├── DESCRIPTION
├── NAMESPACE
├── R
    ├── data.R
    └── progmod.R
├── README.md
├── data
    ├── ADNI_disease_stage_bl.RData
    ├── ADNI_disease_stage_bl.txt
    └── adas_mmse_data.RData
└── man
    ├── ADNI_disease_stage_bl.Rd
    ├── GLF.Rd
    ├── adas_mmse_data.Rd
    ├── exp_model.Rd
    ├── progmod.Rd
    └── readme
        └── adas_progression.gif


/DESCRIPTION:
--------------------------------------------------------------------------------
 1 | Package: progmod
 2 | Type: Package
 3 | Title: Disease progression modeling based on nonlinear mixed effects modeling
 4 | Version: 0.1.0
 5 | Authors@R: person("Lars Lau", "Raket", email = "progmod@larslau.dk",
 6 |                   role = c("aut", "cre"))
 7 | Description: Estimates population-level disease progression patterns
 8 |     based on aligning short-term longitudinal observed patterns.
 9 |     The model takes the form of a nonlinear mixed effect model and estimation
10 |     is done using maximum likelihood estimation.
11 | Depends: 
12 |     R (>= 3.5.0),
13 |     covBM,
14 |     nlme,
15 | License: GPL-3
16 | Encoding: UTF-8
17 | LazyData: true
18 | Suggests:
19 |     ggplot2
20 | RoxygenNote: 7.1.1
21 | 


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/NAMESPACE:
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1 | # Generated by roxygen2: do not edit by hand
2 | 
3 | export(GLF)
4 | export(exp_model)
5 | export(progmod)
6 | import(covBM)
7 | import(nlme)
8 | 


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/R/data.R:
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 1 | #' Simulated longitudinal ADAS-cog and MMSE scores
 2 | #'
 3 | #' A dataset containing longitudinal simulated ADAS-cog and MMSE scores
 4 | #' for a large number of individuals that are cognitively normal, have mild
 5 | #' congnitive impairment (MCI) or dementia.
 6 | #' Data is simulated based on ADNI data.
 7 | #'
 8 | #' @format A data frame with 9378 rows and 7 variables:
 9 | #' \describe{
10 | #'   \item{subject_id}{Subject ID}
11 | #'   \item{Month_bl}{Months since baseline}
12 | #'   \item{ADAS13}{Simulated 13-item ADAS-cog score}
13 | #'   \item{MMSE}{Simulated MMSE score}
14 | #'   \item{CN}{Was subject cognitively normal at baseline (0/1)?}
15 | #'   \item{MCI}{Was subject mild cognitively impaired at baseline (0/1)?}
16 | #'   \item{DEM}{Did subject have dementia at baseline (0/1)?}
17 | #'   \item{blstatus}{Patient status at baseline (Cognitively normal/MCI/Dementia)}
18 | #' }
19 | "adas_mmse_data"
20 | 
21 | 
22 | #' Predicted disease stage at baseline for ADNI participants
23 | #'?AD
24 | #' A dataset containing the predicted disease stage (disease month) for
25 | #' individuals in ADNI based on their longitudinal 13-item ADAS-cog trajectories
26 | #' Data are based on a data cut of ADAS-cog scores from July 2019.
27 | #'
28 | #' @format A data frame with 2130 rows and 3 variables:
29 | #' \describe{
30 | #'   \item{RID}{ADNI roster ID}
31 | #'   \item{pred_AD_month}{Predicted disease time (in months relative to the average cognitive state of the cognitively normal group)}
32 | #' }
33 | "ADNI_disease_stage_bl"
34 | 
35 | 


