelance in the population 39 | # (6) samp = # of samples to analyze 40 | 41 | ind = 1e6; nsnp = 1e4; pve=0.6; rho=0.5; k = 0.01; samp = 500 42 | 43 | ### Simulate the genotypes such that all variants have minor allele frequency (MAF) > 0.05 ### 44 | # NOTE: As in the paper, we center and scale each genotypic vector such that every SNP has mean 0 and standard deviation 1. 45 | maf <- 0.05 + 0.45*runif(nsnp) 46 | Geno <- (runif(ind*nsnp) < maf) + (runif(ind*nsnp) < maf) 47 | Geno <- matrix(as.double(Geno),ind,nsnp,byrow = TRUE) 48 | Xmean=apply(Geno, 2, mean); Xsd=apply(Geno, 2, sd); Geno=t((t(Geno)-Xmean)/Xsd) 49 | 50 | ### Set the size of causal SNP groups ### 51 | ncausal1= 10 # Set 1 of causal SNPs 52 | ncausal2 = 10 # Set 2 of Causal SNPs 53 | ncausal3 = 1e3-ncausal1-ncausal2 # Set 3 of Causal SNPs with only marginal effects 54 | 55 | # NOTE: As in the paper, we randomly choose causal variants that classify into three groups: (i) a small set of interaction SNPs, (ii) a larger set of interaction SNPs, and (iii) a large set of additive SNPs. In the simulations carried out in this study, SNPs interact between sets, so that SNPs in the first group interact with SNPs in the second group, but do not interact with variants in their own group (the same applies to the second group). One may view the SNPs in the first set as the “hubs” in an interaction map. We are reminded that interaction (epistatic) effects are different from additive effects. All causal SNPs in both the first and second groups have additive effects and are involved in pairwise interactions, while causal SNPs in the third set only have additive effects. 56 | 57 | #Select Causal SNPs 58 | s = 1:nsnp 59 | s1=sample(s, ncausal1, replace=F) 60 | s2=sample(s[s%in%s1==FALSE], ncausal2, replace=F) 61 | s3=sample(s[s%in%c(s1,s2)==FALSE], ncausal3, replace=F) 62 | 63 | #Create Causal Epistatic Matrix 64 | Xcausal1=Geno[,s1]; Xcausal2=Geno[,s2]; Xcausal3=Geno[,s3] 65 | Xepi=c() 66 | for(i in 1:ncausal1){ 67 | Xepi=cbind(Xepi,Xcausal1[,i]*Xcausal2) 68 | } 69 | dim(Xepi) 70 | 71 | #Marginal effects only 72 | Xmarginal=cbind(Xcausal1,Xcausal2,Xcausal3) 73 | beta=rnorm(dim(Xmarginal)[2]) 74 | z_marginal=c(Xmarginal%*%beta) 75 | beta=beta*sqrt(pve*rho/var(z_marginal)) 76 | z_marginal=Xmarginal%*%beta 77 | 78 | #Epistatic effects 79 | beta=rnorm(dim(Xepi)[2]) 80 | z_epi=c(Xepi%*%beta) 81 | beta=beta*sqrt(pve*(1-rho)/var(z_epi)) 82 | z_epi=Xepi%*%beta 83 | 84 | # NOTE: Each effect size for the marginal, epistatic, and random error effects are drawn from a standard normal distribution. Meaning beta ~ MVN(0,I), alpha ~ MVN(0,I), and epsilon ~ MVN(0,I). We then scale both the additive and pairwise genetic effects so that collectively they explain a fixed proportion of genetic variance. Namely, the additive effects make up rho%, while the pairwise interactions make up the remaining (1 − rho)%. Once we obtain the final effect sizes for all causal SNPs, we draw errors to achieve the target H^2. 85 | 86 | #Error 87 | z_err=rnorm(ind) 88 | z_err=z_err*sqrt((1-pve)/var(z_err)) 89 | 90 | #Latent Variables 91 | z=z_marginal+z_epi+z_err 92 | 93 | # NOTE: Now that we have the liabilities, we can assign case-control labels according to the disease prevelance parameter. We will treat this like the LT-MAPIT paper and take an equal number of cases and controls. 94 | 95 | ### Set the Threshold ### 96 | thresh=qnorm(1-k,mean=0,sd=1) 97 | 98 | ### Find the Number of Cases and Controls ### 99 | Pheno=rep(0,ind) 100 | Pheno[z>thresh] = 1 101 | 102 | ### Subsample a particular number of cases and controls ### 103 | cases = sample(which(z>thresh),samp/2,replace = FALSE) 104 | controls = sample(which(z<=thresh),samp/2,replace = FALSE) 105 | y = Pheno[c(cases,controls)] 106 | X = Geno[c(cases,controls),] 107 | 108 | ### Remove the variables that are not being used ### 109 | rm(z); rm(z_marginal); rm(z_epi); rm(Xmarginal); rm(Xepi) 110 | rm(Xcausal1); rm(Xcausal2); rm(Xcausal3) 111 | 112 | ### Check dimensions and add SNP names ### 113 | dim(X); length(y) 114 | colnames(X) = paste("SNP",1:ncol(X),sep="") 115 | 116 | ### Save the names of the causal SNPs ### 117 | SNPs = colnames(X)[c(s1,s2)] 118 | 119 | ###################################################################################### 120 | ###################################################################################### 121 | ###################################################################################### 122 | 123 | ### Running LT-MAPIT using Davies Method ### 124 | 125 | ### Set the number of cores ### 126 | cores = detectCores() 127 | 128 | ### Run LT-MAPIT ### 129 | ptm <- proc.time() #Start clock 130 | mapit = MAPIT(t(X),y,hybrid=FALSE,test="davies",k=k,cores=cores) 131 | proc.time() - ptm #Stop clock 132 | 133 | davies.pvals = mapit$pvalues 134 | names(davies.pvals) = colnames(X) 135 | 136 | ### NOTE: The first set of p-values will be deflated (as mentioned in Crawford and Zhou (2018)). To fix this issues we next run the test statistic readjustment procedure ### 137 | pvals = davies.pvals[davies.pvals>=0]; summary(pvals) 138 | q = qchisq(pvals,df=1,lower.tail = FALSE); summary(q) 139 | gs = median(q); m = 0.4549; summary((q/gs)*m) 140 | pvals = pchisq((q/gs)*m,df=1,lower.tail = FALSE) 141 | summary(pvals) 142 | 143 | ### Plot observed the p-values on a QQ-plot ### 144 | ggd.qqplot(pvals) 145 | 146 | ### Look at the causal SNPs in group 1 and 2 ### 147 | pvals[s1]; pvals[s2] 148 | 149 | ###################################################################################### 150 | ###################################################################################### 151 | ###################################################################################### 152 | 153 | ### Running an Informed Exhaustive Search ### 154 | 155 | #NOTE: Now we may take only the significant SNPs according to their marginal epistatic effects and run a simple exhaustive search between them 156 | 157 | thresh = 0.05/length(pvals) #Set a significance threshold 158 | v = pvals[pvals<=thresh] #Call only marginally significant SNPs 159 | pwise = c() 160 | for(k in 1:length(v)){ 161 | fit = c(); m = 1:length(v) 162 | for(w in m[-k]){ 163 | pt = lm(y~X[,names(v)[k]]:X[,names(v)[w]]) 164 | fit[w] = coefficients(summary(pt))[8] 165 | names(fit)[w] = paste(names(v)[k],names(v)[w],sep = "-") 166 | } 167 | pwise = c(pwise,fit) 168 | } 169 | 170 | ### Look at the exhaustive search results ### 171 | vc.pwise = sort(pwise[!is.na(pwise)]) #Get rid of the NAs 172 | vc.pwise = vc.pwise[seq(1,length(vc.pwise),2)] #Only keep the unique pairs 173 | sort(vc.pwise)[1:150] #Sort the pairs in order of significance -------------------------------------------------------------------------------- /Standard Version/Simulations.R: -------------------------------------------------------------------------------- 1 | ### Illustrating the MArginal ePIstasis Test (MAPIT) with Simulations ### 2 | 3 | ### Clear Console ### 4 | cat("\014") 5 | 6 | ### Clear Environment ### 7 | rm(list = ls(all = TRUE)) 8 | 9 | ### Load in the R libraries ### 10 | library(doParallel) 11 | library(Rcpp) 12 | library(RcppArmadillo) 13 | library(RcppParallel) 14 | library(CompQuadForm) 15 | 16 | ### Load in functions to make QQ-plot plots ### 17 | source("QQplot.R") 18 | 19 | #NOTE: This code assumes that the basic C++ functions are set up on the computer in use. If not, the MAPIT functions and Rcpp packages will not work properly. Mac users please refer to the homebrew applications and install the gcc commands listed in the README.md file before running the rest of the code [Warning: This step may take about an hour...]. 20 | 21 | ### Load in the C++ MAPIT wrapper functions ### 22 | source("MAPIT.R"); sourceCpp("MAPIT.cpp") 23 | 24 | ###################################################################################### 25 | ###################################################################################### 26 | ###################################################################################### 27 | 28 | ### Set the Seed for the analysis ### 29 | #set.seed(11151990) 30 | 31 | # Data are p single nucleotide polymorphisms (SNPs) with simulated genotypes. 32 | # Simulation Parameters: 33 | # (1) ind = # of samples 34 | # (2) nsnp = number of SNPs or variants 35 | # (3) PVE = phenotypic variance explained/broad-sense heritability (H^2) 36 | # (4) rho = measures the portion of H^2 that is contributed by the marignal (additive) effects 37 | 38 | ind = 3e3; nsnp = 1e4; pve=0.6; rho=0.5; 39 | 40 | ### Simulate the genotypes such that all variants have minor allele frequency (MAF) > 0.05 ### 41 | # NOTE: As in the paper, we center and scale each genotypic vector such that every SNP has mean 0 and standard deviation 1. 42 | maf <- 0.05 + 0.45*runif(nsnp) 43 | X <- (runif(ind*nsnp) < maf) + (runif(ind*nsnp) < maf) 44 | X <- matrix(as.double(X),ind,nsnp,byrow = TRUE) 45 | Xmean=apply(X, 2, mean); Xsd=apply(X, 2, sd); X=t((t(X)-Xmean)/Xsd) 46 | 47 | ### Set the size of causal SNP groups ### 48 | ncausal1= 10 # Set 1 of causal SNPs 49 | ncausal2 = 10 # Set 2 of Causal SNPs 50 | ncausal3 = 1e3-ncausal1-ncausal2 # Set 3 of Causal SNPs with only marginal effects 51 | 52 | # NOTE: As in the paper, we randomly choose causal variants that classify into three groups: (i) a small set of interaction SNPs, (ii) a larger set of interaction SNPs, and (iii) a large set of additive SNPs. In the simulations carried out in this study, SNPs interact between sets, so that SNPs in the first group interact with SNPs in the second group, but do not interact with variants in their own group (the same applies to the second group). One may view the SNPs in the first set as the “hubs” in an interaction map. We are reminded that interaction (epistatic) effects are different from additive effects. All causal SNPs in both the first and second groups have additive effects and are involved in pairwise interactions, while causal SNPs in the third set only have additive effects. 53 | 54 | ### Select causal SNPs in groups 1 and 2 ### 55 | snp.ids = 1:nsnp 56 | s1=sample(snp.ids, ncausal1, replace=F) 57 | s2=sample(snp.ids[-s1], ncausal2, replace=F) 58 | s3=sample(snp.ids[-c(s1,s2)], ncausal3, replace=F) 59 | 60 | Xcausal1=X[,s1]; Xcausal2=X[,s2]; Xcausal3=X[,s3] 61 | 62 | ### Create the epistatic design matrix ### 63 | W=c() 64 | for(i in 1:ncausal1){ 65 | W=cbind(W,Xcausal1[,i]*Xcausal2) 66 | } 67 | dim(W) 68 | 69 | ### Simulate marginal (additive) effects ### 70 | Xmarginal=cbind(Xcausal1,Xcausal2,Xcausal3) 71 | beta=rnorm(dim(Xmarginal)[2]) 72 | y_marginal=c(Xmarginal%*%beta) 73 | beta=beta*sqrt(pve*rho/var(y_marginal)) 74 | y_marginal=Xmarginal%*%beta 75 | 76 | ### Simulate epistatic effects ### 77 | alpha=rnorm(dim(W)[2]) 78 | y_epi=c(W%*%alpha) 79 | alpha=alpha*sqrt(pve*(1-rho)/var(y_epi)) 80 | y_epi=W%*%alpha 81 | 82 | # NOTE: Each effect size for the marginal, epistatic, and random error effects are drawn from a standard normal distribution. Meaning beta ~ MVN(0,I), alpha ~ MVN(0,I), and epsilon ~ MVN(0,I). We then scale both the additive and pairwise genetic effects so that collectively they explain a fixed proportion of genetic variance. Namely, the additive effects make up rho%, while the pairwise interactions make up the remaining (1 − rho)%. Once we obtain the final effect sizes for all causal SNPs, we draw errors to achieve the target H^2. 83 | 84 | ### Simulate residual error ### 85 | y_err=rnorm(ind) 86 | y_err=y_err*sqrt((1-pve)/var(y_err)) 87 | 88 | # Simulate the continuous phenotypes 89 | y = y_marginal+y_epi+y_err 90 | 91 | ### Check dimensions and add SNP names ### 92 | dim(X); dim(y) 93 | colnames(X) = paste("SNP",1:ncol(X),sep="") 94 | 95 | ### Save the names of the causal SNPs ### 96 | SNPs = colnames(X)[c(s1,s2)] 97 | 98 | ###################################################################################### 99 | ###################################################################################### 100 | ###################################################################################### 101 | 102 | ### Running MAPIT using the Hybrid Method ### 103 | 104 | #IMPORTANT: MAPIT takes the X matrix as pxn --- NOT nxp 105 | 106 | ### Run MAPIT ### 107 | ptm <- proc.time() #Start clock 108 | mapit = MAPIT(t(X),y) 109 | proc.time() - ptm #Stop clock 110 | 111 | hybrid.pvals = mapit$pvalues 112 | names(hybrid.pvals) = colnames(X) 113 | 114 | ###################################################################################### 115 | ###################################################################################### 116 | ###################################################################################### 117 | 118 | ### Running MAPIT using the Normal Z-test ### 119 | 120 | ### Run MAPIT without specifiying test (should get a warning) ### 121 | ptm <- proc.time() #Start clock 122 | mapit = MAPIT(t(X),y,hybrid=FALSE) 123 | proc.time() - ptm #Stop clock 124 | 125 | normal.pvals1 = mapit$pvalues 126 | names(normal.pvals1) = colnames(X) 127 | 128 | ### Run MAPIT while specifiying test ### 129 | ptm <- proc.time() #Start clock 130 | mapit = MAPIT(t(X),y,hybrid=FALSE,test = "normal",cores=cores) 131 | proc.time() - ptm #Stop clock 132 | 133 | normal.pvals2 = mapit$pvalues 134 | names(normal.pvals2) = colnames(X) 135 | 136 | ###################################################################################### 137 | ###################################################################################### 138 | ###################################################################################### 139 | 140 | ### Running MAPIT using Davies Method ### 141 | 142 | ### Run MAPIT ### 143 | ptm <- proc.time() #Start clock 144 | mapit = MAPIT(t(X),y,hybrid=FALSE,test="davies") 145 | proc.time() - ptm #Stop clock 146 | 147 | davies.pvals = mapit$pvalues 148 | names(davies.pvals) = colnames(X) 149 | 150 | ###################################################################################### 151 | ###################################################################################### 152 | ###################################################################################### 153 | 154 | ### Running a fast version of MAPIT using an approximate Davies Method ### 155 | 156 | ### Set the number of cores ### 157 | cores = detectCores() 158 | 159 | ### Run MAPIT ### 160 | ptm <- proc.time() #Start clock 161 | mapit = MAPIT_Davies_Approx(t(X),y) 162 | proc.time() - ptm #Stop clock 163 | 164 | approx.davies.pvals = c() 165 | for(i in 1:length(vc.ts)){ 166 | lambda = sort(mapit$Eigenvalues[,i],decreasing = T) 167 | 168 | Davies_Method = davies(mapit$Est[i], lambda = lambda, acc=1e-8) 169 | approx.davies.pvals[i] = 2*min(Davies_Method$Qq, 1-Davies_Method$Qq) 170 | names(approx.davies.pvals)[i] = colnames(X)[i] 171 | } 172 | 173 | ###################################################################################### 174 | ###################################################################################### 175 | ###################################################################################### 176 | 177 | ### Plot observed the p-values on a QQ-plot ### 178 | ggd.qqplot(hybrid.pvals) 179 | ggd.qqplot(normal.pvals1) 180 | ggd.qqplot(normal.pvals2) 181 | ggd.qqplot(davies.pvals) 182 | ggd.qqplot(approx.davies.pvals) 183 | 184 | ### Look at the causal SNPs in group 1 and 2 ### 185 | hybrid.pvals[s1]; hybrid.pvals[s2] 186 | normal.pvals1[s1]; normal.pvals1[s2] 187 | normal.pvals2[s1]; normal.pvals2[s2] 188 | davies.pvals[s1]; davies.pvals[s2] 189 | approx.davies.pvals[s1]; approx.davies.pvals[s2] 190 | 191 | ###################################################################################### 192 | ###################################################################################### 193 | ###################################################################################### 194 | 195 | ### Running an Informed Exhaustive Search ### 196 | 197 | #NOTE: Now we may take only the significant SNPs