| Title: | Penalized Regression Calibration (PRC) for the DynamicPrediction of Survival |
| Version: | 2.3.0 |
| Description: | Computes penalized regression calibration (PRC), a statistical method for the dynamic prediction of survival when many longitudinal predictors are available. See Signorelli (2024) <doi:10.32614/RJ-2024-014> and Signorelli et al. (2021) <doi:10.1002/sim.9178> for details. |
| License: | GPL (≥ 3) |
| URL: | https://mirkosignorelli.github.io/r |
| Depends: | R (≥ 4.2.0) |
| VignetteBuilder: | knitr |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Imports: | doParallel, dplyr, foreach, glmnet, lcmm, magic, MASS, Matrix,methods, nlme, purrr, riskRegression, stats, survcomp,survival, survivalROC |
| Suggests: | knitr, ptmixed, rmarkdown, survminer |
| NeedsCompilation: | no |
| Packaged: | 2025-06-05 09:44:37 UTC; ms |
| Author: | Mirko Signorelli [aut, cre, cph], Pietro Spitali [ctb], Roula Tsonaka [ctb], Barbara Vreede [ctb] |
| Maintainer: | Mirko Signorelli <msignorelli.rpackages@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-06-05 10:10:02 UTC |
Draw a cluster bootstrap sample from a data frame in long format
Description
This function is part of the cluster bootstrap optimism correctionprocedure described in Signorelli et al. (2021). Note that the function does not perform the random sampling, but itextracts the correct records from a dataframe, given the ids ofthe sampled clusters (subjects)
Usage
draw_cluster_bootstrap(df, idvar, boot.ids)Arguments
df | a data frame in long format |
idvar | name of the subject id in |
boot.ids | identifiers of the subjects to be sampled |
Value
A data frame containing the bootstrapped observations
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.DOI: 10.1002/sim.9178
Step 1 of PRC-LMM (estimation of the linear mixed models)
Description
This function performs the first step for the estimationof the PRC-LMM model (see references for details)
Usage
fit_lmms(y.names, fixefs, ranefs, long.data, surv.data, t.from.base, n.boots = 0, n.cores = 1, max.ymissing = 0.2, verbose = TRUE, seed = 123, control = list(opt = "optim", niterEM = 500, maxIter = 500))Arguments
y.names | character vector with the names of theresponse variables which the LMMs have to be fitted to |
fixefs | fixed effects formula for the model, example: |
ranefs | random effects formula for the model,specified using the representation of random effectstructures of the |
long.data | a data frame with the longitudinal predictors,comprehensive of a variable called |
surv.data | a data frame with the survival data and (if relevant) additional baseline covariates. |
t.from.base | name of the variable containing time from baseline in |
n.boots | number of bootstrap samples to be used in thecluster bootstrap optimism correction procedure (CBOCP). If 0, nobootstrapping is performed |
n.cores | number of cores to use to parallelize part ofthe computations. If |
max.ymissing | maximum proportion of subjects allowed to not have anymeasurement of a longitudinal response variable. Default is 0.2 |
verbose | if |
seed | random seed used for the bootstrap sampling. Default is |
control | a list of control values to be passed to |
Value
A list containing the following objects:
call.info: a list containing the following functioncall information:call,y.names,fixefs,ranefs;lmm.fits.orig: a list with the LMMs fitted on theoriginal dataset (it should comprise as many LMMs as the elementsofy.namesare);df.sanitized: a sanitized version of the suppliedlong.datadataframe, without thelongitudinal measurements that are taken after the eventor after censoring;n.boots: number of bootstrap samples;boot.ids: a list with the ids of bootstrapped subjects (whenn.boots > 0);lmms.fits.boot: a list of lists, which contains the LMMs fitted on each bootstrapped datasets (whenn.boots > 0).
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
simulate_prclmm_data,summarize_lmms (step 2),fit_prclmm (step 3),performance_prc
Examples
# generate example dataset.seed(1234)p = 4 # number of longitudinal predictorssimdata = simulate_prclmm_data(n = 100, p = p, p.relev = 2, seed = 123, t.values = c(0, 0.2, 0.5, 1, 1.5, 2)) # specify options for cluster bootstrap optimism correction# procedure and for parallel computing do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to parallelize and speed computations up!if (!more.cores) n.cores = 1if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 8}# step 1 of PRC-LMM: estimate the LMMsy.names = paste('marker', 1:p, sep = '')step1 = fit_lmms(y.names = y.names, fixefs = ~ age, ranefs = ~ age | id, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = n.boots, n.cores = n.cores)# estimated betas and variances for the 3rd marker:summary(step1, 'marker3', 'betas')summary(step1, 'marker3', 'variances')# usual T table:summary(step1, 'marker3', 'tTable')Step 1 of PRC-MLPMM (estimation of the linear mixed models)
Description
This function performs the first step for the estimationof the PRC-MLPMM model proposed in Signorelli et al. (2021)
Usage
fit_mlpmms(y.names, fixefs, ranef.time, randint.items = TRUE, long.data, surv.data, t.from.base, n.boots = 0, n.cores = 1, verbose = TRUE, seed = 123, maxiter = 100, conv = rep(0.001, 3), lcmm.warnings = FALSE)Arguments
y.names | a list with the names of theresponse variables which the MLPMMs have to be fitted to.Each element in the list contains all the items used to reconstruct a latent biological process of interest |
fixefs | a fixed effects formula for the model, where thetime variable (specified also in |
ranef.time | a character with the name of the time variable for which to include a shared random slope |
randint.items | logical: should item-specific random interceptsbe included in the MLCMMs? Default is |
long.data | a data frame with the longitudinal predictors,comprehensive of a variable called |