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/R/progmod.R:
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  1 | #' Overparametrized exponential function.
  2 | #'
  3 | #' @param t Time variable
  4 | #' @param l Scale parameter for the exponential function
  5 | #' @param s Time-shift parameter
  6 | #' @param g Time-scaling parameter
  7 | #' @param v Intercept parameter
  8 | #' @return The function values at the supplied time values along with a
  9 | #'         "gradient" attribute.
 10 | #' @examples
 11 | #' exp_model(t = c(0, 1), l = 1, s = 0, g = 0, v = 0)
 12 | #' @export
 13 | 
 14 | exp_model <- deriv(
 15 |   expression(l * exp((t + s) / exp(g)) + v),
 16 |   namevec = c('l', 's', 'g', 'v'),
 17 |   function.arg = c('t', 'l', 's', 'g', 'v'))
 18 | 
 19 | #' Overparametrized generalized logistic function.
 20 | #'
 21 | #' @param t Time variable
 22 | #' @param A Lower asymptote parameter
 23 | #' @param K Upper asymptote parameter
 24 | #' @param B Time-scaling parameter
 25 | #' @param s Time-shift parameter
 26 | #' @param v Asymmetry parameter
 27 | #' @param c Intercept parameter, should only be used for random effects
 28 | #' @return The function values at the supplied time values along with a
 29 | #'         "gradient" attribute.
 30 | #' @examples
 31 | #' GLF(t = c(0, 1), A = 30, K = 0, B = 1, s = 0, v = 1, c = 0)
 32 | #' @export
 33 | 
 34 | GLF <- deriv(
 35 |   expression(A + (K - A) / ((1 + exp(-B * (t + s)))^(v)) + c),
 36 |   namevec = c('A', 'K', 'B', 'v', 's', 'c'),
 37 |   function.arg = c('t', 'A', 'K', 'B', 'v', 's', 'c'))
 38 | 
 39 | 
 40 | 
 41 | #' Fit nonlinear mixed-effects disease progression models
 42 | #'
 43 | #' This function fits disease-progression models to longitudinal data.
 44 | #' The function fits nonlinear mixed-effects models by calling
 45 | #' \code{\link[nlme]{nlme}} or \code{\link[nlmeBM]{nlmeBM}} depending on the
 46 | #' model specification.
 47 | #' @param model A nonlinear model formula, with the response on the left of a ~
 48 | #' operator and an expression involving parameters and covariates on the right,
 49 | #' or an nlsList object. If data is given, all names used in the formula should
 50 | #' be defined as parameters or variables in the data frame. The method function
 51 | #' nlme.nlsList is documented separately. See \code{\link[nlme]{nlme}} for details.
 52 | #' @param data An optional data frame containing the variables named in model,
 53 | #' fixed, random, correlation, weights, subset, and naPattern.
 54 | #' By default the variables are taken from the environment.
 55 | #' @param fixed A two-sided linear formula of the form \code{f1+...+fn~x1+...+xm},
 56 | #' or a list of two-sided formulas of the form \code{f1~x1+...+xm}, with possibly
 57 | #' different models for different parameters. The \code{f1,...,fn} are the names of
 58 | #' parameters included on the right hand side of model and the \code{x1+...+xm}
 59 | #' expressions define linear models for these parameters (when the left hand
 60 | #' side of the formula contains several parameters, they all are assumed to
 61 | #' follow the same linear model, described by the right hand side expression).
 62 | #' A \code{1} on the right hand side of the formula(s) indicates a single fixed effects
 63 | #' for the corresponding parameter(s).
 64 | #' @param random A two-sided formula of the form
 65 | #' \code{r1+...+rn~x1+...+xm | g1/.../gQ}, with \code{r1,...,rn} naming parameters included on the
 66 | #' right hand side of model, \code{x1+...+xm} specifying the random-effects model for these
 67 | #' parameters and \code{g1/.../gQ} the grouping structure (\code{Q} may be equal to \code{1}, in which
 68 | #' case no / is required). The random effects formula will be repeated for all
 69 | #' levels of grouping, in the case of multiple levels of grouping. Explicit specification of the
 70 | #' covariance structure between random effects (e.g. using \code{pdMat}) or different formulas for
 71 | #' different random effects can be specified. See \code{\link[nlme]{nlme}} for details.
 72 | #' \strong{Note:} Only simple two-sided formulas are currently supported when a covariance
 73 | #' structure is given (see below).
 74 | #' @param groups an optional one-sided formula of the form \code{~ g1} specifying the partitions
 75 | #' of the data over which the random effects vary. This is needed when different formulas are specified for
 76 | #' different random effects.
 77 | #' @param start A numeric vector or list of initial estimates for the fixed effects and random effects.
 78 | #' If declared as a numeric vector, it is converted internally to a list with a single component fixed, given by the vector.
 79 | #' The \code{fixed} component is required, unless the model function inherits from
 80 | #' class \code{selfStart}, in which case initial values will be derived
 81 | #' from a call to \code{nlsList}. An optional \code{random} component is used to specify
 82 | #' initial values for the random effects and should consist of a matrix,
 83 | #' or a list of matrices with length equal to the number of grouping levels.
 84 | #' Each matrix should have as many rows as the number of groups at the
 85 | #' corresponding level and as many columns as the number of random effects in that level.
 86 | #' @param covariance An optional \code{\link[nlme]{corStruct}} object describing the within-group
 87 | #' covariance structure. In addition to those available in \code{nlme},
 88 | #' \code{\link{covBM}} can be used to incorporate a Brownian motion component, \code{\link{covFracBM}}
 89 | #' can be used to incorporate a fractional Brownian motion component and \code{\link{covIOU}}
 90 | #' can be used to incorporate an integrated Ornstein-Uhlenbeck process in relation to
 91 | #' a continuous variable.
 92 | #' @param weights an optional varFunc object or one-sided formula describing the within-group heteroscedasticity structure.
 93 | #' This argument is primarily used for multivariate modeling of several outcomes where different standard errors are to be expected.
 94 | #' If given as a formula, it is used as the argument to varFixed, corresponding to fixed variance weights.
 95 | #' See the documentation on varClasses for a description of the available varFunc classes.
 96 | #' Defaults to NULL, corresponding to homoscedastic within-group errors. \strong{Note:} weighting is not currently supported
 97 | #' when a covariance structure is given.
 98 | #' @param method a character string. If "\code{REML}" the model is fit by maximizing the restricted log-likelihood.
 99 | #' If "\code{ML}" the log-likelihood is maximized. Defaults to "\code{ML}".
100 | #' @param control A list of control parameters for the estimation algorithm. See \code{\link[nlmeControl]{nlmeControl}}.
101 | #' @param verbose If \code{TRUE} information on the evolution of the iterative
102 | #' algorithm is printed. Default is \code{FALSE}.
103 | #' @return An object of class "nlme" representing the nonlinear mixed effects model fit.
104 | #' @examples
105 | #'
106 | #'#
107 | #'# Fit exponential disease progression model to simulated ADAS-cog scores
108 | #'#
109 | #'
110 | #'# Plot data
111 | #'if (require(ggplot2)) {
112 | #'ggplot(adas_mmse_data, aes(x = Month_bl, y = ADAS13)) +
113 | #'  geom_line(aes(group = subject_id, color = blstatus)) +
114 | #'  ylim(c(85, 0)) +
115 | #'  xlab('Months since baseline')
116 | #'}
117 | #'
118 | #'# Fit exponential model with random shift and intercept
119 | #'fixed_start_coef <- c(0.5, 70, 150, 3.5, 10)
120 | #'ADAS_progmod <- progmod(ADAS13 ~ exp_model(Month_bl, l, s, g, v),
121 | #'                        data = subset(adas_mmse_data, !is.na(ADAS13)),
122 | #'                        fixed = list(l ~ 1,
123 | #'                                     s ~ MCI + DEM - 1,
124 | #'                                     g ~ 1,
125 | #'                                     v ~ 1),
126 | #'                        random = s + v ~ 1 | subject_id,
127 | #'                        start = fixed_start_coef,