according to their marginal epistatic effects and run a simple exhaustive search between them 198 | 199 | thresh = 0.05/length(hybrid.pvals) #Set a significance threshold 200 | v = hybrid.pvals[hybrid.pvals<=thresh] #Call only marginally significant SNPs 201 | pwise = c() 202 | for(k in 1:length(v)){ 203 | fit = c(); m = 1:length(v) 204 | for(w in m[-k]){ 205 | pt = lm(y~X[,names(v)[k]]:X[,names(v)[w]]) 206 | fit[w] = coefficients(summary(pt))[8] 207 | names(fit)[w] = paste(names(v)[k],names(v)[w],sep = "-") 208 | } 209 | pwise = c(pwise,fit) 210 | } 211 | 212 | ### Look at the exhaustive search results ### 213 | vc.pwise = sort(pwise[!is.na(pwise)]) #Get rid of the NAs 214 | vc.pwise = vc.pwise[seq(1,length(vc.pwise),2)] #Only keep the unique pairs 215 | sort(vc.pwise)[1:150] #Sort the pairs in order of significance 216 | -------------------------------------------------------------------------------- /Standard Version/MAPIT.R: -------------------------------------------------------------------------------- 1 | ###***Parallelized Version of the MArginal ePIstasis Test (MAPIT)***### 2 | 3 | #This function will run a version of the MArginal ePIstasis Test (MAPIT) under the following model variations: 4 | 5 | #(1) Standard Model ---> y = m+g+e where m ~ MVN(0,omega^2K), g ~ MVN(0,sigma^2G), e ~ MVN(0,tau^2M). Recall from Crawford et al. (2017) that m is the combined additive effects from all other variants, and effectively rep- resents the additive effect of the kth variant under the polygenic background of all other variants; K = X_{−k}^tX_{−k}/(p − 1) is the genetic relatedness matrix computed using genotypes from all variants other than the kth; g is the summation of all pairwise interaction effects between the kth variant and all other variants; G = DKD represents a relatedness matrix computed based on pairwise interaction terms between the kth variant and all other variants. Here, we also denote D = diag(x_k) to be an n × n diagonal matrix with the genotype vector x_k as its diagonal elements. It is important to note that both K and G change with every new marker k that is considered. Lastly; M is a variant specific projection matrix onto both the null space of the intercept and the corresponding genotypic vector x_k. 6 | 7 | #(2) Standard + Covariate Model ---> y = Wa+m+g+e where W is a matrix of covariates with effect sizes a. 8 | 9 | #(3) Standard + Common Environment Model ---> y = m+g+c+e where c ~ MVN(0,eta^2C) controls for extra environmental effects and population structure with covariance matrix C. 10 | 11 | #(4) Standard + Covariate + Common Environment Model ---> y = Wa+m+g+c+e 12 | 13 | #This function will consider the following three hypothesis testing strategies which are featured in Crawford et al. (2017): 14 | #(1) The Normal or Z-test 15 | #(2) Davies Method 16 | #(3) Hybrid Method (Z-test + Davies Method) 17 | 18 | ### Review of the function parameters ### 19 | #'X' is the pxn genotype matrix where p is the number of variants and n is the number of samples. Must be a matrix and not a data.frame. 20 | #'y' is the nx1 vector of quantitative or continuous traits. 21 | #'W' is the matrix qxn matrix of covariates. Must be a matrix and not a data.frame. 22 | #'C' is an nxn covariance matrix detailing environmental effects and population structure effects. 23 | #'hybrid' is a parameter detailing if the function should run the hybrid hypothesis testing procedure between the normal Z-test and the Davies method. Default is TRUE. 24 | #'threshold' is a parameter detailing the value at which to recalibrate the Z-test p-values. If nothing is defined by the user, the default value will be 0.05 as recommended by the Crawford et al. (2017). 25 | #'test' is a parameter defining what hypothesis test should be implemented. Takes on values 'normal' or 'davies'. This parameter only matters when hybrid = FALSE. If test is not defined when hybrid = FALSE, the function will automatically use test = 'normal'. 26 | #'k' is a parameter specifying the known prevelance of a disease or trait in the population as in Crawford and Zhou (2018). This parameter is only used if y is a binary class of labels (0,1). If this parameter is not set then the default k = 0.5 will used. 27 | 28 | ###################################################################################### 29 | ###################################################################################### 30 | ###################################################################################### 31 | 32 | MAPIT = function(X, y, W = NULL,C = NULL,hybrid = TRUE,threshold = 0.05,test = NULL,k = NULL){ 33 | ### Install the necessary libraries ### 34 | usePackage("doParallel") 35 | usePackage("Rcpp") 36 | usePackage("RcppArmadillo") 37 | usePackage("CompQuadForm") 38 | usePackage("truncnorm") 39 | 40 | ### Check to See if we should run LT-MAPIT ### 41 | if(sum(y%in%c(0,1))==length(y)){ 42 | if(is.null(k)){warning("The liability threshold model is going to be used but no disease prevelance is defined! Using the default 0.5.");k = 0.5} 43 | ### Save the labels ### 44 | cc = y 45 | 46 | ### Find the Number of Cases and Controls ### 47 | n.cases = sum(cc==1) 48 | n.controls = sum(cc==0) 49 | 50 | ### Set the Threshold ### 51 | thresh=qnorm(1-k,mean=0,sd=1) 52 | 53 | ### Bernoulli Distributed Case and Control Data ### 54 | Pheno=rep(NA,length(cc)); 55 | Pheno[cc==0] = rtruncnorm(n.controls,b=thresh) 56 | Pheno[cc==1] = rtruncnorm(n.cases,a=thresh) 57 | y = Pheno 58 | } 59 | 60 | ### Run the analysis using the hybrid Test ### 61 | if(hybrid==TRUE){ 62 | ### Run Model 1 by Default ### 63 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 64 | vc.mod = MAPIT1_Normal(X,y) 65 | } 66 | ### Test to Run Model 2 ### 67 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 68 | vc.mod = MAPIT2_Normal(X,y,W) 69 | } 70 | ### Test to Run Model 3 ### 71 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 72 | vc.mod = MAPIT3_Normal(X,y,C) 73 | } 74 | ### Test to Run Model 4 ### 75 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 76 | vc.mod = MAPIT4_Normal(X,y,W,C) 77 | } 78 | ### Record the Results of the Normal Z-Test ### 79 | pvals = vc.mod$pvalues; names(pvals) = rownames(X) 80 | pves = vc.mod$PVE; names(pves) = rownames(X) 81 | 82 | ### Find the indices of the p-values that are below 0.05 ### 83 | ind = which(pvals<=threshold) 84 | 85 | ### Run Model 1 by Default ### 86 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 87 | vc.mod = MAPIT1_Davies(X,y,ind) 88 | } 89 | ### Test to Run Model 2 ### 90 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 91 | vc.mod = MAPIT2_Davies(X,y,W,ind) 92 | } 93 | ### Test to Run Model 2 ### 94 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 95 | vc.mod = MAPIT3_Davies(X,y,C,ind) 96 | } 97 | ### Test to Run Model 2 ### 98 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 99 | vc.mod = MAPIT4_Davies(X,y,W,C,ind) 100 | } 101 | ### Apply Davies Exact Method ### 102 | vc.ts = vc.mod$Est 103 | names(vc.ts) = rownames(X) 104 | 105 | davies.pvals = c() 106 | for(i in 1:length(vc.ts)){ 107 | lambda = sort(vc.mod$Eigenvalues[,i],decreasing = T) 108 | 109 | Davies_Method = davies(vc.mod$Est[i], lambda = lambda, acc=1e-8) 110 | davies.pvals[i] = 2*min(Davies_Method$Qq, 1-Davies_Method$Qq) 111 | names(davies.pvals)[i] = names(vc.ts[i]) 112 | } 113 | pvals[ind] = davies.pvals[ind] 114 | } 115 | 116 | ### Run the analysis using the either normal test or Davies method ### 117 | if(hybrid==FALSE&&is.null(test)==TRUE){ 118 | warning("No test specified for hypothesis testing. Using normal Z-test (default).") 119 | ### Run Model 1 by Default ### 120 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 121 | vc.mod = MAPIT1_Normal(X,y) 122 | } 123 | ### Test to Run Model 2 ### 124 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 125 | vc.mod = MAPIT2_Normal(X,y,W) 126 | } 127 | ### Test to Run Model 3 ### 128 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 129 | vc.mod = MAPIT3_Normal(X,y,C) 130 | } 131 | ### Test to Run Model 4 ### 132 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 133 | vc.mod = MAPIT4_Normal(X,y,W,C) 134 | } 135 | 136 | ### Record the Results of the Normal Z-Test ### 137 | pvals = vc.mod$pvalues; names(pvals) = rownames(X) 138 | pves = vc.mod$PVE; names(pves) = rownames(X) 139 | } 140 | 141 | ### Run the analysis using the either normal test or Davies method ### 142 | if(hybrid==FALSE&&is.null(test)==FALSE){ 143 | if(test=="normal"||test=="Normal"){ 144 | ### Run Model 1 by Default ### 145 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 146 | vc.mod = MAPIT1_Normal(X,y) 147 | } 148 | ### Test to Run Model 2 ### 149 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 150 | vc.mod = MAPIT2_Normal(X,y,W) 151 | } 152 | ### Test to Run Model 3 ### 153 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 154 | vc.mod = MAPIT3_Normal(X,y,C) 155 | } 156 | ### Test to Run Model 4 ### 157 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 158 | vc.mod = MAPIT4_Normal(X,y,W,C) 159 | } 160 | 161 | ### Record the Results of the Normal Z-Test ### 162 | pvals = vc.mod$pvalues; names(pvals) = rownames(X) 163 | pves = vc.mod$PVE; names(pves) = rownames(X) 164 | } 165 | 166 | if(test=="davies"||test=="Davies"){ 167 | ### Find the indices of the p-values that are below 0.05 ### 168 | ind = 1:nrow(X) 169 | 170 | ### Run Model 1 by Default ### 171 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 172 | vc.mod = MAPIT1_Davies(X,y,ind) 173 | } 174 | ### Test to Run Model 2 ### 175 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 176 | vc.mod = MAPIT2_Davies(X,y,W,ind) 177 | } 178 | ### Test to Run Model 2 ### 179 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 180 | vc.mod = MAPIT3_Davies(X,y,C,ind) 181 | } 182 | ### Test to Run Model 2 ### 183 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 184 | vc.mod = MAPIT4_Davies(X,y,W,C,ind) 185 | } 186 | ### Apply Davies Exact Method ### 187 | vc.ts = vc.mod$Est 188 | names(vc.ts) = rownames(X) 189 | 190 | davies.pvals = c() 191 | for(i in 1:length(vc.ts)){ 192 | lambda = sort(vc.mod$Eigenvalues[,i],decreasing = T) 193 | 194 | Davies_Method = davies(vc.mod$Est[i], lambda = lambda, acc=1e-8) 195 | davies.pvals[i] = 2*min(Davies_Method$Qq, 1-Davies_Method$Qq) 196 | names(davies.pvals)[i] = names(vc.ts[i]) 197 | } 198 | pvals = davies.pvals; pves = vc.mod$PVE 199 | } 200 | } 201 | 202 | 203 | return(list("pvalues"=pvals,"pves"=pves)) 204 | } 205 | 206 | usePackage <- function(p) { 207 | if (!is.element(p, installed.packages()[,1])) 208 | install.packages(p, dep = TRUE) 209 | require(p, character.only = TRUE) 210 | } -------------------------------------------------------------------------------- /OpenMP Version/Simulations_OpenMP.R: -------------------------------------------------------------------------------- 1 | ### Illustrating the MArginal ePIstasis Test (MAPIT) with Simulations ### 2 | 3 | ### Clear Console ### 4 | cat("\014") 5 | 6 | ### Clear Environment ### 7 | rm(list = ls(all = TRUE)) 8 | 9 | ### Load in the R libraries ### 10 | library(doParallel) 11 | library(Rcpp) 12 | library(RcppArmadillo) 13 | library(RcppParallel) 14 | library(CompQuadForm) 15 | 16 | ### Load in functions to make QQ-plot plots ### 17 | source("QQplot.R") 18 | 19 | #NOTE: This code assumes that the basic C++ functions are set up on the computer in use. If not, the MAPIT functions and Rcpp packages will not work properly. Mac users please refer to the homebrew applications and install the gcc commands listed in the README.md file before running the rest of the code [Warning: This step may take about an hour...]. 20 | 21 | ### Load in the C++ MAPIT wrapper functions ### 22 | source("MAPIT_OpenMP.R"); sourceCpp("MAPIT_OpenMP.cpp") 23 | 24 | ###################################################################################### 25 | ###################################################################################### 26 | ###################################################################################### 27 | 28 | ### Set the Seed for the analysis ### 29 | #set.seed(11151990) 30 | 31 | # Data are p single nucleotide polymorphisms (SNPs) with simulated genotypes. 32 | # Simulation Parameters: 33 | # (1) ind = # of samples 34 | # (2) nsnp = number of SNPs or variants 35 | # (3) PVE = phenotypic variance explained/broad-sense heritability (H^2) 36 | # (4) rho = measures the portion of H^2 that is contributed by the marignal (additive) effects 37 | 38 | ind = 3e3; nsnp = 1e4; pve=0.6; rho=0.5; 39 | 40 | ### Simulate the genotypes such that all variants have minor allele frequency (MAF) > 0.05 ### 41 | # NOTE: As in the paper, we center and scale each genotypic vector such that every SNP has mean 0 and standard deviation 1. 42 | maf <- 0.05 + 0.45*runif(nsnp) 43 | X <- (runif(ind*nsnp) < maf) + (runif(ind*nsnp) < maf) 44 | X <- matrix(as.double(X),ind,nsnp,byrow = TRUE) 45 | Xmean=apply(X, 2, mean); Xsd=apply(X, 2, sd); X=t((t(X)-Xmean)/Xsd) 46 | 47 | ### Set the size of causal SNP groups ### 48 | ncausal1= 10 # Set 1 of causal SNPs 49 | ncausal2 = 10 # Set 2 of Causal SNPs 50 | ncausal3 = 1e3-ncausal1-ncausal2 # Set 3 of Causal SNPs with only marginal effects 51 | 52 | # NOTE: As in the paper, we randomly choose causal variants that classify into three groups: (i) a small set of interaction SNPs, (ii) a larger set of interaction SNPs, and (iii) a large set of additive SNPs. In the simulations carried out in this study, SNPs interact between sets, so that SNPs in the first group interact with SNPs in the second group, but do not interact with variants in their own group (the same applies to the second group). One may view the SNPs in the first set as the “hubs” in an interaction map. We are reminded that interaction (epistatic) effects are different from additive effects. All causal SNPs in both the first and second groups have additive effects and are involved in pairwise interactions, while causal SNPs in the third set only have additive effects. 53 | 54 | ### Select causal SNPs in groups 1 and 2 ### 55 | snp.ids = 1:nsnp 56 | s1=sample(snp.ids, ncausal1, replace=F) 57 | s2=sample(snp.ids[-s1], ncausal2, replace=F) 58 | s3=sample(snp.ids[-c(s1,s2)], ncausal3, replace=F) 59 | 60 | Xcausal1=X[,s1]; Xcausal2=X[,s2]; Xcausal3=X[,s3] 61 | 62 | ### Create the epistatic design matrix ### 63 | W=c() 64 | for(i in 1:ncausal1){ 65 | W=cbind(W,Xcausal1[,i]*Xcausal2) 66 | } 67 | dim(W) 68 | 69 | ### Simulate marginal (additive) effects ### 70 | Xmarginal=cbind(Xcausal1,Xcausal2,Xcausal3) 71 | beta=rnorm(dim(Xmarginal)[2]) 72 | y_marginal=c(Xmarginal%*%beta) 73 | beta=beta*sqrt(pve*rho/var(y_marginal)) 74 | y_marginal=Xmarginal%*%beta 75 | 76 | ### Simulate epistatic effects ### 77 | alpha=rnorm(dim(W)[2]) 78 | y_epi=c(W%*%alpha) 79 | alpha=alpha*sqrt(pve*(1-rho)/var(y_epi)) 80 | y_epi=W%*%alpha 81 | 82 | # NOTE: Each effect size for the marginal, epistatic, and random error effects are drawn from a standard normal distribution. Meaning beta ~ MVN(0,I), alpha ~ MVN(0,I), and epsilon ~ MVN(0,I). We then scale both the additive and pairwise genetic effects so that collectively they explain a fixed proportion of genetic variance. Namely, the additive effects make up rho%, while the pairwise interactions make up the remaining (1 − rho)%. Once we obtain the final effect sizes for all causal SNPs, we draw errors to achieve the target H^2. 83 | 84 | ### Simulate residual error ### 85 | y_err=rnorm(ind) 86 | y_err=y_err*sqrt((1-pve)/var(y_err)) 87 | 88 | # Simulate the continuous phenotypes 89 | y = y_marginal+y_epi+y_err 90 | 91 | ### Check dimensions and add SNP names ### 92 | dim(X); dim(y) 93 | colnames(X) = paste("SNP",1:ncol(X),sep="") 94 | 95 | ### Save the names of the causal SNPs ### 96 | SNPs = colnames(X)[c(s1,s2)] 97 | 98 | ###################################################################################### 99 | ###################################################################################### 100 | ###################################################################################### 101 | 102 | ### Running MAPIT using the Hybrid Method ### 103 | 104 | #IMPORTANT: MAPIT takes the X matrix as pxn --- NOT nxp 105 | 106 | ### Set the number of cores ### 107 | cores = detectCores() 108 | 109 | ### Run MAPIT ### 110 | ptm <- proc.time() #Start clock 111 | mapit = MAPIT(t(X),y,cores=cores) 112 | proc.time() - ptm #Stop clock 113 | 114 | hybrid.pvals = mapit$pvalues 115 | names(hybrid.pvals) = colnames(X) 116 | 117 | ###################################################################################### 118 | ###################################################################################### 119 | ###################################################################################### 120 | 121 | ### Running MAPIT using the Normal Z-test ### 122 | 123 | ### Set the number of cores ### 124 | cores = detectCores() 125 | 126 | ### Run MAPIT without specifiying test (should get a warning) ### 127 | ptm <- proc.time() #Start clock 128 | mapit = MAPIT(t(X),y,hybrid=FALSE,cores=cores) 129 | proc.time() - ptm #Stop clock 130 | 131 | normal.pvals1 = mapit$pvalues 132 | names(normal.pvals1) = colnames(X) 133 | 134 | ### Run MAPIT while specifiying test ### 135 | ptm <- proc.time() #Start clock 136 | mapit = MAPIT(t(X),y,hybrid=FALSE,test = "normal",cores=cores) 137 | proc.time() - ptm #Stop clock 138 | 139 | normal.pvals2 = mapit$pvalues 140 | names(normal.pvals2) = colnames(X) 141 | 142 | ###################################################################################### 143 | ###################################################################################### 144 | ###################################################################################### 145 | 146 | ### Running MAPIT using Davies Method ### 147 | 148 | ### Set the number of cores ### 149 | cores = detectCores() 150 | 151 | ### Run MAPIT ### 152 | ptm <- proc.time() #Start clock 153 | mapit = MAPIT(t(X),y,hybrid=FALSE,test="davies",cores=cores) 154 | proc.time() - ptm #Stop clock 155 | 156 | davies.pvals = mapit$pvalues 157 | names(davies.pvals) = colnames(X) 158 | 159 | ###################################################################################### 160 | ###################################################################################### 161 | ###################################################################################### 162 | 163 | ### Running a fast version of MAPIT using an approximate Davies Method ### 164 | 165 | ### Set the number of cores ### 166 | cores = detectCores() 167 | 168 | ### Run MAPIT ### 169 | ptm <- proc.time() #Start clock 170 | mapit = MAPIT_Davies_Approx(t(X),y,cores=cores) 171 | proc.time() - ptm #Stop clock 172 | 173 | approx.davies.pvals = c() 174 | for(i in 1:length(vc.ts)){ 175 | lambda = sort(mapit$Eigenvalues[,i],decreasing = T) 176 | 177 | Davies_Method = davies(mapit$Est[i], lambda = lambda, acc=1e-8) 178 | approx.davies.pvals[i] = 2*min(Davies_Method$Qq, 1-Davies_Method$Qq) 179 | names(approx.davies.pvals)[i] = colnames(X)[i] 180 | } 181 | 182 | ###################################################################################### 183 | ###################################################################################### 184 | ###################################################################################### 185 | 186 | ### Plot observed the p-values on a QQ-plot ### 187 | ggd.qqplot(hybrid.pvals) 188 | ggd.qqplot(normal.pvals1) 189 | ggd.qqplot(normal.pvals2) 190 | ggd.qqplot(davies.pvals) 191 | ggd.qqplot(approx.davies.pvals) 192 | 193 | ### Look at the causal SNPs in group 1 and 2 ### 194 | hybrid.pvals[s1]; hybrid.pvals[s2] 195 | normal.pvals1[s1]; normal.pvals1[s2] 196 | normal.pvals2[s1]; normal.pvals2[s2] 197 | davies.pvals[s1]; davies.pvals[s2] 198 | approx.davies.pvals[s1]; approx.davies.pvals[s2] 199 | 200 | ###################################################################################### 201 | ###################################################################################### 202 | ###################################################################################### 203 | 204 | ### Running an Informed Exhaustive Search ### 205 | 206 | #NOTE: Now we may take only the significant SNPs according to their marginal epistatic effects and run a simple exhaustive search between them 207 | 208 | thresh = 0.05/length(hybrid.pvals) #Set a significance threshold 209 | v = hybrid.pvals[hybrid.pvals<=thresh] #Call only marginally significant SNPs 210 | pwise = c() 211 | for(k in 1:length(v)){ 212 | fit = c(); m = 1:length(v) 213 | for(w in m[-k]){ 214 | pt = lm(y~X[,names(v)[k]]:X[,names(v)[w]]) 215 | fit[w] = coefficients(summary(pt))[8] 216 | names(fit)[w] = paste(names(v)[k],names(v)[w],sep = "-") 217 | } 218 | pwise = c(pwise,fit) 219 | } 220 | 221 | ### Look at the exhaustive search results ### 222 | vc.pwise = sort(pwise[!is.na(pwise)]) #Get rid of the NAs 223 | vc.pwise = vc.pwise[seq(1,length(vc.pwise),2)] #Only keep the unique pairs 224 | sort(vc.pwise)[1:150] #Sort the pairs in order of significance 225 | -------------------------------------------------------------------------------- /OpenMP Version/MAPIT_OpenMP.R: -------------------------------------------------------------------------------- 1 | ###***Parallelized Version of the MArginal ePIstasis Test (MAPIT)***### 2 | 3 | #This function will run a version of the MArginal ePIstasis Test (MAPIT) under the following model variations for quantitative or binary traits (which we analyze using a liability threshold model): 4 | 5 | #(1) Standard Model ---> y = m+g+e where m ~ MVN(0,omega^2K), g ~ MVN(0,sigma^2G), e ~ MVN(0,tau^2M). Recall from Crawford et al. (2017) that m is the combined additive effects from all other variants, and effectively rep- resents the additive effect of the kth variant under the polygenic background of all other variants; K = X_{−k}^tX_{−k}/(p − 1) is the genetic relatedness matrix computed using genotypes from all variants other than the kth; g is the summation of all pairwise interaction effects between the kth variant and all other variants; G = DKD represents a relatedness matrix computed based on pairwise interaction terms between the kth variant and all other variants. Here, we also denote D = diag(x_k) to be an n × n diagonal matrix with the genotype vector x_k as its diagonal elements. It is important to note that both K and G change with every new marker k that is considered. Lastly; M is a variant specific projection matrix onto both the null space of the intercept and the corresponding genotypic vector x_k. 6 | 7 | #(2) Standard + Covariate Model ---> y = Wa+m+g+e where W is a matrix of covariates with effect sizes a. 8 | 9 | #(3) Standard + Common Environment Model ---> y = m+g+c+e where c ~ MVN(0,eta^2C) controls for extra environmental effects and population structure with covariance matrix C. 10 | 11 | #(4) Standard + Covariate + Common Environment Model ---> y = Wa+m+g+c+e 12 | 13 | #This function will consider the following three hypothesis testing strategies which are featured in Crawford et al. (2017): 14 | #(1) The Normal or Z-test 15 | #(2) Davies Method 16 | #(3) Hybrid Method (Z-test + Davies Method) 17 | 18 | ### Review of the function parameters ### 19 | #'X' is the pxn genotype matrix where p is the number of variants and n is the number of samples. Must be a matrix and not a data.frame. 20 | #'y' is the nx1 vector of quantitative (e.g. continuous) or binary traits. 21 | #'W' is the matrix qxn matrix of covariates. Must be a matrix and not a data.frame. 22 | #'C' is an nxn covariance matrix detailing environmental effects and population structure effects. 23 | #'hybrid' is a parameter detailing if the function should run the hybrid hypothesis testing procedure between the normal Z-test and the Davies method. Default is TRUE. 24 | #'threshold' is a parameter detailing the value at which to recalibrate the Z-test p-values. If nothing is defined by the user, the default value will be 0.05 as recommended by the Crawford et al. (2017). 25 | #'test' is a parameter defining what hypothesis test should be implemented. Takes on values 'normal' or 'davies'. This parameter only matters when hybrid = FALSE. If test is not defined when hybrid = FALSE, the function will automatically use test = 'normal'. 26 | #'#'k' is a parameter specifying the known prevelance of a disease or trait in the population as in Crawford and Zhou (2018). This parameter is only used if y is a binary class of labels (0,1). If this parameter is not set then the default k = 0.5 will used. 27 | #'cores' is a parameter detailing the number of cores to parallelize over. It is important to note that this value only matters when the user has implemented OPENMP on their operating system. If OPENMP is not installed, then please leave cores = 1 and use the standard version of this code and software. 28 | 29 | ###################################################################################### 30 | ###################################################################################### 31 | ###################################################################################### 32 | 33 | MAPIT = function(X, y, W = NULL,C = NULL,hybrid = TRUE,threshold = 0.05,test = NULL,k = NULL,cores = 1){ 34 | ### Install the necessary libraries ### 35 | usePackage("doParallel") 36 | usePackage("Rcpp") 37 | usePackage("RcppArmadillo") 38 | usePackage("CompQuadForm") 39 | usePackage("truncnorm") 40 | 41 | if(cores > 1){ 42 | if(cores>detectCores()){warning("The number of cores you're setting is larger than detected cores!");cores = detectCores()} 43 | } 44 | 45 | ### Check to See if we should run LT-MAPIT ### 46 | if(sum(y%in%c(0,1))==length(y)){ 47 | if(is.null(k)){warning("The liability threshold model is going to be used but no disease prevelance is defined! Using the default 0.5.");k = 0.5} 48 | ### Save the labels ### 49 | cc = y 50 | 51 | ### Find the Number of Cases and Controls ### 52 | n.cases = sum(cc==1) 53 | n.controls = sum(cc==0) 54 | 55 | ### Set the Threshold ### 56 | thresh=qnorm(1-k,mean=0,sd=1) 57 | 58 | ### Bernoulli Distributed Case and Control Data ### 59 | Pheno=rep(NA,length(cc)); 60 | Pheno[cc==0] = rtruncnorm(n.controls,b=thresh) 61 | Pheno[cc==1] = rtruncnorm(n.cases,a=thresh) 62 | y = Pheno 63 | } 64 | 65 | ### Run the analysis using the hybrid Test ### 66 | if(hybrid==TRUE){ 67 | ### Run Model 1 by Default ### 68 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 69 | vc.mod = MAPIT1_Normal(X,y,cores=cores) 70 | } 71 | ### Test to Run Model 2 ### 72 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 73 | vc.mod = MAPIT2_Normal(X,y,W,cores=cores) 74 | } 75 | ### Test to Run Model 3 ### 76 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 77 | vc.mod = MAPIT3_Normal(X,y,C,cores=cores) 78 | } 79 | ### Test to Run Model 4 ### 80 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 81 | vc.mod = MAPIT4_Normal(X,y,W,C,cores=cores) 82 | } 83 | ### Record the Results of the Normal Z-Test ### 84 | pvals = vc.mod$pvalues; names(pvals) = rownames(X) 85 | pves = vc.mod$PVE; names(pves) = rownames(X) 86 | 87 | ### Find the indices of the p-values that are below 0.05 ### 88 | ind = which(pvals<=threshold) 89 | 90 | ### Run Model 1 by Default ### 91 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 92 | vc.mod = MAPIT1_Davies(X,y,ind,cores=cores) 93 | } 94 | ### Test to Run Model 2 ### 95 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 96 | vc.mod = MAPIT2_Davies(X,y,W,ind,cores=cores) 97 | } 98 | ### Test to Run Model 2 ### 99 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 100 | vc.mod = MAPIT3_Davies(X,y,C,ind,cores=cores) 101 | } 102 | ### Test to Run Model 2 ### 103 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 104 | vc.mod = MAPIT4_Davies(X,y,W,C,ind,cores=cores) 105 | } 106 | ### Apply Davies Exact Method ### 107 | vc.ts = vc.mod$Est 108 | names(vc.ts) = rownames(X) 109 | 110 | davies.pvals = c() 111 | for(i in 1:length(vc.ts)){ 112 | lambda = sort(vc.mod$Eigenvalues[,i],decreasing = T) 113 | 114 | Davies_Method = davies(vc.mod$Est[i], lambda = lambda, acc=1e-8) 115 | davies.pvals[i] = 2*min(Davies_Method$Qq, 1-Davies_Method$Qq) 116 | names(davies.pvals)[i] = names(vc.ts[i]) 117 | } 118 | pvals[ind] = davies.pvals[ind] 119 | } 120 | 121 | ### Run the analysis using the either normal test or Davies method ### 122 | if(hybrid==FALSE&&is.null(test)==TRUE){ 123 | warning("No test specified for hypothesis testing. Using normal Z-test (default).") 124 | ### Run Model 1 by Default ### 125 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 126 | vc.mod = MAPIT1_Normal(X,y,cores=cores) 127 | } 128 | ### Test to Run Model 2 ### 129 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 130 | vc.mod = MAPIT2_Normal(X,y,W,cores=cores) 131 | } 132 | ### Test to Run Model 3 ### 133 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 134 | vc.mod = MAPIT3_Normal(X,y,C,cores=cores) 135 | } 136 | ### Test to Run Model 4 ### 137 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 138 | vc.mod = MAPIT4_Normal(X,y,W,C,cores=cores) 139 | } 140 | 141 | ### Record the Results of the Normal Z-Test ### 142 | pvals = vc.mod$pvalues; names(pvals) = rownames(X) 143 | pves = vc.mod$PVE; names(pves) = rownames(X) 144 | } 145 | 146 | ### Run the analysis using the either normal test or Davies method ### 147 | if(hybrid==FALSE&&is.null(test)==FALSE){ 148 | if(test=="normal"||test=="Normal"){ 149 | ### Run Model 1 by Default ### 150 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 151 | vc.mod = MAPIT1_Normal(X,y,cores=cores) 152 | } 153 | ### Test to Run Model 2 ### 154 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 155 | vc.mod = MAPIT2_Normal(X,y,W,cores=cores) 156 | } 157 | ### Test to Run Model 3 ### 158 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 159 | vc.mod = MAPIT3_Normal(X,y,C,cores=cores) 160 | } 161 | ### Test to Run Model 4 ### 162 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 163 | vc.mod = MAPIT4_Normal(X,y,W,C,cores=cores) 164 | } 165 | 166 | ### Record the Results of the Normal Z-Test ### 167 | pvals = vc.mod$pvalues; names(pvals) = rownames(X) 168 | pves = vc.mod$PVE; names(pves) = rownames(X) 169 | } 170 | 171 | if(test=="davies"||test=="Davies"){ 172 | ### Find the indices of the p-values that are below 0.05 ### 173 | ind = 1:nrow(X) 174 | 175 | ### Run Model 1 by Default ### 176 | if(is.null(W)==TRUE&&is.null(C)==TRUE){ 177 | vc.mod = MAPIT1_Davies(X,y,ind,cores=cores) 178 | } 179 | ### Test to Run Model 2 ### 180 | if(is.null(W)==FALSE&&is.null(C)==TRUE){ 181 | vc.mod = MAPIT2_Davies(X,y,W,ind,cores=cores) 182 | } 183 | ### Test to Run Model 2 ### 184 | if(is.null(W)==TRUE&&is.null(C)==FALSE){ 185 | vc.mod = MAPIT3_Davies(X,y,C,ind,cores=cores) 186 | } 187 | ### Test to Run Model 2 ### 188 | if(is.null(W)==FALSE&&is.null(C)==FALSE){ 189 | vc.mod = MAPIT4_Davies(X,y,W,C,ind,cores=cores) 190 | } 191 | ### Apply Davies Exact Method ### 192 | vc.ts = vc.mod$Est 193 | names(vc.ts) = rownames(X) 194 | 195 | davies.pvals = c() 196 | for(i in 1:length(vc.ts)){ 197 | lambda = sort(vc.mod$Eigenvalues[,i],decreasing = T) 198 | 199 | Davies_Method = davies(vc.mod$Est[i], lambda = lambda, acc=1e-8) 200 | davies.pvals[i] = 2*min(Davies_Method$Qq, 1-Davies_Method$Qq) 201 | names(davies.pvals)[i] = names(vc.ts[i]) 202 | } 203 | pvals = davies.pvals; pves = vc.mod$PVE 204 | } 205 | } 206 | return(list("pvalues"=pvals,"pves"=pves)) 207 | } 208 | 209 | usePackage <- function(p) { 210 | if (!is.element(p, installed.packages()[,1])) 211 | install.packages(p, dep = TRUE) 212 | require(p, character.only = TRUE) 213 | } -------------------------------------------------------------------------------- /License.md: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. We, the Free Software Foundation, use the 18 | GNU General Public License for most of our software; it applies also to 19 | any other work released this way by its authors. You can apply it to 20 | your programs, too. 21 | 22 | When we speak of free software, we are referring to freedom, not 23 | price. Our General Public Licenses are designed to make sure that you 24 | have the freedom to distribute copies of free software (and charge for 25 | them if you wish), that you receive source code or can get it if you 26 | want it, that you can change the software or use pieces of it in new 27 | free programs, and that you know you can do these things. 