128 | #'                        covariance = NULL)
129 | #'
130 | #'# Predict from model and visualize results
131 | #'adas_mmse_data$fixed_shift_adas <- with(adas_mmse_data,
132 | #'                                        MCI * fixed.effects(ADAS_progmod)[2] +
133 | #'                                          DEM * fixed.effects(ADAS_progmod)[3])
134 | #'pred_rand <- random.effects(ADAS_progmod)
135 | #'adas_mmse_data$random_shift_adas <- pred_rand[match(adas_mmse_data$subject_id, rownames(pred_rand)), 's.(Intercept)']
136 | #'
137 | #'if (require(ggplot2)) {
138 | #'  ggplot(adas_mmse_data, aes(x = Month_bl + fixed_shift_adas, y = ADAS13)) +
139 | #'    geom_line(aes(group = subject_id, color = blstatus)) +
140 | #'    ylim(c(85, 0)) +
141 | #'    xlab('Months since baseline')
142 | #'}
143 | #'
144 | #'
145 | #'if (require(ggplot2)) {
146 | #'  ggplot(adas_mmse_data, aes(x = Month_bl + fixed_shift_adas + random_shift_adas, y = ADAS13)) +
147 | #'    geom_line(aes(group = subject_id, color = blstatus)) +
148 | #'    ylim(c(85, 0)) +
149 | #'    xlab('Months since baseline')
150 | #'}
151 | #'
152 | #'#
153 | #'# Fit generalized logistic disease progression model to simulated MMSE scores
154 | #'#
155 | #'
156 | #' # Plot data
157 | #'
158 | #'if (require(ggplot2)) {
159 | #'  ggplot(adas_mmse_data, aes(x = Month_bl, y = MMSE)) +
160 | #'    geom_line(aes(group = subject_id, color = blstatus)) +
161 | #'    ylim(c(0, 30)) +
162 | #'    xlab('Months since baseline')
163 | #'}
164 | #'
165 | #'# Fit generalized logistic model with range [30, 0] and a random time shift
166 | #'fixed_start_coef <- c(B = 0.025,
167 | #'                      v = 1.4,
168 | #'                      `s.(Intercept)` = -100,
169 | #'                      s.MCI = 26,
170 | #'                      s.DEM = 75)
171 | #'
172 | #'MMSE_progmod_glf <- progmod(MMSE ~ GLF(Month_bl, A = 30, K = 0, B, v, s, c = 0),
173 | #'                            data = subset(adas_mmse_data, !is.na(MMSE)),
174 | #'                            fixed = list(B ~ 1,
175 | #'                                         v ~ 1,
176 | #'                                         s ~ MCI + DEM + 1),
177 | #'                            random = s ~ 1 | subject_id,
178 | #'                            start = fixed_start_coef,
179 | #'                            covariance = NULL)
180 | #'
181 | #'# Predict from model and visualize results
182 | #'adas_mmse_data$fixed_shift_mmse <- with(adas_mmse_data,
183 | #'                                        fixed.effects(MMSE_progmod_glf)[3] +
184 | #'                                        MCI * fixed.effects(MMSE_progmod_glf)[4] +
185 | #'                                        DEM * fixed.effects(MMSE_progmod_glf)[5])
186 | #'pred_rand <- random.effects(MMSE_progmod_glf)
187 | #'adas_mmse_data$random_shift_mmse <- pred_rand[match(adas_mmse_data$subject_id, rownames(pred_rand)), 's.(Intercept)']
188 | #'
189 | #'
190 | #'
191 | #'if (require(ggplot2)) {
192 | #'  ggplot(adas_mmse_data, aes(x = Month_bl + fixed_shift_mmse + random_shift_mmse, y = MMSE)) +
193 | #'    geom_line(aes(group = subject_id, color = blstatus)) +
194 | #'    xlab('Months since baseline')
195 | #'}
196 | #'
197 | #'#
198 | # Fit a multivariate model to simulated ADAS-cog and MMSE scores
199 | #
200 | #'
201 | #'# Stack data to long format
202 | #'tmp1 <- adas_mmse_data[, c('subject_id', 'Month_bl', 'CN', 'MCI', 'DEM', 'ADAS13')]
203 | #'names(tmp1)[6] <- 'value'
204 | #'tmp1$scale <- 'ADAS13'
205 | #'
206 | #'tmp2 <- adas_mmse_data[, c('subject_id', 'Month_bl', 'CN', 'MCI', 'DEM', 'MMSE')]
207 | #'names(tmp2)[6] <- 'value'
208 | #'tmp2$scale <- 'MMSE'
209 | #'
210 | #'# Long data
211 | #'adas_mmse_data_long <- na.omit(rbind(tmp1, tmp2))
212 | #'adas_mmse_data_long$scale <- factor(adas_mmse_data_long$scale)
213 | #'
214 | #'# Remove temporary files
215 | #'rm(tmp1, tmp2)
216 | #'
217 | #'# Fit multivariate exponential model
218 | #'fixed_start_coef <- c(l.scaleADAS13 = 0.5,
219 | #'                      l.scaleMMSE = -0.1,
220 | #'                      s.MCI = 70,
221 | #'                      s.DEM = 150,
222 | #'                      g.scaleADAS13 = 3.5,
223 | #'                      g.scaleMMSE = 3,
224 | #'                      v.scaleADAS13 = 10,
225 | #'                      v.scaleMMSE = 30)
226 | #'
227 | #'multi_progmod_glf <- progmod(value ~ exp_model(Month_bl, l, s, g, v),
228 | #'                             data = adas_mmse_data_long,
229 | #'                             fixed = list(l ~ scale + 0,
230 | #'                                          s ~ MCI + DEM + 0,
231 | #'                                          g ~ scale + 0,
232 | #'                                          v ~ scale + 0),
233 | #'                             random = list(s ~ 1,
234 | #'                                           v ~ scale),
235 | #'                             groups = ~ subject_id,
236 | #'                             start = fixed_start_coef,
237 | #'                             weights = varIdent(form = ~ 1 | scale))
238 | #'
239 | #'# Predict from model and compare to univariate models
240 | #'adas_mmse_data$fixed_shift_multi <- with(adas_mmse_data,
241 | #'                                         MCI * fixed.effects(multi_progmod_glf)[3] +
242 | #'                                           DEM * fixed.effects(multi_progmod_glf)[4])
243 | #'pred_rand <- random.effects(multi_progmod_glf)
244 | #'adas_mmse_data$random_shift_multi <- pred_rand[match(adas_mmse_data$subject_id, rownames(pred_rand)), 's.(Intercept)']
245 | #'
246 | #'
247 | #'# Correlations between predicted disease months
248 | #'with(adas_mmse_data, cor(cbind(fixed_shift_adas + random_shift_adas,
249 | #'                               fixed_shift_mmse + random_shift_mmse,
250 | #'                               fixed_shift_multi + random_shift_multi), method = 'spearman'))
251 | #'
252 | #'
253 | #'
254 | #'
255 | #' @export
256 | #' @import nlme covBM
257 | 
258 | progmod <- function(model, data, fixed, random, groups, start, covariance = NULL, weights = NULL,
259 |                     method = c("ML", "REML"), control = NULL, verbose = FALSE) {
260 | 
261 |   # Set control parameters if not given
262 |   if (is.null(control)) {
263 |     control <- nlmeControl(maxIter = 50, # Can be increased
264 |                            pnlsMaxIter = 7, # Should not be increased too much beyond 7
265 |                            msMaxIter = 500, # 50-500
266 |                            minScale = 0.01,
267 |                            tolerance = 1e-5,
268 |                            niterEM = 25, # 25-100
269 |                            pnlsTol = 0.001,
270 |                            msTol = 1e-6,
271 |                            msVerbose = FALSE,
272 |                            apVar = TRUE,
273 |                            .relStep = 1-06,
274 |                            minAbsParApVar = 0.05,
275 |                            natural = TRUE)
276 |   }
277 | 
278 |   if (is.null(covariance)) {
279 |     nlme(model = model,
280 |          data = data,
281 |          fixed = fixed,
282 |          random = random,
283 |          groups = groups,
284 |          start = start,
285 |          weights = weights,
286 |          method = method,
287 |          control = control,
288 |          verbose = verbose)
289 |   } else {
290 |     if (!missing(groups)) {
291 |       stop('\'groups\' argument is not currently supported when a stochastic process component is given.')
292 |     }
293 |     if (!is.null(weights)) {
294 |       stop('\'weights\' argument is not currently supported when a stochastic process component is given.')
295 |     }
296 |     nlmeBM(model = model,
297 |            data = data,
298 |            fixed = fixed,
299 |            random = random,
300 |            start = start,
301 |            covariance = covariance,
302 |            method = method,
303 |            control = control,
304 |            verbose = verbose)
305 |   }
306 | }
307 | 
308 | 