28 | 29 | To protect your rights, we need to prevent others from denying you 30 | these rights or asking you to surrender the rights. Therefore, you have 31 | certain responsibilities if you distribute copies of the software, or if 32 | you modify it: responsibilities to respect the freedom of others. 33 | 34 | For example, if you distribute copies of such a program, whether 35 | gratis or for a fee, you must pass on to the recipients the same 36 | freedoms that you received. You must make sure that they, too, receive 37 | or can get the source code. And you must show them these terms so they 38 | know their rights. 39 | 40 | Developers that use the GNU GPL protect your rights with two steps: 41 | (1) assert copyright on the software, and (2) offer you this License 42 | giving you legal permission to copy, distribute and/or modify it. 43 | 44 | For the developers' and authors' protection, the GPL clearly explains 45 | that there is no warranty for this free software. For both users' and 46 | authors' sake, the GPL requires that modified versions be marked as 47 | changed, so that their problems will not be attributed erroneously to 48 | authors of previous versions. 49 | 50 | Some devices are designed to deny users access to install or run 51 | modified versions of the software inside them, although the manufacturer 52 | can do so. This is fundamentally incompatible with the aim of 53 | protecting users' freedom to change the software. The systematic 54 | pattern of such abuse occurs in the area of products for individuals to 55 | use, which is precisely where it is most unacceptable. Therefore, we 56 | have designed this version of the GPL to prohibit the practice for those 57 | products. If such problems arise substantially in other domains, we 58 | stand ready to extend this provision to those domains in future versions 59 | of the GPL, as needed to protect the freedom of users. 60 | 61 | Finally, every program is threatened constantly by software patents. 62 | States should not allow patents to restrict development and use of 63 | software on general-purpose computers, but in those that do, we wish to 64 | avoid the special danger that patents applied to a free program could 65 | make it effectively proprietary. To prevent this, the GPL assures that 66 | patents cannot be used to render the program non-free. 67 | 68 | The precise terms and conditions for copying, distribution and 69 | modification follow. 70 | 71 | TERMS AND CONDITIONS 72 | 73 | 0. Definitions. 74 | 75 | "This License" refers to version 3 of the GNU General Public License. 76 | 77 | "Copyright" also means copyright-like laws that apply to other kinds of 78 | works, such as semiconductor masks. 79 | 80 | "The Program" refers to any copyrightable work licensed under this 81 | License. Each licensee is addressed as "you". "Licensees" and 82 | "recipients" may be individuals or organizations. 83 | 84 | To "modify" a work means to copy from or adapt all or part of the work 85 | in a fashion requiring copyright permission, other than the making of an 86 | exact copy. The resulting work is called a "modified version" of the 87 | earlier work or a work "based on" the earlier work. 88 | 89 | A "covered work" means either the unmodified Program or a work based 90 | on the Program. 91 | 92 | To "propagate" a work means to do anything with it that, without 93 | permission, would make you directly or secondarily liable for 94 | infringement under applicable copyright law, except executing it on a 95 | computer or modifying a private copy. Propagation includes copying, 96 | distribution (with or without modification), making available to the 97 | public, and in some countries other activities as well. 98 | 99 | To "convey" a work means any kind of propagation that enables other 100 | parties to make or receive copies. Mere interaction with a user through 101 | a computer network, with no transfer of a copy, is not conveying. 102 | 103 | An interactive user interface displays "Appropriate Legal Notices" 104 | to the extent that it includes a convenient and prominently visible 105 | feature that (1) displays an appropriate copyright notice, and (2) 106 | tells the user that there is no warranty for the work (except to the 107 | extent that warranties are provided), that licensees may convey the 108 | work under this License, and how to view a copy of this License. If 109 | the interface presents a list of user commands or options, such as a 110 | menu, a prominent item in the list meets this criterion. 111 | 112 | 1. Source Code. 113 | 114 | The "source code" for a work means the preferred form of the work 115 | for making modifications to it. "Object code" means any non-source 116 | form of a work. 117 | 118 | A "Standard Interface" means an interface that either is an official 119 | standard defined by a recognized standards body, or, in the case of 120 | interfaces specified for a particular programming language, one that 121 | is widely used among developers working in that language. 122 | 123 | The "System Libraries" of an executable work include anything, other 124 | than the work as a whole, that (a) is included in the normal form of 125 | packaging a Major Component, but which is not part of that Major 126 | Component, and (b) serves only to enable use of the work with that 127 | Major Component, or to implement a Standard Interface for which an 128 | implementation is available to the public in source code form. A 129 | "Major Component", in this context, means a major essential component 130 | (kernel, window system, and so on) of the specific operating system 131 | (if any) on which the executable work runs, or a compiler used to 132 | produce the work, or an object code interpreter used to run it. 133 | 134 | The "Corresponding Source" for a work in object code form means all 135 | the source code needed to generate, install, and (for an executable 136 | work) run the object code and to modify the work, including scripts to 137 | control those activities. However, it does not include the work's 138 | System Libraries, or general-purpose tools or generally available free 139 | programs which are used unmodified in performing those activities but 140 | which are not part of the work. For example, Corresponding Source 141 | includes interface definition files associated with source files for 142 | the work, and the source code for shared libraries and dynamically 143 | linked subprograms that the work is specifically designed to require, 144 | such as by intimate data communication or control flow between those 145 | subprograms and other parts of the work. 146 | 147 | The Corresponding Source need not include anything that users 148 | can regenerate automatically from other parts of the Corresponding 149 | Source. 150 | 151 | The Corresponding Source for a work in source code form is that 152 | same work. 153 | 154 | 2. Basic Permissions. 155 | 156 | All rights granted under this License are granted for the term of 157 | copyright on the Program, and are irrevocable provided the stated 158 | conditions are met. This License explicitly affirms your unlimited 159 | permission to run the unmodified Program. The output from running a 160 | covered work is covered by this License only if the output, given its 161 | content, constitutes a covered work. This License acknowledges your 162 | rights of fair use or other equivalent, as provided by copyright law. 163 | 164 | You may make, run and propagate covered works that you do not 165 | convey, without conditions so long as your license otherwise remains 166 | in force. You may convey covered works to others for the sole purpose 167 | of having them make modifications exclusively for you, or provide you 168 | with facilities for running those works, provided that you comply with 169 | the terms of this License in conveying all material for which you do 170 | not control copyright. Those thus making or running the covered works 171 | for you must do so exclusively on your behalf, under your direction 172 | and control, on terms that prohibit them from making any copies of 173 | your copyrighted material outside their relationship with you. 174 | 175 | Conveying under any other circumstances is permitted solely under 176 | the conditions stated below. Sublicensing is not allowed; section 10 177 | makes it unnecessary. 178 | 179 | 3. Protecting Users' Legal Rights From Anti-Circumvention Law. 180 | 181 | No covered work shall be deemed part of an effective technological 182 | measure under any applicable law fulfilling obligations under article 183 | 11 of the WIPO copyright treaty adopted on 20 December 1996, or 184 | similar laws prohibiting or restricting circumvention of such 185 | measures. 186 | 187 | When you convey a covered work, you waive any legal power to forbid 188 | circumvention of technological measures to the extent such circumvention 189 | is effected by exercising rights under this License with respect to 190 | the covered work, and you disclaim any intention to limit operation or 191 | modification of the work as a means of enforcing, against the work's 192 | users, your or third parties' legal rights to forbid circumvention of 193 | technological measures. 194 | 195 | 4. Conveying Verbatim Copies. 196 | 197 | You may convey verbatim copies of the Program's source code as you 198 | receive it, in any medium, provided that you conspicuously and 199 | appropriately publish on each copy an appropriate copyright notice; 200 | keep intact all notices stating that this License and any 201 | non-permissive terms added in accord with section 7 apply to the code; 202 | keep intact all notices of the absence of any warranty; and give all 203 | recipients a copy of this License along with the Program. 204 | 205 | You may charge any price or no price for each copy that you convey, 206 | and you may offer support or warranty protection for a fee. 207 | 208 | 5. Conveying Modified Source Versions. 209 | 210 | You may convey a work based on the Program, or the modifications to 211 | produce it from the Program, in the form of source code under the 212 | terms of section 4, provided that you also meet all of these conditions: 213 | 214 | a) The work must carry prominent notices stating that you modified 215 | it, and giving a relevant date. 216 | 217 | b) The work must carry prominent notices stating that it is 218 | released under this License and any conditions added under section 219 | 7. This requirement modifies the requirement in section 4 to 220 | "keep intact all notices". 221 | 222 | c) You must license the entire work, as a whole, under this 223 | License to anyone who comes into possession of a copy. This 224 | License will therefore apply, along with any applicable section 7 225 | additional terms, to the whole of the work, and all its parts, 226 | regardless of how they are packaged. This License gives no 227 | permission to license the work in any other way, but it does not 228 | invalidate such permission if you have separately received it. 229 | 230 | d) If the work has interactive user interfaces, each must display 231 | Appropriate Legal Notices; however, if the Program has interactive 232 | interfaces that do not display Appropriate Legal Notices, your 233 | work need not make them do so. 234 | 235 | A compilation of a covered work with other separate and independent 236 | works, which are not by their nature extensions of the covered work, 237 | and which are not combined with it such as to form a larger program, 238 | in or on a volume of a storage or distribution medium, is called an 239 | "aggregate" if the compilation and its resulting copyright are not 240 | used to limit the access or legal rights of the compilation's users 241 | beyond what the individual works permit. Inclusion of a covered work 242 | in an aggregate does not cause this License to apply to the other 243 | parts of the aggregate. 244 | 245 | 6. Conveying Non-Source Forms. 246 | 247 | You may convey a covered work in object code form under the terms 248 | of sections 4 and 5, provided that you also convey the 249 | machine-readable Corresponding Source under the terms of this License, 250 | in one of these ways: 251 | 252 | a) Convey the object code in, or embodied in, a physical product 253 | (including a physical distribution medium), accompanied by the 254 | Corresponding Source fixed on a durable physical medium 255 | customarily used for software interchange. 256 | 257 | b) Convey the object code in, or embodied in, a physical product 258 | (including a physical distribution medium), accompanied by a 259 | written offer, valid for at least three years and valid for as 260 | long as you offer spare parts or customer support for that product 261 | model, to give anyone who possesses the object code either (1) a 262 | copy of the Corresponding Source for all the software in the 263 | product that is covered by this License, on a durable physical 264 | medium customarily used for software interchange, for a price no 265 | more than your reasonable cost of physically performing this 266 | conveying of source, or (2) access to copy the 267 | Corresponding Source from a network server at no charge. 268 | 269 | c) Convey individual copies of the object code with a copy of the 270 | written offer to provide the Corresponding Source. This 271 | alternative is allowed only occasionally and noncommercially, and 272 | only if you received the object code with such an offer, in accord 273 | with subsection 6b. 274 | 275 | d) Convey the object code by offering access from a designated 276 | place (gratis or for a charge), and offer equivalent access to the 277 | Corresponding Source in the same way through the same place at no 278 | further charge. You need not require recipients to copy the 279 | Corresponding Source along with the object code. If the place to 280 | copy the object code is a network server, the Corresponding Source 281 | may be on a different server (operated by you or a third party) 282 | that supports equivalent copying facilities, provided you maintain 283 | clear directions next to the object code saying where to find the 284 | Corresponding Source. Regardless of what server hosts the 285 | Corresponding Source, you remain obligated to ensure that it is 286 | available for as long as needed to satisfy these requirements. 287 | 288 | e) Convey the object code using peer-to-peer transmission, provided 289 | you inform other peers where the object code and Corresponding 290 | Source of the work are being offered to the general public at no 291 | charge under subsection 6d. 292 | 293 | A separable portion of the object code, whose source code is excluded 294 | from the Corresponding Source as a System Library, need not be 295 | included in conveying the object code work. 296 | 297 | A "User Product" is either (1) a "consumer product", which means any 298 | tangible personal property which is normally used for personal, family, 299 | or household purposes, or (2) anything designed or sold for incorporation 300 | into a dwelling. In determining whether a product is a consumer product, 301 | doubtful cases shall be resolved in favor of coverage. For a particular 302 | product received by a particular user, "normally used" refers to a 303 | typical or common use of that class of product, regardless of the status 304 | of the particular user or of the way in which the particular user 305 | actually uses, or expects or is expected to use, the product. A product 306 | is a consumer product regardless of whether the product has substantial 307 | commercial, industrial or non-consumer uses, unless such uses represent 308 | the only significant mode of use of the product. 