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/README.md:
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 1 | # Disease progression modeling based on nonlinear mixed effects modeling
 2 | progmod is an R package for estimating population-level disease progression patterns based on aligning short-term longitudinal observed patterns. The models are formulated as nonlinear mixed effect models and estimation in these models is done using maximum likelihood estimation. 
 3 | 
 4 | The basic idea of the model is to use patterns in data to map observed time (e.g. time since baseline) to disease time (both on a group level and individual level). The animation below shows an example in Alzheimer's disease where the observation times of ADAS-cog total scores from the [ADNI study](http://adni.loni.usc.edu/) are mapped to predicted disease time of the five baseline groups (Cognitively normal, Significant memory concern, early and late MCI, dementia) and to individual disease time.
 5 | 
 6 | 
 7 | ![](man/readme/adas_progression.gif)
 8 | 
 9 | The results shown in the animation are from the basic model presented in the paper 
10 | 
11 | <dl>
12 |   <dd>
13 | Raket, Lars Lau. "Statistical Disease Progression Modeling in Alzheimer Disease." <em>Frontiers in Big Data</em> (2020). <a href="https://doi.org/10.3389/fdata.2020.00024">DOI: 10.3389/fdata.2020.00024</a>
14 |   </dd>
15 | </dl>
16 | 
17 | These model predictions for ADNI based on the 13-item ADAS-cog scores are available in [data/ADNI_disease_stage_bl.txt](data/ADNI_disease_stage_bl.txt). If you use this package or data, please cite the above paper.
18 | 
19 | ## Multivariate disease progression models
20 | progmod supports simultaneous modeling of progression on multiple outcomes as described in the paper
21 | 
22 | <dl>
23 |   <dd>
24 | Kühnel, Line, Anna-Karin Berger, Bo Markussen, and Lars Lau Raket. "Simultaneous Modelling of Alzheimer’s Disease Progression via Multiple Cognitive Scales." <em>Statistics in Medicine</em> (2021). <a href="https://doi.org/10.1002/sim.8932">DOI: 10.1002/sim.8932</a>
25 |   </dd>
26 | </dl>
27 | 
28 | An example of multivariate modeling is available in the documentation.
29 | 
30 | ## Installation
31 | 
32 | You can install `progmod` directly from github using devtools:
33 | 
34 | ``` r
35 | # install.packages('devtools')
36 | devtools::install_github('larslau/progmod')
37 | ```
38 | 
39 | ## Use and examples
40 | The package contains simulated ADAS-cog and MMSE data for exploration of models. Examples of how to specify models for these data are available by running
41 | ``` r
42 | library(progmod)
43 | example(progmod)
44 | ```
45 | 
46 | 