309 | 310 | "Installation Information" for a User Product means any methods, 311 | procedures, authorization keys, or other information required to install 312 | and execute modified versions of a covered work in that User Product from 313 | a modified version of its Corresponding Source. The information must 314 | suffice to ensure that the continued functioning of the modified object 315 | code is in no case prevented or interfered with solely because 316 | modification has been made. 317 | 318 | If you convey an object code work under this section in, or with, or 319 | specifically for use in, a User Product, and the conveying occurs as 320 | part of a transaction in which the right of possession and use of the 321 | User Product is transferred to the recipient in perpetuity or for a 322 | fixed term (regardless of how the transaction is characterized), the 323 | Corresponding Source conveyed under this section must be accompanied 324 | by the Installation Information. But this requirement does not apply 325 | if neither you nor any third party retains the ability to install 326 | modified object code on the User Product (for example, the work has 327 | been installed in ROM). 328 | 329 | The requirement to provide Installation Information does not include a 330 | requirement to continue to provide support service, warranty, or updates 331 | for a work that has been modified or installed by the recipient, or for 332 | the User Product in which it has been modified or installed. Access to a 333 | network may be denied when the modification itself materially and 334 | adversely affects the operation of the network or violates the rules and 335 | protocols for communication across the network. 336 | 337 | Corresponding Source conveyed, and Installation Information provided, 338 | in accord with this section must be in a format that is publicly 339 | documented (and with an implementation available to the public in 340 | source code form), and must require no special password or key for 341 | unpacking, reading or copying. 342 | 343 | 7. Additional Terms. 344 | 345 | "Additional permissions" are terms that supplement the terms of this 346 | License by making exceptions from one or more of its conditions. 347 | Additional permissions that are applicable to the entire Program shall 348 | be treated as though they were included in this License, to the extent 349 | that they are valid under applicable law. If additional permissions 350 | apply only to part of the Program, that part may be used separately 351 | under those permissions, but the entire Program remains governed by 352 | this License without regard to the additional permissions. 353 | 354 | When you convey a copy of a covered work, you may at your option 355 | remove any additional permissions from that copy, or from any part of 356 | it. (Additional permissions may be written to require their own 357 | removal in certain cases when you modify the work.) You may place 358 | additional permissions on material, added by you to a covered work, 359 | for which you have or can give appropriate copyright permission. 360 | 361 | Notwithstanding any other provision of this License, for material you 362 | add to a covered work, you may (if authorized by the copyright holders of 363 | that material) supplement the terms of this License with terms: 364 | 365 | a) Disclaiming warranty or limiting liability differently from the 366 | terms of sections 15 and 16 of this License; or 367 | 368 | b) Requiring preservation of specified reasonable legal notices or 369 | author attributions in that material or in the Appropriate Legal 370 | Notices displayed by works containing it; or 371 | 372 | c) Prohibiting misrepresentation of the origin of that material, or 373 | requiring that modified versions of such material be marked in 374 | reasonable ways as different from the original version; or 375 | 376 | d) Limiting the use for publicity purposes of names of licensors or 377 | authors of the material; or 378 | 379 | e) Declining to grant rights under trademark law for use of some 380 | trade names, trademarks, or service marks; or 381 | 382 | f) Requiring indemnification of licensors and authors of that 383 | material by anyone who conveys the material (or modified versions of 384 | it) with contractual assumptions of liability to the recipient, for 385 | any liability that these contractual assumptions directly impose on 386 | those licensors and authors. 387 | 388 | All other non-permissive additional terms are considered "further 389 | restrictions" within the meaning of section 10. If the Program as you 390 | received it, or any part of it, contains a notice stating that it is 391 | governed by this License along with a term that is a further 392 | restriction, you may remove that term. If a license document contains 393 | a further restriction but permits relicensing or conveying under this 394 | License, you may add to a covered work material governed by the terms 395 | of that license document, provided that the further restriction does 396 | not survive such relicensing or conveying. 397 | 398 | If you add terms to a covered work in accord with this section, you 399 | must place, in the relevant source files, a statement of the 400 | additional terms that apply to those files, or a notice indicating 401 | where to find the applicable terms. 402 | 403 | Additional terms, permissive or non-permissive, may be stated in the 404 | form of a separately written license, or stated as exceptions; 405 | the above requirements apply either way. 406 | 407 | 8. Termination. 408 | 409 | You may not propagate or modify a covered work except as expressly 410 | provided under this License. Any attempt otherwise to propagate or 411 | modify it is void, and will automatically terminate your rights under 412 | this License (including any patent licenses granted under the third 413 | paragraph of section 11). 414 | 415 | However, if you cease all violation of this License, then your 416 | license from a particular copyright holder is reinstated (a) 417 | provisionally, unless and until the copyright holder explicitly and 418 | finally terminates your license, and (b) permanently, if the copyright 419 | holder fails to notify you of the violation by some reasonable means 420 | prior to 60 days after the cessation. 421 | 422 | Moreover, your license from a particular copyright holder is 423 | reinstated permanently if the copyright holder notifies you of the 424 | violation by some reasonable means, this is the first time you have 425 | received notice of violation of this License (for any work) from that 426 | copyright holder, and you cure the violation prior to 30 days after 427 | your receipt of the notice. 428 | 429 | Termination of your rights under this section does not terminate the 430 | licenses of parties who have received copies or rights from you under 431 | this License. If your rights have been terminated and not permanently 432 | reinstated, you do not qualify to receive new licenses for the same 433 | material under section 10. 434 | 435 | 9. Acceptance Not Required for Having Copies. 436 | 437 | You are not required to accept this License in order to receive or 438 | run a copy of the Program. Ancillary propagation of a covered work 439 | occurring solely as a consequence of using peer-to-peer transmission 440 | to receive a copy likewise does not require acceptance. However, 441 | nothing other than this License grants you permission to propagate or 442 | modify any covered work. These actions infringe copyright if you do 443 | not accept this License. Therefore, by modifying or propagating a 444 | covered work, you indicate your acceptance of this License to do so. 445 | 446 | 10. Automatic Licensing of Downstream Recipients. 447 | 448 | Each time you convey a covered work, the recipient automatically 449 | receives a license from the original licensors, to run, modify and 450 | propagate that work, subject to this License. You are not responsible 451 | for enforcing compliance by third parties with this License. 452 | 453 | An "entity transaction" is a transaction transferring control of an 454 | organization, or substantially all assets of one, or subdividing an 455 | organization, or merging organizations. If propagation of a covered 456 | work results from an entity transaction, each party to that 457 | transaction who receives a copy of the work also receives whatever 458 | licenses to the work the party's predecessor in interest had or could 459 | give under the previous paragraph, plus a right to possession of the 460 | Corresponding Source of the work from the predecessor in interest, if 461 | the predecessor has it or can get it with reasonable efforts. 462 | 463 | You may not impose any further restrictions on the exercise of the 464 | rights granted or affirmed under this License. For example, you may 465 | not impose a license fee, royalty, or other charge for exercise of 466 | rights granted under this License, and you may not initiate litigation 467 | (including a cross-claim or counterclaim in a lawsuit) alleging that 468 | any patent claim is infringed by making, using, selling, offering for 469 | sale, or importing the Program or any portion of it. 470 | 471 | 11. Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. For 483 | purposes of this definition, "control" includes the right to grant 484 | patent sublicenses in a manner consistent with the requirements of 485 | this License. 486 | 487 | Each contributor grants you a non-exclusive, worldwide, royalty-free 488 | patent license under the contributor's essential patent claims, to 489 | make, use, sell, offer for sale, import and otherwise run, modify and 490 | propagate the contents of its contributor version. 491 | 492 | In the following three paragraphs, a "patent license" is any express 493 | agreement or commitment, however denominated, not to enforce a patent 494 | (such as an express permission to practice a patent or covenant not to 495 | sue for patent infringement). To "grant" such a patent license to a 496 | party means to make such an agreement or commitment not to enforce a 497 | patent against the party. 498 | 499 | If you convey a covered work, knowingly relying on a patent license, 500 | and the Corresponding Source of the work is not available for anyone 501 | to copy, free of charge and under the terms of this License, through a 502 | publicly available network server or other readily accessible means, 503 | then you must either (1) cause the Corresponding Source to be so 504 | available, or (2) arrange to deprive yourself of the benefit of the 505 | patent license for this particular work, or (3) arrange, in a manner 506 | consistent with the requirements of this License, to extend the patent 507 | license to downstream recipients. "Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) {year} {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /Standard Version/MAPIT.cpp: -------------------------------------------------------------------------------- 1 | // load Rcpp 2 | #include 3 | #include 4 | using namespace Rcpp; 5 | using namespace arma; 6 | 7 | // [[Rcpp::depends(RcppArmadillo)]] 8 | // [[Rcpp::plugins(openmp)]] 9 | 10 | // [[Rcpp::export]] 11 | arma::mat GetLinearKernel(arma::mat X){ 12 | double p = X.n_rows; 13 | return X.t()*X/p; 14 | } 15 | 16 | // [[Rcpp::export]] 17 | arma::mat ComputePCs(arma::mat X,int top = 10){ 18 | mat U; 19 | vec s; 20 | mat V; 21 | svd(U,s,V,X); 22 | 23 | mat PCs = U*diagmat(s); 24 | return PCs.cols(0,top-1); 25 | } 26 | 27 | //////////////////////////////////////////////////////////////////////////// 28 | 29 | //Below are functions for MAPIT using two hypothesis testing strategies: 30 | //(1) MAPIT using the Normal or Z-Test 31 | //(2) MAPIT using the Davies Method 32 | 33 | //Considered are the following submodels: 34 | //(1) Standard Model ---> y = m+g+e 35 | //(2) Standard + Covariate Model ---> y = Wa+m+g+e 36 | //(3) Standard + Common Environment Model ---> y = m+g+c+e 37 | //(4) Standard + Covariate + Common Environment Model ---> y = Wa+m+g+c+e 38 | 39 | //NOTE: delta = {delta(0),delta(1),delta(2)} = {sigma^2,omega^2,tau^2} for models (1) and (2) 40 | //NOTE: delta = {delta(0),delta(1),delta(2),delta(3)} = {sigma^2,omega^2,nu^2,tau^2} for models (3) and (4) 41 | 42 | //////////////////////////////////////////////////////////////////////////// 43 | 44 | // Model 1: Standard Model ---> y = m+g+e 45 | 46 | // [[Rcpp::export]] 47 | List MAPIT1_Normal(mat X,vec y){ 48 | int i; 49 | const int n = X.n_cols; 50 | const int p = X.n_rows; 51 | 52 | //Set up the vectors to save the outputs 53 | NumericVector sigma_est(p); 54 | NumericVector sigma_se(p); 55 | NumericVector pve(p); 56 | 57 | //Pre-compute the Linear GSM 58 | mat GSM = GetLinearKernel(X); 59 | 60 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 71 | mat btb_inv = inv(b.t()*b); 72 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 73 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 74 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 75 | 76 | //Compute the quantities q and S 77 | vec q = zeros(3); //Create k-vector q to save 78 | mat S = zeros(3,3); //Create kxk-matrix S to save 79 | 80 | q(0) = as_scalar(yc.t()*Gc*yc); 81 | q(1) = as_scalar(yc.t()*Kc*yc); 82 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 83 | 84 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 85 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 86 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 87 | S(1,0) = S(0,1); 88 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 89 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 90 | S(2,0) = S(0,2); 91 | S(2,1) = S(1,2); 92 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 93 | 94 | //Compute sigma(0) and sigma(1) 95 | mat Sinv = inv(S); 96 | vec delta = Sinv*q; 97 | 98 | //Compute var(sigma(0)) 99 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 100 | 101 | //Save point estimates and SE of the epistasis component 102 | sigma_est(i) = delta(0); 103 | sigma_se(i) = sqrt(V_sigma); 104 | 105 | //Compute the PVE 106 | pve(i) = delta(0)/accu(delta); 107 | } 108 | 109 | //Compute the p-values for each estimate 110 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 111 | 112 | //Return a list of the arguments 113 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 114 | } 115 | 116 | //////////////////////////////////////////////////////////////////////////// 117 | 118 | // Model 2: Standard + Covariate Model ---> y = Wa+m+g+e 119 | 120 | // [[Rcpp::export]] 121 | List MAPIT2_Normal(mat X,vec y,mat Z){ 122 | int i; 123 | const int n = X.n_cols; 124 | const int p = X.n_rows; 125 | const int q = Z.n_rows; 126 | 127 | //Set up the vectors to save the outputs 128 | NumericVector sigma_est(p); 129 | NumericVector sigma_se(p); 130 | NumericVector pve(p); 131 | 132 | //Pre-compute the Linear GSM 133 | mat GSM = GetLinearKernel(X); 134 | 135 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 146 | mat btb_inv = inv(b.t()*b); 147 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 148 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 149 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 150 | 151 | //Compute the quantities q and S 152 | vec q = zeros(3); //Create k-vector q to save 153 | mat S = zeros(3,3); //Create kxk-matrix S to save 154 | 155 | q(0) = as_scalar(yc.t()*Gc*yc); 156 | q(1) = as_scalar(yc.t()*Kc*yc); 157 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 158 | 159 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 160 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 161 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 162 | S(1,0) = S(0,1); 163 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 164 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 