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/data/ADNI_disease_stage_bl.RData:
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https://raw.githubusercontent.com/larslau/progmod/d374fb34a87d469891ab675f2c7294676e62dec9/data/ADNI_disease_stage_bl.RData


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/data/ADNI_disease_stage_bl.txt:
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   1 | "RID" "pred_AD_month"
   2 | "1" 2 -13.3052482930144
   3 | "2" 3 126.262553943568
   4 | "3" 4 79.4196676545141
   5 | "4" 5 -5.58262304917352
   6 | "5" 6 74.8777980600364
   7 | "6" 7 133.96137753365
   8 | "7" 8 -14.5188452266496
   9 | "8" 10 118.696057832206
  10 | "9" 14 5.34710573975268
  11 | "10" 15 3.05343429041844
  12 | "11" 16 -5.09609079190008
  13 | "12" 19 15.4972232529689
  14 | "13" 21 -18.5199702345299
  15 | "14" 22 -4.71853151940967
  16 | "15" 23 -1.56991358656421
  17 | "16" 29 140.1714074641
  18 | "17" 30 108.78793516497
  19 | "18" 31 -39.9858077913628
  20 | "19" 33 95.8257364121776
  21 | "20" 35 7.40511699242928
  22 | "21" 38 77.5653890713612
  23 | "22" 40 -0.578276341354623
  24 | "23" 41 98.17463839121
  25 | "24" 42 41.5244189363257
  26 | "25" 43 0.978370739540885
  27 | "26" 44 132.186205361288
  28 | "27" 45 121.397050803408
  29 | "28" 47 12.6702204646642
  30 | "29" 48 6.96845216613499
  31 | "30" 50 155.45738104
  32 | "31" 51 42.4256079594149
  33 | "32" 53 121.273787899927
  34 | "33" 54 110.328461159087
  35 | "34" 55 -17.5122728787861
  36 | "35" 56 -29.9860781049266
  37 | "36" 57 141.992092064474
  38 | "37" 58 -1.69269510161055
  39 | "38" 59 -6.22948760462976
  40 | "39" 60 78.0074110641921
  41 | "40" 61 23.2573335238227
  42 | "41" 66 14.4560745951936
  43 | "42" 67 4.75584226589035
  44 | "43" 68 13.7007474584375
  45 | "44" 69 -30.4493722929495
  46 | "45" 70 -4.75778980132738
  47 | "46" 72 -7.08914859206448
  48 | "47" 74 -26.5091439718453
  49 | "48" 76 99.9325156049018
  50 | "49" 77 115.127044180481
  51 | "50" 78 167.130093967962
  52 | "51" 80 67.4795534884906
  53 | "52" 81 13.5927966432799
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1903 | "1902" 6308 31.2362880096104
1904 | "1903" 6310 29.8323723439804
1905 | "1904" 6312 35.1904189675967
1906 | "1905" 6313 9.30328130366808
1907 | "1906" 6314 22.2039669991765
1908 | "1907" 6315 106.393849627651
1909 | "1908" 6316 30.1871902762732
1910 | "1909" 6318 1.61625318097941
1911 | "1910" 6319 26.4101472108763
1912 | "1911" 6320 5.3307460779199
1913 | "1912" 6321 22.2039669991765
1914 | "1913" 6323 29.8323723439804
1915 | "1914" 6326 40.6556908892829
1916 | "1915" 6327 28.7309721367288
1917 | "1916" 6328 4.41380995005477
1918 | "1917" 6329 84.2190761111589
1919 | "1918" 6330 15.1521447713305
1920 | "1919" 6333 23.9340443285725
1921 | "1920" 6334 87.9902142592311
1922 | "1921" 6335 34.1515099791305
1923 | "1922" 6336 96.5103774498473
1924 | "1923" 6341 138.864596578045
1925 | "1924" 6343 -8.7941939928905
1926 | "1925" 6345 141.799326295634
1927 | "1926" 6346 -6.73609105171796
1928 | "1927" 6347 150.948334574641
1929 | "1928" 6348 5.77849577501212
1930 | "1929" 6349 -4.72142095869469
1931 | "1930" 6350 20.3961192418175
1932 | "1931" 6351 5.3307460779199
1933 | "1932" 6352 -7.76173670507947
1934 | "1933" 6354 -5.73269254580467
1935 | "1934" 6356 90.9587756702342
1936 | "1935" 6357 31.2362880096104
1937 | "1936" 6358 26.4101472108763
1938 | "1937" 6359 -0.29160371824223
1939 | "1938" 6360 21.3079984290616
1940 | "1939" 6362 33.8475708544639
1941 | "1940" 6364 45.5147687185795
1942 | "1941" 6367 -9.81762535274936
1943 | "1942" 6369 37.7086008455174
1944 | "1943" 6370 91.7633668049271
1945 | "1944" 6371 21.3079984290616
1946 | "1945" 6372 28.3588611400315
1947 | "1946" 6373 89.4794214741403
1948 | "1947" 6374 33.5395535207436
1949 | "1948" 6375 30.8944163983527
1950 | "1949" 6376 40.6556908892829
1951 | "1950" 6377 127.152120773732
1952 | "1951" 6378 41.945719172265
1953 | "1952" 6381 4.88042828759437
1954 | "1953" 6384 -0.770544782465484
1955 | "1954" 6385 3.95837029249608
1956 | "1955" 6386 24.353112170483
1957 | "1956" 6389 117.206101716596
1958 | "1957" 6393 35.3444050508682
1959 | "1958" 6394 -1.74949674262372
1960 | "1959" 6396 29.8323723439804
1961 | "1960" 6399 30.1871902762732
1962 | "1961" 6400 26.0121835259561
1963 | "1962" 6401 29.0987914145299
1964 | "1963" 6402 116.50306553449
1965 | "1964" 6404 26.0121835259561
1966 | "1965" 6405 26.0121835259561
1967 | "1966" 6408 33.5395535207436
1968 | "1967" 6411 4.11801790693905
1969 | "1968" 6412 30.8944163983527
1970 | "1969" 6413 22.6393082809677
1971 | "1970" 6414 39.404913147844
1972 | "1971" 6415 23.0706652328223
1973 | "1972" 6416 4.88042828759437
1974 | "1973" 6417 -7.25569891437069
1975 | "1974" 6418 3.95837029249608
1976 | "1975" 6419 -0.770544782465484
1977 | "1976" 6421 35.8680065520653
1978 | "1977" 6422 31.58407455033
1979 | "1978" 6423 -23.1896280153149
1980 | "1979" 6424 30.1871902762732
1981 | "1980" 6426 41.8212522372442
1982 | "1981" 6427 26.1045276548154
1983 | "1982" 6428 87.0335847334043
1984 | "1983" 6429 2.56325881403258
1985 | "1984" 6432 39.0710628096063
1986 | "1985" 6433 139.27137027936
1987 | "1986" 6436 31.9173330195976
1988 | "1987" 6437 1.14629529440431
1989 | "1988" 6439 3.02610540253454
1990 | "1989" 6441 90.2059728791171
1991 | "1990" 6442 24.7805706611631
1992 | "1991" 6443 1.14629529440431
1993 | "1992" 6446 37.7086008455174
1994 | "1993" 6447 25.5977502666929
1995 | "1994" 6448 -1.74949674262372
1996 | "1995" 6449 33.2179080441168
1997 | "1996" 6450 135.399512369963
1998 | "1997" 6452 31.2362880096104
1999 | "1998" 6454 -0.29160371824223
2000 | "1999" 6455 27.970988800188
2001 | "2000" 6456 31.2362880096104
2002 | "2001" 6457 31.9173330195976
2003 | "2002" 6459 3.50045438756324
2004 | "2003" 6462 29.4732669867683
2005 | "2004" 6463 26.5988890988924
2006 | "2005" 6465 -4.72142095869469
2007 | "2006" 6467 119.77909162965
2008 | "2007" 6468 2.09803227219746
2009 | "2008" 6470 32.2463734311385
2010 | "2009" 6471 17.583389215461
2011 | "2010" 6472 -0.770544782465484
2012 | "2011" 6473 -12.9548976415311
2013 | "2012" 6474 34.2975706163627
2014 | "2013" 6476 24.7805706611631
2015 | "2014" 6479 107.568021420469
2016 | "2015" 6480 98.0860082044281
2017 | "2016" 6483 92.6521693775046
2018 | "2017" 6485 2.09803227219746
2019 | "2018" 6487 10.5768081401625
2020 | "2019" 6488 0.674057331151509
2021 | "2020" 6492 6.23709680907976
2022 | "2021" 6493 31.2362880096104
2023 | "2022" 6494 6.23709680907976
2024 | "2023" 6495 30.5482823715903
2025 | "2024" 6496 21.3079984290616
2026 | "2025" 6497 42.1060146697128
2027 | "2026" 6498 38.7414449106603
2028 | "2027" 6499 -11.3797527731004
2029 | "2028" 6500 33.8475708544639
2030 | "2029" 6502 29.4732669867683
2031 | "2030" 6503 39.404913147844
2032 | "2031" 6504 -4.22613476699858
2033 | "2032" 6509 -10.8627674695139
2034 | "2033" 6510 32.5809927119929
2035 | "2034" 6512 87.5886341734181
2036 | "2035" 6513 20.8608291843275
2037 | "2036" 6514 25.1912468254211
2038 | "2037" 6515 23.5108875322771
2039 | "2038" 6516 19.9412524083126
2040 | "2039" 6517 29.0987914145299
2041 | "2040" 6518 31.9173330195976
2042 | "2041" 6519 33.2179080441168
2043 | "2042" 6521 2.56325881403258
2044 | "2043" 6522 21.751307372042
2045 | "2044" 6524 -2.73699390298397
2046 | "2045" 6528 1.61625318097941
2047 | "2046" 6529 104.113833402695
2048 | "2047" 6533 84.2190761111589
2049 | "2048" 6534 39.7234027109161
2050 | "2049" 6535 125.508050695395
2051 | "2050" 6541 37.7086008455174
2052 | "2051" 6542 6.67954335038525
2053 | "2052" 6543 144.702071824208
2054 | "2053" 6544 40.0364811108555
2055 | "2054" 6545 165.253176833091
2056 | "2055" 6546 22.6393082809677
2057 | "2056" 6547 19.0063482631229
2058 | "2057" 6548 -3.71782403932635
2059 | "2058" 6549 149.972689296675
2060 | "2059" 6550 94.5752198594424
2061 | "2060" 6551 -8.26942690142106
2062 | "2061" 6559 -2.23482608892804
2063 | "2062" 6563 18.5403685609412
2064 | "2063" 6564 27.5901770206748
2065 | "2064" 6566 4.41380995005477
2066 | "2065" 6570 1.14629529440431
2067 | "2066" 6572 31.2362880096104
2068 | "2067" 6573 141.159170949358
2069 | "2068" 6574 -8.7941939928905
2070 | "2069" 6575 -6.23351352969349
2071 | "2070" 6577 0.185159860104919
2072 | "2071" 6578 26.8038762326525
2073 | "2072" 6580 18.0708269683919
2074 | "2073" 6581 29.4732669867683
2075 | "2074" 6582 -5.73269254580467
2076 | "2075" 6586 95.6814190967672
2077 | "2076" 6589 -4.72142095869469
2078 | "2077" 6591 41.8212522372442
2079 | "2078" 6592 141.159170949358
2080 | "2079" 6593 85.0706381122293
2081 | "2080" 6597 121.295818893892
2082 | "2081" 6600 161.598853182898
2083 | "2082" 6601 135.940939090738
2084 | "2083" 6602 160.526859826979
2085 | "2084" 6605 45.7305081142812
2086 | "2085" 6606 124.179487866936
2087 | "2086" 6610 109.411676433618
2088 | "2087" 6611 89.4794214741403
2089 | "2088" 6612 116.503065534489
2090 | "2089" 6615 133.473953927097
2091 | "2090" 6619 114.800025362236
2092 | "2091" 6621 27.5901770206748
2093 | "2092" 6622 29.965258377898
2094 | "2093" 6624 28.7309721367288
2095 | "2094" 6629 29.0987914145299
2096 | "2095" 6632 153.244635979999
2097 | "2096" 6634 141.210857188579
2098 | "2097" 6635 38.0551273275982
2099 | "2098" 6640 124.179487866936
2100 | "2099" 6641 114.800025362236
2101 | "2100" 6643 99.4686168148618
2102 | "2101" 6644 17.1067855588586
2103 | "2102" 6648 148.466145692097
2104 | "2103" 6651 37.3564317170851
2105 | "2104" 6652 38.0551273275982
2106 | "2105" 6653 21.3079984290616
2107 | "2106" 6654 109.411676433618
2108 | "2107" 6655 162.288065261563
2109 | "2108" 6657 102.44183224541
2110 | "2109" 6658 136.636948898746
2111 | "2110" 6660 146.895884207338
2112 | "2111" 6661 152.356930839225
2113 | "2112" 6668 121.295818893892
2114 | "2113" 6672 37.7086008455174
2115 | "2114" 6677 36.623968668927
2116 | "2115" 6679 20.3212658712265
2117 | "2116" 6681 82.3994092493654
2118 | "2117" 6683 155.016035457631
2119 | "2118" 6686 114.800025362236
2120 | "2119" 6687 144.138200614712
2121 | "2120" 6688 90.9587756702342
2122 | "2121" 6690 166.185607572572
2123 | "2122" 6695 129.203638123744
2124 | "2123" 6697 42.3773957861534
2125 | "2124" 6702 22.489557038663
2126 | "2125" 6703 87.5886341734181
2127 | "2126" 6704 26.0121835259561
2128 | "2127" 6705 135.940939090738
2129 | "2128" 6713 139.27137027936
2130 | "2129" 6721 140.544964022013
2131 | "2130" 6722 26.0121835259561
2132 | 


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/data/adas_mmse_data.RData:
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https://raw.githubusercontent.com/larslau/progmod/d374fb34a87d469891ab675f2c7294676e62dec9/data/adas_mmse_data.RData


--------------------------------------------------------------------------------
/man/ADNI_disease_stage_bl.Rd:
--------------------------------------------------------------------------------
 1 | % Generated by roxygen2: do not edit by hand
 2 | % Please edit documentation in R/data.R
 3 | \docType{data}
 4 | \name{ADNI_disease_stage_bl}
 5 | \alias{ADNI_disease_stage_bl}
 6 | \title{Predicted disease stage at baseline for ADNI participants
 7 | ?AD
 8 | A dataset containing the predicted disease stage (disease month) for
 9 | individuals in ADNI based on their longitudinal 13-item ADAS-cog trajectories
10 | Data are based on a data cut of ADAS-cog scores from July 2019.}
11 | \format{
12 | A data frame with 2130 rows and 3 variables:
13 | \describe{
14 |   \item{RID}{ADNI roster ID}
15 |   \item{pred_AD_month}{Predicted disease time (in months relative to the average cognitive state of the cognitively normal group)}
16 | }
17 | }
18 | \usage{
19 | ADNI_disease_stage_bl
20 | }
21 | \description{
22 | Predicted disease stage at baseline for ADNI participants
23 | ?AD
24 | A dataset containing the predicted disease stage (disease month) for
25 | individuals in ADNI based on their longitudinal 13-item ADAS-cog trajectories
26 | Data are based on a data cut of ADAS-cog scores from July 2019.
27 | }
28 | \keyword{datasets}
29 | 


--------------------------------------------------------------------------------
/man/GLF.Rd:
--------------------------------------------------------------------------------
 1 | % Generated by roxygen2: do not edit by hand
 2 | % Please edit documentation in R/progmod.R
 3 | \name{GLF}
 4 | \alias{GLF}
 5 | \title{Overparametrized generalized logistic function.}
 6 | \usage{
 7 | GLF(t, A, K, B, v, s, c)
 8 | }
 9 | \arguments{
10 | \item{t}{Time variable}
11 | 
12 | \item{A}{Lower asymptote parameter}
13 | 
14 | \item{K}{Upper asymptote parameter}
15 | 
16 | \item{B}{Time-scaling parameter}
17 | 
18 | \item{v}{Asymmetry parameter}
19 | 
20 | \item{s}{Time-shift parameter}
21 | 
22 | \item{c}{Intercept parameter, should only be used for random effects}
23 | }
24 | \value{
25 | The function values at the supplied time values along with a
26 |         "gradient" attribute.
27 | }
28 | \description{
29 | Overparametrized generalized logistic function.
30 | }
31 | \examples{
32 | GLF(t = c(0, 1), A = 30, K = 0, B = 1, s = 0, v = 1, c = 0)
33 | }
34 | 


--------------------------------------------------------------------------------
/man/adas_mmse_data.Rd:
--------------------------------------------------------------------------------
 1 | % Generated by roxygen2: do not edit by hand
 2 | % Please edit documentation in R/data.R
 3 | \docType{data}
 4 | \name{adas_mmse_data}
 5 | \alias{adas_mmse_data}
 6 | \title{Simulated longitudinal ADAS-cog and MMSE scores}
 7 | \format{
 8 | A data frame with 9378 rows and 7 variables:
 9 | \describe{
10 |   \item{subject_id}{Subject ID}
11 |   \item{Month_bl}{Months since baseline}
12 |   \item{ADAS13}{Simulated 13-item ADAS-cog score}
13 |   \item{MMSE}{Simulated MMSE score}
14 |   \item{CN}{Was subject cognitively normal at baseline (0/1)?}
15 |   \item{MCI}{Was subject mild cognitively impaired at baseline (0/1)?}
16 |   \item{DEM}{Did subject have dementia at baseline (0/1)?}
17 |   \item{blstatus}{Patient status at baseline (Cognitively normal/MCI/Dementia)}
18 | }
19 | }
20 | \usage{
21 | adas_mmse_data
22 | }
23 | \description{
24 | A dataset containing longitudinal simulated ADAS-cog and MMSE scores
25 | for a large number of individuals that are cognitively normal, have mild
26 | congnitive impairment (MCI) or dementia.
27 | Data is simulated based on ADNI data.
28 | }
29 | \keyword{datasets}
30 | 