165 | S(2,0) = S(0,2); 166 | S(2,1) = S(1,2); 167 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 168 | 169 | //Compute delta and Sinv 170 | mat Sinv = inv(S); 171 | vec delta = Sinv*q; 172 | 173 | //Compute var(delta(0)) 174 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 175 | 176 | //Save point estimates and SE of the epistasis component 177 | sigma_est(i) = delta(0); 178 | sigma_se(i) = sqrt(V_sigma); 179 | 180 | //Compute the PVE 181 | pve(i) = delta(0)/accu(delta); 182 | } 183 | 184 | //Compute the p-values for each estimate 185 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 186 | 187 | //Return a list of the arguments 188 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 189 | } 190 | 191 | //////////////////////////////////////////////////////////////////////////// 192 | 193 | // Model 3: Standard + Common Environment Model ---> y = m+g+c+e 194 | 195 | // [[Rcpp::export]] 196 | List MAPIT3_Normal(mat X,vec y,mat C){ 197 | int i; 198 | const int n = X.n_cols; 199 | const int p = X.n_rows; 200 | 201 | //Set up the vectors to save the outputs 202 | NumericVector sigma_est(p); 203 | NumericVector sigma_se(p); 204 | NumericVector pve(p); 205 | 206 | //Pre-compute the Linear GSM 207 | mat GSM = GetLinearKernel(X); 208 | 209 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 220 | mat btb_inv = inv(b.t()*b); 221 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 222 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 223 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 224 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 225 | 226 | //Compute the quantities q and S 227 | vec q = zeros(4); //Create k-vector q to save 228 | mat S = zeros(4,4); //Create kxk-matrix S to save 229 | 230 | q(0) = as_scalar(yc.t()*Gc*yc); 231 | q(1) = as_scalar(yc.t()*Kc*yc); 232 | q(2) = as_scalar(yc.t()*Cc*yc); 233 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 234 | 235 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 236 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 237 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 238 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 239 | 240 | S(1,0) = S(0,1); 241 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 242 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 243 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 244 | 245 | S(2,0) = S(0,2); 246 | S(2,1) = S(1,2); 247 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 248 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 249 | 250 | S(3,0) = S(0,3); 251 | S(3,1) = S(1,3); 252 | S(3,2) = S(2,3); 253 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 254 | 255 | //Compute delta and Sinv 256 | mat Sinv = inv(S); 257 | vec delta = Sinv*q; 258 | 259 | //Compute var(delta(0)) 260 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*Cc+delta(3)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 261 | 262 | //Save point estimates and SE of the epistasis component 263 | sigma_est(i) = delta(0); 264 | sigma_se(i) = sqrt(V_sigma); 265 | 266 | //Compute the PVE 267 | pve(i) = delta(0)/accu(delta); 268 | } 269 | 270 | //Compute the p-values for each estimate 271 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 272 | 273 | //Return a list of the arguments 274 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 275 | } 276 | 277 | //////////////////////////////////////////////////////////////////////////// 278 | 279 | // Model 4: Standard + Covariate + Common Environment Model ---> y = Wa+m+g+c+e 280 | 281 | // [[Rcpp::export]] 282 | List MAPIT4_Normal(mat X,vec y,mat Z,mat C){ 283 | int i; 284 | const int n = X.n_cols; 285 | const int p = X.n_rows; 286 | const int q = Z.n_rows; 287 | 288 | //Set up the vectors to save the outputs 289 | NumericVector sigma_est(p); 290 | NumericVector sigma_se(p); 291 | NumericVector pve(p); 292 | 293 | //Pre-compute the Linear GSM 294 | mat GSM = GetLinearKernel(X); 295 | 296 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 307 | mat btb_inv = inv(b.t()*b); 308 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 309 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 310 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 311 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 312 | 313 | //Compute the quantities q and S 314 | vec q = zeros(4); //Create k-vector q to save 315 | mat S = zeros(4,4); //Create kxk-matrix S to save 316 | 317 | q(0) = as_scalar(yc.t()*Gc*yc); 318 | q(1) = as_scalar(yc.t()*Kc*yc); 319 | q(2) = as_scalar(yc.t()*Cc*yc); 320 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 321 | 322 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 323 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 324 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 325 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 326 | 327 | S(1,0) = S(0,1); 328 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 329 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 330 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 331 | 332 | S(2,0) = S(0,2); 333 | S(2,1) = S(1,2); 334 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 335 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 336 | 337 | S(3,0) = S(0,3); 338 | S(3,1) = S(1,3); 339 | S(3,2) = S(2,3); 340 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 341 | 342 | //Compute delta and Sinv 343 | mat Sinv = inv(S); 344 | vec delta = Sinv*q; 345 | 346 | //Compute var(delta(0)) 347 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*Cc+delta(3)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 348 | 349 | //Save point estimates and SE of the epistasis component 350 | sigma_est(i) = delta(0); 351 | sigma_se(i) = sqrt(V_sigma); 352 | 353 | //Compute the PVE 354 | pve(i) = delta(0)/accu(delta); 355 | } 356 | 357 | //Compute the p-values for each estimate 358 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 359 | 360 | //Return a list of the arguments 361 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 362 | } 363 | 364 | //////////////////////////////////////////////////////////////////////////// 365 | //////////////////////////////////////////////////////////////////////////// 366 | //////////////////////////////////////////////////////////////////////////// 367 | //////////////////////////////////////////////////////////////////////////// 368 | 369 | //Here is MAPIT using the Davies Method for hypothesis testing 370 | 371 | //////////////////////////////////////////////////////////////////////////// 372 | //////////////////////////////////////////////////////////////////////////// 373 | //////////////////////////////////////////////////////////////////////////// 374 | //////////////////////////////////////////////////////////////////////////// 375 | 376 | // Model 1: Standard Model ---> y = m+g+e 377 | 378 | // [[Rcpp::export]] 379 | List MAPIT1_Davies(mat X,vec y,const vec ind){ 380 | int i; 381 | const int n = X.n_cols; 382 | const int p = X.n_rows; 383 | 384 | //Set up the vectors to save the outputs 385 | NumericVector sigma_est(p); 386 | NumericVector pve(p); 387 | mat Lambda(n,p); 388 | 389 | //Pre-compute the Linear GSM 390 | mat GSM = GetLinearKernel(X); 391 | 392 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 405 | mat btb_inv = inv(b.t()*b); 406 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 407 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); //Scale Kn = MKnM^t 408 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 409 | 410 | //Compute the quantities q and S 411 | vec q = zeros(3); //Create k-vector q to save 412 | mat S = zeros(3,3); //Create kxk-matrix S to save 413 | 414 | q(0) = as_scalar(yc.t()*Gc*yc); 415 | q(1) = as_scalar(yc.t()*Kc*yc); 416 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 417 | 418 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 419 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 420 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 421 | 422 | S(1,0) = S(0,1); 423 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 424 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 425 | 426 | S(2,0) = S(0,2); 427 | S(2,1) = S(1,2); 428 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 429 | 430 | //Compute delta and Sinv 431 | mat Sinv = inv(S); 432 | vec delta = Sinv*q; 433 | 434 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 435 | vec q_sub = zeros(2); 436 | mat S_sub = zeros(2,2); 437 | 438 | q_sub(0)=q(1); 439 | q_sub(1)=q(2); 440 | 441 | S_sub(0,0)=S(1,1); 442 | S_sub(0,1)=S(1,2); 443 | 444 | S_sub(1,0)=S(2,1); 445 | S_sub(1,1)=S(2,2); 446 | 447 | //Save point estimates and SE of the epistasis component 448 | sigma_est(i) = delta(0); 449 | 450 | //Compute P and P^{1/2} matrix 451 | vec delta_null = inv(S_sub)*q_sub; 452 | 453 | vec eigval; 454 | mat eigvec; 455 | 456 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*(eye(n,n)-(b*btb_inv)*b.t())); 457 | 458 | //Find the eigenvalues of the projection matrix 459 | vec evals; 460 | 461 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 462 | Lambda.col(i) = evals; 463 | 464 | //Compute the PVE 465 | pve(i) = delta(0)/accu(delta); 466 | } 467 | } 468 | 469 | //Return a list of the arguments 470 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 471 | } 472 | 473 | //////////////////////////////////////////////////////////////////////////// 474 | 475 | // Model 2: Standard + Covariate Model ---> y = Wa+m+g+e 476 | 477 | // [[Rcpp::export]] 478 | List MAPIT2_Davies(mat X,vec y,mat Z,const vec ind){ 479 | int i; 480 | const int n = X.n_cols; 481 | const int p = X.n_rows; 482 | const int q = Z.n_rows; 483 | 484 | //Set up the vectors to save the outputs 485 | NumericVector sigma_est(p); 486 | NumericVector pve(p); 487 | mat Lambda(n,p); 488 | 489 | //Pre-compute the Linear GSM 490 | mat GSM = GetLinearKernel(X); 491 | 492 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 505 | mat btb_inv = inv(b.t()*b); 506 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 507 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); //Scale Kn = MKnM^t 508 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 509 | 510 | //Compute the quantities q and S 511 | vec q = zeros(3); //Create k-vector q to save 512 | mat S = zeros(3,3); //Create kxk-matrix S to save 513 | 514 | q(0) = as_scalar(yc.t()*Gc*yc); 515 | q(1) = as_scalar(yc.t()*Kc*yc); 516 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 517 | 518 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 519 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 520 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 521 | 522 | S(1,0) = S(0,1); 523 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 524 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 525 | 526 | S(2,0) = S(0,2); 527 | S(2,1) = S(1,2); 528 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 529 | 530 | //Compute delta and Sinv 531 | mat Sinv = inv(S); 532 | vec delta = Sinv*q; 533 | 534 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 535 | vec q_sub = zeros(2); 536 | mat S_sub = zeros(2,2); 537 | 538 | q_sub(0)=q(1); 539 | q_sub(1)=q(2); 540 | 541 | S_sub(0,0)=S(1,1); 542 | S_sub(0,1)=S(1,2); 543 | 544 | S_sub(1,0)=S(2,1); 545 | S_sub(1,1)=S(2,2); 546 | 547 | //Save point estimates and SE of the epistasis component 548 | sigma_est(i) = delta(0); 549 | 550 | //Compute P and P^{1/2} matrix 551 | vec delta_null = inv(S_sub)*q_sub; 552 | 553 | vec eigval; 554 | mat eigvec; 555 | 556 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*(eye(n,n)-(b*btb_inv)*b.t())); 557 | 558 | //Find the eigenvalues of the projection matrix 559 | vec evals; 560 | 561 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 562 | Lambda.col(i) = evals; 563 | 564 | //Compute the PVE 565 | pve(i) = delta(0)/accu(delta); 566 | } 567 | } 568 | 569 | //Return a list of the arguments 570 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 571 | } 572 | 573 | //////////////////////////////////////////////////////////////////////////// 574 | 575 | // Model 3: Standard + Common Environment Model ---> y = m+g+c+e 576 | 577 | // [[Rcpp::export]] 578 | List MAPIT3_Davies(mat X,vec y,mat C,const vec ind){ 579 | int i; 580 | const int n = X.n_cols; 581 | const int p = X.n_rows; 582 | 583 | //Set up the vectors to save the outputs 584 | NumericVector sigma_est(p); 585 | NumericVector pve(p); 586 | mat Lambda(n,p); 587 | 588 | //Pre-compute the Linear GSM 589 | mat GSM = GetLinearKernel(X); 590 | 591 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 604 | mat btb_inv = inv(b.t()*b); 605 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 606 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 607 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 608 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 609 | 610 | //Compute the quantities q and S 611 | vec q = zeros(4); //Create k-vector q to save 612 | mat S = zeros(4,4); //Create kxk-matrix S to save 613 | 614 | q(0) = as_scalar(yc.t()*Gc*yc); 615 | q(1) = as_scalar(yc.t()*Kc*yc); 616 | q(2) = as_scalar(yc.t()*Cc*yc); 617 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 618 | 619 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 620 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 621 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 622 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 623 | 624 | S(1,0) = S(0,1); 625 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 626 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 627 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 628 | 629 | S(2,0) = S(0,2); 630 | S(2,1) = S(1,2); 631 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 632 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 633 | 634 | S(3,0) = S(0,3); 635 | S(3,1) = S(1,3); 636 | S(3,2) = S(2,3); 637 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 638 | 639 | //Compute delta and Sinv 640 | mat Sinv = inv(S); 641 | vec delta = Sinv*q; 642 | 643 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 644 | vec q_sub = zeros(3); 645 | mat S_sub = zeros(3,3); 646 | 647 | q_sub(0)=q(1); 648 | q_sub(1)=q(2); 649 | q_sub(2)=q(3); 650 | 651 | S_sub(0,0)=S(1,1); 652 | S_sub(0,1)=S(1,2); 653 | S_sub(0,2)=S(1,3); 654 | 655 | S_sub(1,0)=S(2,1); 656 | S_sub(1,1)=S(2,2); 657 | S_sub(1,2)=S(2,3); 658 | 659 | S_sub(2,0)=S(3,1); 660 | S_sub(2,1)=S(3,2); 661 | S_sub(2,2)=S(3,3); 662 | 663 | //Save point estimates and SE of the epistasis component 664 | sigma_est(i) = delta(0); 665 | 666 | //Compute P and P^{1/2} matrix 667 | vec delta_null = inv(S_sub)*q_sub; 668 | 669 | vec eigval; 670 | mat eigvec; 671 | 672 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*Cc+delta_null(2)*(eye(n,n)-(b*btb_inv)*b.t())); 673 | 674 | //Find the eigenvalues of the projection matrix 675 | vec evals; 676 | 677 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 678 | Lambda.col(i) = evals; 679 | 680 | //Compute the PVE 681 | pve(i) = delta(0)/accu(delta); 682 | } 683 | } 684 | 685 | //Return a list of the arguments 686 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 687 | } 688 | 689 | //////////////////////////////////////////////////////////////////////////// 690 | 691 | // Model 4: Standard + Common Environment Model ---> y = Wa+m+g+c+e 692 | 693 | // [[Rcpp::export]] 694 | List MAPIT4_Davies(mat X,vec y,mat Z,mat C,const vec ind){ 695 | int i; 696 | const int n = X.n_cols; 697 | const int p = X.n_rows; 698 | const int q = Z.n_rows; 699 | 700 | //Set up the vectors to save the outputs 701 | NumericVector sigma_est(p); 702 | NumericVector pve(p); 703 | mat Lambda(n,p); 704 | 705 | //Pre-compute the Linear GSM 706 | mat GSM = GetLinearKernel(X); 707 | 708 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 721 | mat btb_inv = inv(b.t()*b); 722 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 723 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 724 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 725 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 726 | 727 | //Compute the quantities q and S 728 | vec q = zeros(4); //Create k-vector q to save 729 | mat S = zeros(4,4); //Create kxk-matrix S to save 730 | 731 | q(0) = as_scalar(yc.t()*Gc*yc); 732 | q(1) = as_scalar(yc.t()*Kc*yc); 733 | q(2) = as_scalar(yc.t()*Cc*yc); 734 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 735 | 736 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 737 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 738 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 739 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 740 | 741 | S(1,0) = S(0,1); 742 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 743 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 744 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 745 | 746 | S(2,0) = S(0,2); 747 | S(2,1) = S(1,2); 748 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 749 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 750 | 751 | S(3,0) = S(0,3); 752 | S(3,1) = S(1,3); 753 | S(3,2) = S(2,3); 754 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 755 | 756 | //Compute delta and Sinv 757 | mat Sinv = inv(S); 758 | vec delta = Sinv*q; 759 | 760 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 761 | vec q_sub = zeros(3); 762 | mat S_sub = zeros(3,3); 763 | 764 | q_sub(0)=q(1); 765 | q_sub(1)=q(2); 766 | q_sub(2)=q(3); 767 | 768 | S_sub(0,0)=S(1,1); 769 | S_sub(0,1)=S(1,2); 770 | S_sub(0,2)=S(1,3); 771 | 772 | S_sub(1,0)=S(2,1); 773 | S_sub(1,1)=S(2,2); 774 | S_sub(1,2)=S(2,3); 775 | 776 | S_sub(2,0)=S(3,1); 777 | S_sub(2,1)=S(3,2); 778 | S_sub(2,2)=S(3,3); 779 | 780 | //Save point estimates and SE of the epistasis component 781 | sigma_est(i) = delta(0); 782 | 783 | //Compute P and P^{1/2} matrix 784 | vec delta_null = inv(S_sub)*q_sub; 785 | 786 | vec eigval; 787 | mat eigvec; 788 | 789 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*Cc+delta_null(2)*(eye(n,n)-(b*btb_inv)*b.t())); 790 | 791 | //Find the eigenvalues of the projection matrix 792 | vec evals; 793 | 794 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 795 | Lambda.col(i) = evals; 796 | 797 | //Compute the PVE 798 | pve(i) = delta(0)/accu(delta); 799 | } 800 | } 801 | 802 | //Return a list of the arguments 803 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 804 | } 805 | 806 | //////////////////////////////////////////////////////////////////////////////// 807 | //////////////////////////////////////////////////////////////////////////////// 808 | //////////////////////////////////////////////////////////////////////////////// 809 | //////////////////////////////////////////////////////////////////////////////// 810 | 811 | //Here is MAPIT using the Davies Method for the hypothesis testing of every SNP 812 | 813 | //////////////////////////////////////////////////////////////////////////////// 814 | /////////////////////////////////////////////////////////////////////////////// 815 | ////////////////////////////////////////////////////////////////////////////// 816 | ///////////////////////////////////////////////////////////////////////////// 817 | 818 | // [[Rcpp::export]] 819 | List MAPIT_Davies_Approx(mat X,vec y){ 820 | int i; 821 | const int n = X.n_cols; 822 | const int p = X.n_rows; 823 | 824 | //Set up the vectors to save the outputs 825 | NumericVector sigma_est(p); 826 | NumericVector pve(p); 827 | mat Lambda(n,p); 828 | 829 | //Pre-compute the Linear GSM 830 | mat GSM = GetLinearKernel(X); 831 | 832 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 842 | mat btb_inv = inv(b.t()*b); 843 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); //Scale Kn = MKnM^t 844 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 845 | 846 | //Compute the quantities q and S 847 | vec q = zeros(2); //Create k-vector q to save 848 | mat S = zeros(2,2); //Create kxk-matrix S to save 849 | 850 | q(0) = as_scalar(yc.t()*Gc*yc); 851 | q(1) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 852 | 853 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 854 | S(0,1) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 855 | S(1,0) = S(0,1); 856 | S(1,1) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 857 | 858 | //Compute delta and Sinv 859 | mat Sinv = inv(S); 860 | vec delta = Sinv*q; 861 | 862 | //Save point estimates and SE of the epistasis component 863 | sigma_est(i) = delta(0); 864 | 865 | //Find the eigenvalues of the projection matrix 866 | vec evals; 867 | eig_sym(evals,(Sinv(0,0)*Gc+Sinv(0,1)*(eye(n,n)-(b*btb_inv)*b.t()))*q(1)/S(1,1)); 868 | Lambda.col(i) = evals; 869 | 870 | //Compute the PVE 871 | pve(i) = delta(0)/accu(delta); 872 | } 873 | 874 | //Return a list of the arguments 875 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 876 | } 877 | -------------------------------------------------------------------------------- /OpenMP Version/MAPIT_OpenMP.cpp: -------------------------------------------------------------------------------- 1 | // load Rcpp 2 | #include 3 | #include 4 | using namespace Rcpp; 5 | using namespace arma; 6 | 7 | // [[Rcpp::depends(RcppArmadillo)]] 8 | // [[Rcpp::plugins(openmp)]] 9 | 10 | // [[Rcpp::export]] 11 | arma::mat GetLinearKernel(arma::mat X){ 12 | double p = X.n_rows; 13 | return X.t()*X/p; 14 | } 15 | 16 | // [[Rcpp::export]] 17 | arma::mat ComputePCs(arma::mat X,int top = 10){ 18 | mat U; 19 | vec s; 20 | mat V; 21 | svd(U,s,V,X); 22 | 23 | mat PCs = U*diagmat(s); 24 | return PCs.cols(0,top-1); 25 | } 26 | 27 | //////////////////////////////////////////////////////////////////////////// 28 | 29 | //Below are functions for MAPIT using two hypothesis testing strategies: 30 | //(1) MAPIT using the Normal or Z-Test 31 | //(2) MAPIT using the Davies Method 32 | 33 | //Considered are the following submodels: 34 | //(1) Standard Model ---> y = m+g+e 35 | //(2) Standard + Covariate Model ---> y = Wa+m+g+e 36 | //(3) Standard + Common Environment Model ---> y = m+g+c+e 37 | //(4) Standard + Covariate + Common Environment Model ---> y = Wa+m+g+c+e 38 | 39 | //NOTE: delta = {delta(0),delta(1),delta(2)} = {sigma^2,omega^2,tau^2} for models (1) and (2) 40 | //NOTE: delta = {delta(0),delta(1),delta(2),delta(3)} = {sigma^2,omega^2,nu^2,tau^2} for models (3) and (4) 41 | 42 | //////////////////////////////////////////////////////////////////////////// 43 | 44 | // Model 1: Standard Model ---> y = m+g+e 45 | 46 | // [[Rcpp::export]] 47 | List MAPIT1_Normal(mat X,vec y,int cores = 1){ 48 | int i; 49 | const int n = X.n_cols; 50 | const int p = X.n_rows; 51 | 52 | //Set up the vectors to save the outputs 53 | NumericVector sigma_est(p); 54 | NumericVector sigma_se(p); 55 | NumericVector pve(p); 56 | 57 | //Pre-compute the Linear GSM 58 | mat GSM = GetLinearKernel(X); 59 | 60 | omp_set_num_threads(cores); 61 | #pragma omp parallel for schedule(dynamic) 62 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 73 | mat btb_inv = inv(b.t()*b); 74 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 75 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 76 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 77 | 78 | //Compute the quantities q and S 79 | vec q = zeros(3); //Create k-vector q to save 80 | mat S = zeros(3,3); //Create kxk-matrix S to save 81 | 82 | q(0) = as_scalar(yc.t()*Gc*yc); 83 | q(1) = as_scalar(yc.t()*Kc*yc); 84 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 85 | 86 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 87 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 88 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 89 | S(1,0) = S(0,1); 90 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 91 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 92 | S(2,0) = S(0,2); 93 | S(2,1) = S(1,2); 94 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 95 | 96 | //Compute sigma(0) and sigma(1) 97 | mat Sinv = inv(S); 98 | vec delta = Sinv*q; 99 | 100 | //Compute var(sigma(0)) 101 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 102 | 103 | //Save point estimates and SE of the epistasis component 104 | sigma_est(i) = delta(0); 105 | sigma_se(i) = sqrt(V_sigma); 106 | 107 | //Compute the PVE 108 | pve(i) = delta(0)/accu(delta); 109 | } 110 | 111 | //Compute the p-values for each estimate 112 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 113 | 114 | //Return a list of the arguments 115 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 116 | } 117 | 118 | //////////////////////////////////////////////////////////////////////////// 119 | 120 | // Model 2: Standard + Covariate Model ---> y = Wa+m+g+e 121 | 122 | // [[Rcpp::export]] 123 | List MAPIT2_Normal(mat X,vec y,mat Z,int cores = 1){ 124 | int i; 125 | const int n = X.n_cols; 126 | const int p = X.n_rows; 127 | const int q = Z.n_rows; 128 | 129 | //Set up the vectors to save the outputs 130 | NumericVector sigma_est(p); 131 | NumericVector sigma_se(p); 132 | NumericVector pve(p); 133 | 134 | //Pre-compute the Linear GSM 135 | mat GSM = GetLinearKernel(X); 136 | 137 | omp_set_num_threads(cores); 138 | #pragma omp parallel for schedule(dynamic) 139 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 150 | mat btb_inv = inv(b.t()*b); 151 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 152 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 153 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 154 | 155 | //Compute the quantities q and S 156 | vec q = zeros(3); //Create k-vector q to save 157 | mat S = zeros(3,3); //Create kxk-matrix S to save 158 | 159 | q(0) = as_scalar(yc.t()*Gc*yc); 160 | q(1) = as_scalar(yc.t()*Kc*yc); 161 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 162 | 163 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 164 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 165 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 166 | S(1,0) = S(0,1); 167 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 168 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 169 | S(2,0) = S(0,2); 170 | S(2,1) = S(1,2); 171 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 172 | 173 | //Compute delta and Sinv 174 | mat Sinv = inv(S); 175 | vec delta = Sinv*q; 176 | 177 | //Compute var(delta(0)) 178 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 179 | 180 | //Save point estimates and SE of the epistasis component 181 | sigma_est(i) = delta(0); 182 | sigma_se(i) = sqrt(V_sigma); 183 | 184 | //Compute the PVE 185 | pve(i) = delta(0)/accu(delta); 186 | } 187 | 188 | //Compute the p-values for each estimate 189 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 190 | 191 | //Return a list of the arguments 192 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 193 | } 194 | 195 | //////////////////////////////////////////////////////////////////////////// 196 | 197 | // Model 3: Standard + Common Environment Model ---> y = m+g+c+e 198 | 199 | // [[Rcpp::export]] 200 | List MAPIT3_Normal(mat X,vec y,mat C,int cores = 1){ 201 | int i; 202 | const int n = X.n_cols; 203 | const int p = X.n_rows; 204 | 205 | //Set up the vectors to save the outputs 206 | NumericVector sigma_est(p); 207 | NumericVector sigma_se(p); 208 | NumericVector pve(p); 209 | 210 | //Pre-compute the Linear GSM 211 | mat GSM = GetLinearKernel(X); 212 | 213 | omp_set_num_threads(cores); 214 | #pragma omp parallel for schedule(dynamic) 215 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 226 | mat btb_inv = inv(b.t()*b); 227 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 228 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 229 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 230 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 231 | 232 | //Compute the quantities q and S 233 | vec q = zeros(4); //Create k-vector q to save 234 | mat S = zeros(4,4); //Create kxk-matrix S to save 235 | 236 | q(0) = as_scalar(yc.t()*Gc*yc); 237 | q(1) = as_scalar(yc.t()*Kc*yc); 238 | q(2) = as_scalar(yc.t()*Cc*yc); 239 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 240 | 241 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 242 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 243 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 244 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 245 | 246 | S(1,0) = S(0,1); 247 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 248 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 249 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 250 | 251 | S(2,0) = S(0,2); 252 | S(2,1) = S(1,2); 253 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 254 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 255 | 256 | S(3,0) = S(0,3); 257 | S(3,1) = S(1,3); 258 | S(3,2) = S(2,3); 259 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 260 | 261 | //Compute delta and Sinv 262 | mat Sinv = inv(S); 263 | vec delta = Sinv*q; 264 | 265 | //Compute var(delta(0)) 266 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*Cc+delta(3)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 267 | 268 | //Save point estimates and SE of the epistasis component 269 | sigma_est(i) = delta(0); 270 | sigma_se(i) = sqrt(V_sigma); 271 | 272 | //Compute the PVE 273 | pve(i) = delta(0)/accu(delta); 274 | } 275 | 276 | //Compute the p-values for each estimate 277 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 278 | 279 | //Return a list of the arguments 280 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 281 | } 282 | 283 | //////////////////////////////////////////////////////////////////////////// 284 | 285 | // Model 4: Standard + Covariate + Common Environment Model ---> y = Wa+m+g+c+e 286 | 287 | // [[Rcpp::export]] 288 | List MAPIT4_Normal(mat X,vec y,mat Z,mat C,int cores = 1){ 289 | int i; 290 | const int n = X.n_cols; 291 | const int p = X.n_rows; 292 | const int q = Z.n_rows; 293 | 294 | //Set up the vectors to save the outputs 295 | NumericVector sigma_est(p); 296 | NumericVector sigma_se(p); 297 | NumericVector pve(p); 298 | 299 | //Pre-compute the Linear GSM 300 | mat GSM = GetLinearKernel(X); 301 | 302 | omp_set_num_threads(cores); 303 | #pragma omp parallel for schedule(dynamic) 304 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 315 | mat btb_inv = inv(b.t()*b); 316 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 317 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 318 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 319 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 320 | 321 | //Compute the quantities q and S 322 | vec q = zeros(4); //Create k-vector q to save 323 | mat S = zeros(4,4); //Create kxk-matrix S to save 324 | 325 | q(0) = as_scalar(yc.t()*Gc*yc); 326 | q(1) = as_scalar(yc.t()*Kc*yc); 327 | q(2) = as_scalar(yc.t()*Cc*yc); 328 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 329 | 330 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 331 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 332 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 333 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 334 | 335 | S(1,0) = S(0,1); 336 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 337 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 338 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 339 | 340 | S(2,0) = S(0,2); 341 | S(2,1) = S(1,2); 342 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 343 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 344 | 345 | S(3,0) = S(0,3); 346 | S(3,1) = S(1,3); 347 | S(3,2) = S(2,3); 348 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 349 | 350 | //Compute delta and Sinv 351 | mat Sinv = inv(S); 352 | vec delta = Sinv*q; 353 | 354 | //Compute var(delta(0)) 355 | double V_sigma = as_scalar(2*yc.t()*trans(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(delta(0)*Gc+delta(1)*Kc+delta(2)*Cc+delta(3)*(eye(n,n)-(b*btb_inv)*b.t()))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*yc); 356 | 357 | //Save point estimates and SE of the epistasis component 358 | sigma_est(i) = delta(0); 359 | sigma_se(i) = sqrt(V_sigma); 360 | 361 | //Compute the PVE 362 | pve(i) = delta(0)/accu(delta); 363 | } 364 | 365 | //Compute the p-values for each estimate 366 | NumericVector sigma_pval = 2*Rcpp::pnorm(abs(sigma_est/sigma_se),0.0,1.0,0,0); //H0: sigma = 0 vs. H1: sigma != 0 367 | 368 | //Return a list of the arguments 369 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("SE") = sigma_se,Rcpp::Named("pvalues") = sigma_pval,Rcpp::Named("PVE") = pve); 370 | } 371 | 372 | //////////////////////////////////////////////////////////////////////////// 373 | //////////////////////////////////////////////////////////////////////////// 374 | //////////////////////////////////////////////////////////////////////////// 375 | //////////////////////////////////////////////////////////////////////////// 376 | 377 | //Here is MAPIT using the Davies Method for hypothesis testing 378 | 379 | //////////////////////////////////////////////////////////////////////////// 380 | //////////////////////////////////////////////////////////////////////////// 381 | //////////////////////////////////////////////////////////////////////////// 382 | //////////////////////////////////////////////////////////////////////////// 383 | 384 | // Model 1: Standard Model ---> y = m+g+e 385 | 386 | // [[Rcpp::export]] 387 | List MAPIT1_Davies(mat X,vec y,const vec ind,int cores = 1){ 388 | int i; 389 | const int n = X.n_cols; 390 | const int p = X.n_rows; 391 | 392 | //Set up the vectors to save the outputs 393 | NumericVector sigma_est(p); 394 | NumericVector pve(p); 395 | mat Lambda(n,p); 396 | 397 | //Pre-compute the Linear GSM 398 | mat GSM = GetLinearKernel(X); 399 | 400 | omp_set_num_threads(cores); 401 | #pragma omp parallel for schedule(dynamic) 402 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 415 | mat btb_inv = inv(b.t()*b); 416 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 417 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); //Scale Kn = MKnM^t 418 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 419 | 420 | //Compute the quantities q and S 421 | vec q = zeros(3); //Create k-vector q to save 422 | mat S = zeros(3,3); //Create kxk-matrix S to save 423 | 424 | q(0) = as_scalar(yc.t()*Gc*yc); 425 | q(1) = as_scalar(yc.t()*Kc*yc); 426 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 427 | 428 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 429 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 430 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 431 | 432 | S(1,0) = S(0,1); 433 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 434 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 435 | 436 | S(2,0) = S(0,2); 437 | S(2,1) = S(1,2); 438 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 439 | 440 | //Compute delta and Sinv 441 | mat Sinv = inv(S); 442 | vec delta = Sinv*q; 443 | 444 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 445 | vec q_sub = zeros(2); 446 | mat S_sub = zeros(2,2); 447 | 448 | q_sub(0)=q(1); 449 | q_sub(1)=q(2); 450 | 451 | S_sub(0,0)=S(1,1); 452 | S_sub(0,1)=S(1,2); 453 | 454 | S_sub(1,0)=S(2,1); 455 | S_sub(1,1)=S(2,2); 456 | 457 | //Save point estimates and SE of the epistasis component 458 | sigma_est(i) = delta(0); 459 | 460 | //Compute P and P^{1/2} matrix 461 | vec delta_null = inv(S_sub)*q_sub; 462 | 463 | vec eigval; 464 | mat eigvec; 465 | 466 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*(eye(n,n)-(b*btb_inv)*b.t())); 467 | 468 | //Find the eigenvalues of the projection matrix 469 | vec evals; 470 | 471 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 472 | Lambda.col(i) = evals; 473 | 474 | //Compute the PVE 475 | pve(i) = delta(0)/accu(delta); 476 | } 477 | } 478 | 479 | //Return a list of the arguments 480 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 481 | } 482 | 483 | //////////////////////////////////////////////////////////////////////////// 484 | 485 | // Model 2: Standard + Covariate Model ---> y = Wa+m+g+e 486 | 487 | // [[Rcpp::export]] 488 | List MAPIT2_Davies(mat X,vec y,mat Z,const vec ind,int cores = 1){ 489 | int i; 490 | const int n = X.n_cols; 491 | const int p = X.n_rows; 492 | const int q = Z.n_rows; 493 | 494 | //Set up the vectors to save the outputs 495 | NumericVector sigma_est(p); 496 | NumericVector pve(p); 497 | mat Lambda(n,p); 498 | 499 | //Pre-compute the Linear GSM 500 | mat GSM = GetLinearKernel(X); 501 | 502 | omp_set_num_threads(cores); 503 | #pragma omp parallel for schedule(dynamic) 504 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 517 | mat btb_inv = inv(b.t()*b); 518 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 519 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); //Scale Kn = MKnM^t 520 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 521 | 522 | //Compute the quantities q and S 523 | vec q = zeros(3); //Create k-vector q to save 524 | mat S = zeros(3,3); //Create kxk-matrix S to save 525 | 526 | q(0) = as_scalar(yc.t()*Gc*yc); 527 | q(1) = as_scalar(yc.t()*Kc*yc); 528 | q(2) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 529 | 530 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 531 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 532 | S(0,2) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 533 | 534 | S(1,0) = S(0,1); 535 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 536 | S(1,2) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 537 | 538 | S(2,0) = S(0,2); 539 | S(2,1) = S(1,2); 540 | S(2,2) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 541 | 542 | //Compute delta and Sinv 543 | mat Sinv = inv(S); 544 | vec delta = Sinv*q; 545 | 546 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 547 | vec q_sub = zeros(2); 548 | mat S_sub = zeros(2,2); 549 | 550 | q_sub(0)=q(1); 551 | q_sub(1)=q(2); 552 | 553 | S_sub(0,0)=S(1,1); 554 | S_sub(0,1)=S(1,2); 555 | 556 | S_sub(1,0)=S(2,1); 557 | S_sub(1,1)=S(2,2); 558 | 559 | //Save point estimates and SE of the epistasis component 560 | sigma_est(i) = delta(0); 561 | 562 | //Compute P and P^{1/2} matrix 563 | vec delta_null = inv(S_sub)*q_sub; 564 | 565 | vec eigval; 566 | mat eigvec; 567 | 568 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*(eye(n,n)-(b*btb_inv)*b.t())); 569 | 570 | //Find the eigenvalues of the projection matrix 571 | vec evals; 572 | 573 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 574 | Lambda.col(i) = evals; 575 | 576 | //Compute the PVE 577 | pve(i) = delta(0)/accu(delta); 578 | } 579 | } 580 | 581 | //Return a list of the arguments 582 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 583 | } 584 | 585 | //////////////////////////////////////////////////////////////////////////// 586 | 587 | // Model 3: Standard + Common Environment Model ---> y = m+g+c+e 588 | 589 | // [[Rcpp::export]] 590 | List MAPIT3_Davies(mat X,vec y,mat C,const vec ind,int cores = 1){ 591 | int i; 592 | const int n = X.n_cols; 593 | const int p = X.n_rows; 594 | 595 | //Set up the vectors to save the outputs 596 | NumericVector sigma_est(p); 597 | NumericVector pve(p); 598 | mat Lambda(n,p); 599 | 600 | //Pre-compute the Linear GSM 601 | mat GSM = GetLinearKernel(X); 602 | 603 | omp_set_num_threads(cores); 604 | #pragma omp parallel for schedule(dynamic) 605 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 618 | mat btb_inv = inv(b.t()*b); 619 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 620 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 621 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 622 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 623 | 624 | //Compute the quantities q and S 625 | vec q = zeros(4); //Create k-vector q to save 626 | mat S = zeros(4,4); //Create kxk-matrix S to save 627 | 628 | q(0) = as_scalar(yc.t()*Gc*yc); 629 | q(1) = as_scalar(yc.t()*Kc*yc); 630 | q(2) = as_scalar(yc.t()*Cc*yc); 631 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 632 | 633 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 634 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 635 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 636 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 637 | 638 | S(1,0) = S(0,1); 639 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 640 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 641 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 642 | 643 | S(2,0) = S(0,2); 644 | S(2,1) = S(1,2); 645 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 646 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 647 | 648 | S(3,0) = S(0,3); 649 | S(3,1) = S(1,3); 650 | S(3,2) = S(2,3); 651 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 652 | 653 | //Compute delta and Sinv 654 | mat Sinv = inv(S); 655 | vec delta = Sinv*q; 656 | 657 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 658 | vec q_sub = zeros(3); 659 | mat S_sub = zeros(3,3); 660 | 661 | q_sub(0)=q(1); 662 | q_sub(1)=q(2); 663 | q_sub(2)=q(3); 664 | 665 | S_sub(0,0)=S(1,1); 666 | S_sub(0,1)=S(1,2); 667 | S_sub(0,2)=S(1,3); 668 | 669 | S_sub(1,0)=S(2,1); 670 | S_sub(1,1)=S(2,2); 671 | S_sub(1,2)=S(2,3); 672 | 673 | S_sub(2,0)=S(3,1); 674 | S_sub(2,1)=S(3,2); 675 | S_sub(2,2)=S(3,3); 676 | 677 | //Save point estimates and SE of the epistasis component 678 | sigma_est(i) = delta(0); 679 | 680 | //Compute P and P^{1/2} matrix 681 | vec delta_null = inv(S_sub)*q_sub; 682 | 683 | vec eigval; 684 | mat eigvec; 685 | 686 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*Cc+delta_null(2)*(eye(n,n)-(b*btb_inv)*b.t())); 687 | 688 | //Find the eigenvalues of the projection matrix 689 | vec evals; 690 | 691 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 692 | Lambda.col(i) = evals; 693 | 694 | //Compute the PVE 695 | pve(i) = delta(0)/accu(delta); 696 | } 697 | } 698 | 699 | //Return a list of the arguments 700 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 701 | } 702 | 703 | //////////////////////////////////////////////////////////////////////////// 704 | 705 | // Model 4: Standard + Common Environment Model ---> y = Wa+m+g+c+e 706 | 707 | // [[Rcpp::export]] 708 | List MAPIT4_Davies(mat X,vec y,mat Z,mat C,const vec ind,int cores = 1){ 709 | int i; 710 | const int n = X.n_cols; 711 | const int p = X.n_rows; 712 | const int q = Z.n_rows; 713 | 714 | //Set up the vectors to save the outputs 715 | NumericVector sigma_est(p); 716 | NumericVector pve(p); 717 | mat Lambda(n,p); 718 | 719 | //Pre-compute the Linear GSM 720 | mat GSM = GetLinearKernel(X); 721 | 722 | omp_set_num_threads(cores); 723 | #pragma omp parallel for schedule(dynamic) 724 | for(i=0; i(n); b.cols(1,q) = Z.t(); b.col(q+1) = trans(X.row(i)); 737 | mat btb_inv = inv(b.t()*b); 738 | mat Kc = K-b*btb_inv*(b.t()*K)-(K*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(K*b))*btb_inv*b.t(); 739 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); 740 | mat Cc = C-b*btb_inv*(b.t()*C)-(C*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(C*b))*btb_inv*b.t(); 741 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 742 | 743 | //Compute the quantities q and S 744 | vec q = zeros(4); //Create k-vector q to save 745 | mat S = zeros(4,4); //Create kxk-matrix S to save 746 | 747 | q(0) = as_scalar(yc.t()*Gc*yc); 748 | q(1) = as_scalar(yc.t()*Kc*yc); 749 | q(2) = as_scalar(yc.t()*Cc*yc); 750 | q(3) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 751 | 752 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 753 | S(0,1) = as_scalar(accu(Gc.t()%Kc)); 754 | S(0,2) = as_scalar(accu(Gc.t()%Cc)); 755 | S(0,3) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 756 | 757 | S(1,0) = S(0,1); 758 | S(1,1) = as_scalar(accu(Kc.t()%Kc)); 759 | S(1,2) = as_scalar(accu(Kc.t()%Cc)); 760 | S(1,3) = as_scalar(accu(Kc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 761 | 762 | S(2,0) = S(0,2); 763 | S(2,1) = S(1,2); 764 | S(2,2) = as_scalar(accu(Cc.t()%Cc)); 765 | S(2,3) = as_scalar(accu(Cc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 766 | 767 | S(3,0) = S(0,3); 768 | S(3,1) = S(1,3); 769 | S(3,2) = S(2,3); 770 | S(3,3) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 771 | 772 | //Compute delta and Sinv 773 | mat Sinv = inv(S); 774 | vec delta = Sinv*q; 775 | 776 | //Record omega^2, nu^2, and tau^2 under the null hypothesis 777 | vec q_sub = zeros(3); 778 | mat S_sub = zeros(3,3); 779 | 780 | q_sub(0)=q(1); 781 | q_sub(1)=q(2); 782 | q_sub(2)=q(3); 783 | 784 | S_sub(0,0)=S(1,1); 785 | S_sub(0,1)=S(1,2); 786 | S_sub(0,2)=S(1,3); 787 | 788 | S_sub(1,0)=S(2,1); 789 | S_sub(1,1)=S(2,2); 790 | S_sub(1,2)=S(2,3); 791 | 792 | S_sub(2,0)=S(3,1); 793 | S_sub(2,1)=S(3,2); 794 | S_sub(2,2)=S(3,3); 795 | 796 | //Save point estimates and SE of the epistasis component 797 | sigma_est(i) = delta(0); 798 | 799 | //Compute P and P^{1/2} matrix 800 | vec delta_null = inv(S_sub)*q_sub; 801 | 802 | vec eigval; 803 | mat eigvec; 804 | 805 | eig_sym(eigval,eigvec,delta_null(0)*Kc+delta_null(1)*Cc+delta_null(2)*(eye(n,n)-(b*btb_inv)*b.t())); 806 | 807 | //Find the eigenvalues of the projection matrix 808 | vec evals; 809 | 810 | eig_sym(evals, (eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))*(Sinv(0,0)*Gc+Sinv(0,1)*Kc+Sinv(0,2)*Cc+Sinv(0,3)*(eye(n,n)-(b*btb_inv)*b.t()))*(eigvec.cols(find(eigval>0))*diagmat(sqrt(eigval(find(eigval>0))))*trans(eigvec.cols(find(eigval>0))))); 811 | Lambda.col(i) = evals; 812 | 813 | //Compute the PVE 814 | pve(i) = delta(0)/accu(delta); 815 | } 816 | } 817 | 818 | //Return a list of the arguments 819 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 820 | } 821 | 822 | //////////////////////////////////////////////////////////////////////////////// 823 | //////////////////////////////////////////////////////////////////////////////// 824 | //////////////////////////////////////////////////////////////////////////////// 825 | //////////////////////////////////////////////////////////////////////////////// 826 | 827 | //Here is MAPIT using the Davies Method for the hypothesis testing of every SNP 828 | 829 | //////////////////////////////////////////////////////////////////////////////// 830 | /////////////////////////////////////////////////////////////////////////////// 831 | ////////////////////////////////////////////////////////////////////////////// 832 | ///////////////////////////////////////////////////////////////////////////// 833 | 834 | // [[Rcpp::export]] 835 | List MAPIT_Davies_Approx(mat X,vec y,int cores = 1){ 836 | int i; 837 | const int n = X.n_cols; 838 | const int p = X.n_rows; 839 | 840 | //Set up the vectors to save the outputs 841 | NumericVector sigma_est(p); 842 | NumericVector pve(p); 843 | mat Lambda(n,p); 844 | 845 | //Pre-compute the Linear GSM 846 | mat GSM = GetLinearKernel(X); 847 | 848 | omp_set_num_threads(cores); 849 | #pragma omp parallel for schedule(dynamic) 850 | for(i=0; i(n); b.col(1) = trans(X.row(i)); 860 | mat btb_inv = inv(b.t()*b); 861 | mat Gc = G-b*btb_inv*(b.t()*G)-(G*b)*btb_inv*b.t()+b*btb_inv*(b.t()*(G*b))*btb_inv*b.t(); //Scale Kn = MKnM^t 862 | vec yc = (eye(n,n)-(b*btb_inv)*b.t())*y; 863 | 864 | //Compute the quantities q and S 865 | vec q = zeros(2); //Create k-vector q to save 866 | mat S = zeros(2,2); //Create kxk-matrix S to save 867 | 868 | q(0) = as_scalar(yc.t()*Gc*yc); 869 | q(1) = as_scalar(yc.t()*(eye(n,n)-(b*btb_inv)*b.t())*yc); 870 | 871 | S(0,0) = as_scalar(accu(Gc.t()%Gc)); 872 | S(0,1) = as_scalar(accu(Gc.t()%(eye(n,n)-(b*btb_inv)*b.t()))); 873 | S(1,0) = S(0,1); 874 | S(1,1) = as_scalar(accu(trans(eye(n,n)-(b*btb_inv)*b.t())%(eye(n,n)-(b*btb_inv)*b.t()))); 875 | 876 | //Compute delta and Sinv 877 | mat Sinv = inv(S); 878 | vec delta = Sinv*q; 879 | 880 | //Save point estimates and SE of the epistasis component 881 | sigma_est(i) = delta(0); 882 | 883 | //Find the eigenvalues of the projection matrix 884 | vec evals; 885 | eig_sym(evals,(Sinv(0,0)*Gc+Sinv(0,1)*(eye(n,n)-(b*btb_inv)*b.t()))*q(1)/S(1,1)); 886 | Lambda.col(i) = evals; 887 | 888 | //Compute the PVE 889 | pve(i) = delta(0)/accu(delta); 890 | } 891 | 892 | //Return a list of the arguments 893 | return Rcpp::List::create(Rcpp::Named("Est") = sigma_est, Rcpp::Named("Eigenvalues") = Lambda,Rcpp::Named("PVE") = pve); 894 | } 895 | --------------------------------------------------------------------------------