--------------------------------------------------------------------------------
/man/exp_model.Rd:
--------------------------------------------------------------------------------
 1 | % Generated by roxygen2: do not edit by hand
 2 | % Please edit documentation in R/progmod.R
 3 | \name{exp_model}
 4 | \alias{exp_model}
 5 | \title{Overparametrized exponential function.}
 6 | \usage{
 7 | exp_model(t, l, s, g, v)
 8 | }
 9 | \arguments{
10 | \item{t}{Time variable}
11 | 
12 | \item{l}{Scale parameter for the exponential function}
13 | 
14 | \item{s}{Time-shift parameter}
15 | 
16 | \item{g}{Time-scaling parameter}
17 | 
18 | \item{v}{Intercept parameter}
19 | }
20 | \value{
21 | The function values at the supplied time values along with a
22 |         "gradient" attribute.
23 | }
24 | \description{
25 | Overparametrized exponential function.
26 | }
27 | \examples{
28 | exp_model(t = c(0, 1), l = 1, s = 0, g = 0, v = 0)
29 | }
30 | 


--------------------------------------------------------------------------------
/man/progmod.Rd:
--------------------------------------------------------------------------------
  1 | % Generated by roxygen2: do not edit by hand
  2 | % Please edit documentation in R/progmod.R
  3 | \name{progmod}
  4 | \alias{progmod}
  5 | \title{Fit nonlinear mixed-effects disease progression models}
  6 | \usage{
  7 | progmod(
  8 |   model,
  9 |   data,
 10 |   fixed,
 11 |   random,
 12 |   groups,
 13 |   start,
 14 |   covariance = NULL,
 15 |   weights = NULL,
 16 |   method = c("ML", "REML"),
 17 |   control = NULL,
 18 |   verbose = FALSE
 19 | )
 20 | }
 21 | \arguments{
 22 | \item{model}{A nonlinear model formula, with the response on the left of a ~
 23 | operator and an expression involving parameters and covariates on the right,
 24 | or an nlsList object. If data is given, all names used in the formula should
 25 | be defined as parameters or variables in the data frame. The method function
 26 | nlme.nlsList is documented separately. See \code{\link[nlme]{nlme}} for details.}
 27 | 
 28 | \item{data}{An optional data frame containing the variables named in model,
 29 | fixed, random, correlation, weights, subset, and naPattern.
 30 | By default the variables are taken from the environment.}
 31 | 
 32 | \item{fixed}{A two-sided linear formula of the form \code{f1+...+fn~x1+...+xm},
 33 | or a list of two-sided formulas of the form \code{f1~x1+...+xm}, with possibly
 34 | different models for different parameters. The \code{f1,...,fn} are the names of
 35 | parameters included on the right hand side of model and the \code{x1+...+xm}
 36 | expressions define linear models for these parameters (when the left hand
 37 | side of the formula contains several parameters, they all are assumed to
 38 | follow the same linear model, described by the right hand side expression).
 39 | A \code{1} on the right hand side of the formula(s) indicates a single fixed effects
 40 | for the corresponding parameter(s).}
 41 | 
 42 | \item{random}{A two-sided formula of the form
 43 | \code{r1+...+rn~x1+...+xm | g1/.../gQ}, with \code{r1,...,rn} naming parameters included on the
 44 | right hand side of model, \code{x1+...+xm} specifying the random-effects model for these
 45 | parameters and \code{g1/.../gQ} the grouping structure (\code{Q} may be equal to \code{1}, in which
 46 | case no / is required). The random effects formula will be repeated for all
 47 | levels of grouping, in the case of multiple levels of grouping. Explicit specification of the
 48 | covariance structure between random effects (e.g. using \code{pdMat}) or different formulas for
 49 | different random effects can be specified. See \code{\link[nlme]{nlme}} for details.
 50 | \strong{Note:} Only simple two-sided formulas are currently supported when a covariance
 51 | structure is given (see below).}
 52 | 
 53 | \item{groups}{an optional one-sided formula of the form \code{~ g1} specifying the partitions
 54 | of the data over which the random effects vary. This is needed when different formulas are specified for
 55 | different random effects.}
 56 | 
 57 | \item{start}{A numeric vector or list of initial estimates for the fixed effects and random effects.
 58 | If declared as a numeric vector, it is converted internally to a list with a single component fixed, given by the vector.
 59 | The \code{fixed} component is required, unless the model function inherits from
 60 | class \code{selfStart}, in which case initial values will be derived
 61 | from a call to \code{nlsList}. An optional \code{random} component is used to specify
 62 | initial values for the random effects and should consist of a matrix,
 63 | or a list of matrices with length equal to the number of grouping levels.
 64 | Each matrix should have as many rows as the number of groups at the
 65 | corresponding level and as many columns as the number of random effects in that level.}
 66 | 
 67 | \item{covariance}{An optional \code{\link[nlme]{corStruct}} object describing the within-group
 68 | covariance structure. In addition to those available in \code{nlme},
 69 | \code{\link{covBM}} can be used to incorporate a Brownian motion component, \code{\link{covFracBM}}
 70 | can be used to incorporate a fractional Brownian motion component and \code{\link{covIOU}}
 71 | can be used to incorporate an integrated Ornstein-Uhlenbeck process in relation to
 72 | a continuous variable.}
 73 | 
 74 | \item{weights}{an optional varFunc object or one-sided formula describing the within-group heteroscedasticity structure.
 75 | This argument is primarily used for multivariate modeling of several outcomes where different standard errors are to be expected.
 76 | If given as a formula, it is used as the argument to varFixed, corresponding to fixed variance weights.
 77 | See the documentation on varClasses for a description of the available varFunc classes.
 78 | Defaults to NULL, corresponding to homoscedastic within-group errors. \strong{Note:} weighting is not currently supported
 79 | when a covariance structure is given.}
 80 | 
 81 | \item{method}{a character string. If "\code{REML}" the model is fit by maximizing the restricted log-likelihood.
 82 | If "\code{ML}" the log-likelihood is maximized. Defaults to "\code{ML}".}
 83 | 
 84 | \item{control}{A list of control parameters for the estimation algorithm. See \code{\link[nlmeControl]{nlmeControl}}.}
 85 | 
 86 | \item{verbose}{If \code{TRUE} information on the evolution of the iterative
 87 | algorithm is printed. Default is \code{FALSE}.}
 88 | }
 89 | \value{
 90 | An object of class "nlme" representing the nonlinear mixed effects model fit.
 91 | }
 92 | \description{
 93 | This function fits disease-progression models to longitudinal data.
 94 | The function fits nonlinear mixed-effects models by calling
 95 | \code{\link[nlme]{nlme}} or \code{\link[nlmeBM]{nlmeBM}} depending on the
 96 | model specification.
 97 | }
 98 | \examples{
 99 | 
100 | #
101 | # Fit exponential disease progression model to simulated ADAS-cog scores
102 | #
103 | 
104 | # Plot data
105 | if (require(ggplot2)) {
106 | ggplot(adas_mmse_data, aes(x = Month_bl, y = ADAS13)) +
107 |  geom_line(aes(group = subject_id, color = blstatus)) +
108 |  ylim(c(85, 0)) +
109 |  xlab('Months since baseline')
110 | }
111 | 
112 | # Fit exponential model with random shift and intercept
113 | fixed_start_coef <- c(0.5, 70, 150, 3.5, 10)
114 | ADAS_progmod <- progmod(ADAS13 ~ exp_model(Month_bl, l, s, g, v),
115 |                        data = subset(adas_mmse_data, !is.na(ADAS13)),
116 |                        fixed = list(l ~ 1,
117 |                                     s ~ MCI + DEM - 1,
118 |                                     g ~ 1,
119 |                                     v ~ 1),
120 |                        random = s + v ~ 1 | subject_id,
121 |                        start = fixed_start_coef,
122 |                        covariance = NULL)
123 | 
124 | # Predict from model and visualize results
125 | adas_mmse_data$fixed_shift_adas <- with(adas_mmse_data,
126 |                                        MCI * fixed.effects(ADAS_progmod)[2] +
127 |                                          DEM * fixed.effects(ADAS_progmod)[3])
128 | pred_rand <- random.effects(ADAS_progmod)
129 | adas_mmse_data$random_shift_adas <- pred_rand[match(adas_mmse_data$subject_id, rownames(pred_rand)), 's.(Intercept)']
130 | 
131 | if (require(ggplot2)) {
132 |  ggplot(adas_mmse_data, aes(x = Month_bl + fixed_shift_adas, y = ADAS13)) +
133 |    geom_line(aes(group = subject_id, color = blstatus)) +
134 |    ylim(c(85, 0)) +
135 |    xlab('Months since baseline')
136 | }
137 | 
138 | 
139 | if (require(ggplot2)) {
140 |  ggplot(adas_mmse_data, aes(x = Month_bl + fixed_shift_adas + random_shift_adas, y = ADAS13)) +
141 |    geom_line(aes(group = subject_id, color = blstatus)) +
142 |    ylim(c(85, 0)) +
143 |    xlab('Months since baseline')
144 | }
145 | 
146 | #
147 | # Fit generalized logistic disease progression model to simulated MMSE scores
148 | #
149 | 
150 | # Plot data
151 | 
152 | if (require(ggplot2)) {
153 |  ggplot(adas_mmse_data, aes(x = Month_bl, y = MMSE)) +
154 |    geom_line(aes(group = subject_id, color = blstatus)) +
155 |    ylim(c(0, 30)) +
156 |    xlab('Months since baseline')
157 | }
158 | 
159 | # Fit generalized logistic model with range [30, 0] and a random time shift
160 | fixed_start_coef <- c(B = 0.025,
161 |                      v = 1.4,
162 |                      `s.(Intercept)` = -100,
163 |                      s.MCI = 26,
164 |                      s.DEM = 75)
165 | 
166 | MMSE_progmod_glf <- progmod(MMSE ~ GLF(Month_bl, A = 30, K = 0, B, v, s, c = 0),
167 |                            data = subset(adas_mmse_data, !is.na(MMSE)),
168 |                            fixed = list(B ~ 1,
169 |                                         v ~ 1,
170 |                                         s ~ MCI + DEM + 1),
171 |                            random = s ~ 1 | subject_id,
172 |                            start = fixed_start_coef,
173 |                            covariance = NULL)
174 | 
175 | # Predict from model and visualize results
176 | adas_mmse_data$fixed_shift_mmse <- with(adas_mmse_data,
177 |                                        fixed.effects(MMSE_progmod_glf)[3] +
178 |                                        MCI * fixed.effects(MMSE_progmod_glf)[4] +
179 |                                        DEM * fixed.effects(MMSE_progmod_glf)[5])
180 | pred_rand <- random.effects(MMSE_progmod_glf)
181 | adas_mmse_data$random_shift_mmse <- pred_rand[match(adas_mmse_data$subject_id, rownames(pred_rand)), 's.(Intercept)']
182 | 
183 | 
184 | 
185 | if (require(ggplot2)) {
186 |  ggplot(adas_mmse_data, aes(x = Month_bl + fixed_shift_mmse + random_shift_mmse, y = MMSE)) +
187 |    geom_line(aes(group = subject_id, color = blstatus)) +
188 |    xlab('Months since baseline')
189 | }
190 | 
191 | #
192 | 
193 | # Stack data to long format
194 | tmp1 <- adas_mmse_data[, c('subject_id', 'Month_bl', 'CN', 'MCI', 'DEM', 'ADAS13')]
195 | names(tmp1)[6] <- 'value'
196 | tmp1$scale <- 'ADAS13'
197 | 
198 | tmp2 <- adas_mmse_data[, c('subject_id', 'Month_bl', 'CN', 'MCI', 'DEM', 'MMSE')]
199 | names(tmp2)[6] <- 'value'
200 | tmp2$scale <- 'MMSE'
201 | 
202 | # Long data
203 | adas_mmse_data_long <- na.omit(rbind(tmp1, tmp2))
204 | adas_mmse_data_long$scale <- factor(adas_mmse_data_long$scale)
205 | 
206 | # Remove temporary files
207 | rm(tmp1, tmp2)
208 | 
209 | # Fit multivariate exponential model
210 | fixed_start_coef <- c(l.scaleADAS13 = 0.5,
211 |                      l.scaleMMSE = -0.1,
212 |                      s.MCI = 70,
213 |                      s.DEM = 150,
214 |                      g.scaleADAS13 = 3.5,
215 |                      g.scaleMMSE = 3,
216 |                      v.scaleADAS13 = 10,
217 |                      v.scaleMMSE = 30)
218 | 
219 | multi_progmod_glf <- progmod(value ~ exp_model(Month_bl, l, s, g, v),
220 |                             data = adas_mmse_data_long,
221 |                             fixed = list(l ~ scale + 0,
222 |                                          s ~ MCI + DEM + 0,
223 |                                          g ~ scale + 0,
224 |                                          v ~ scale + 0),
225 |                             random = list(s ~ 1,
226 |                                           v ~ scale),
227 |                             groups = ~ subject_id,
228 |                             start = fixed_start_coef,
229 |                             weights = varIdent(form = ~ 1 | scale))
230 | 
231 | # Predict from model and compare to univariate models
232 | adas_mmse_data$fixed_shift_multi <- with(adas_mmse_data,
233 |                                         MCI * fixed.effects(multi_progmod_glf)[3] +
234 |                                           DEM * fixed.effects(multi_progmod_glf)[4])
235 | pred_rand <- random.effects(multi_progmod_glf)
236 | adas_mmse_data$random_shift_multi <- pred_rand[match(adas_mmse_data$subject_id, rownames(pred_rand)), 's.(Intercept)']
237 | 
238 | 
239 | # Correlations between predicted disease months
240 | with(adas_mmse_data, cor(cbind(fixed_shift_adas + random_shift_adas,
241 |                               fixed_shift_mmse + random_shift_mmse,
242 |                               fixed_shift_multi + random_shift_multi), method = 'spearman'))
243 | 
244 | 
245 | 
246 | 
247 | }
248 | 


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https://raw.githubusercontent.com/larslau/progmod/d374fb34a87d469891ab675f2c7294676e62dec9/man/readme/adas_progression.gif


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