surv.data | a data frame with the survival data and (if relevant) additional baseline covariates. |
t.from.base | name of the variable containing time from baseline in |
n.boots | number of bootstrap samples to be used in thecluster bootstrap optimism correction procedure (CBOCP). If 0, nobootstrapping is performed |
n.cores | number of cores to use to parallelize part ofthe computations. If |
verbose | if |
seed | random seed used for the bootstrap sampling. Default is |
maxiter | maximum number of iterations to use when callingthe function |
conv | a vector containing the three convergence criteria( |
lcmm.warnings | logical. If TRUE, a warning is printed every time the (strict) convergence criteria of the |
Details
This function is essentially a wrapper of themultlcmm that is meant to simplifythe estimation of several MLPMMs. In general, ensuring convergence of the algorithm implemented inmultlcmmis sometimes difficult, and it is hard to write a function thatcan automatically solve all possible convergence problems.fit_mplmmsreturns a warning when estimation did not converge for one or more MLPMMs. If this happens, try to change the convergence criteria inconv or the relevantrandint.items value.If doing this doesn't solve the problem, it is recommended tore-estimate the specific MLPMMs for which estimation didn't convergedirectly withmultlcmm, trying to manually solvethe convergence issues
Value
A list containing the following objects:
call.info: a list containing the following functioncall information:call,y.names,fixefs,ranef.time,randint.items;mlpmm.fits.orig: a list with the MLPMMs fitted on theoriginal dataset (it should comprise as many MLPMMs as the elementsofy.namesare);df.sanitized: a sanitized version of the suppliedlong.datadataframe, without thelongitudinal measurements that are taken after the eventor after censoring;n.boots: number of bootstrap samples;boot.ids: a list with the ids of bootstrapped subjects (whenn.boots > 0);mlpmm.fits.boot: a list of lists, which contains the MLPMMs fitted on each bootstrapped datasets (whenn.boots > 0).
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. To appear in: The R Journal. Preprint: arXiv:2309.15600
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.DOI: 10.1002/sim.9178
See Also
simulate_prcmlpmm_data,summarize_mlpmms (step 2),fit_prcmlpmm (step 3),performance_prc
Examples
# generate example dataset.seed(123)n.items = c(4,2,2,3,4,2)simdata = simulate_prcmlpmm_data(n = 100, p = length(n.items), p.relev = 3, n.items = n.items, type = 'u+b', seed = 1) # specify options for cluster bootstrap optimism correction# procedure and for parallel computing do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to speed computations up!if (!more.cores) n.cores = 2if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 2}# step 1 of PRC-MLPMM: estimate the MLPMMsy.names = vector('list', length(n.items))for (i in 1:length(n.items)) { y.names[[i]] = paste('marker', i, '_', 1:n.items[i], sep = '')}step1 = fit_mlpmms(y.names, fixefs = ~ contrast(age), ranef.time = age, randint.items = TRUE, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = n.boots, n.cores = n.cores)# print MLPMM summary for marker 5 (all items involved in that MLPMM):summary(step1, 'marker5_2')Step 3 of PRC-LMM (estimation of the penalized Cox model(s))
Description
This function performs the third step for the estimationof the PRC-LMM model (see references for methodological details)
Usage
fit_prclmm(object, surv.data, baseline.covs = NULL, penalty = "ridge", standardize = TRUE, pfac.base.covs = 0, cv.seed = 19920207, n.alpha.elnet = 11, n.folds.elnet = 5, n.cores = 1, verbose = TRUE)Arguments
object | the output of step 2 of the PRC-LMM procedure, as produced by the |
surv.data | a data frame with the survival data and (if relevant) additional baseline covariates. |
baseline.covs | a formula specifying the variables (e.g., baseline age) in |
penalty | the type of penalty function used for regularization.Default is |
standardize | logical argument: should the predictors (both baseline covariatesand predicted random effects) be standardized when included as covariatesin the penalized Cox model? Default is |
pfac.base.covs | a single value, or a vector of values, indicatingwhether the baseline covariates (if any) should be penalized (1) or not (0).Default is |
cv.seed | value of the random seed to use for the cross-validationdone to select the optimal value of the tuning parameter |
n.alpha.elnet | number of alpha values for the two-dimensional grid of tuning parameteres in elasticnet.Only relevant if |
n.folds.elnet | number of folds to be used for the selectionof the tuning parameter in elasticnet. Only relevant if |
n.cores | number of cores to use to parallelize part ofthe computations. If |
verbose | if |
Value
A list containing the following objects:
call: the function callpcox.orig: the penalized Cox model fitted on theoriginal dataset;tuning: the values of the tuning parameter(s) selected through cross-validationsurv.data: the supplied survival data (ordered bysubject id)n.boots: number of bootstrap samples;boot.ids: a list with the ids of bootstrapped subjects (whenn.boots > 0);pcox.boot: a list where each element is a fitted penalizedCox model for a given bootstrap sample (whenn.boots > 0).
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
fit_lmms (step 1),summarize_lmms (step 2),performance_prc
Examples
# generate example dataset.seed(1234)p = 4 # number of longitudinal predictorssimdata = simulate_prclmm_data(n = 100, p = p, p.relev = 2, seed = 123, t.values = c(0, 0.2, 0.5, 1, 1.5, 2)) # specify options for cluster bootstrap optimism correction# procedure and for parallel computing do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to parallelize and speed computations up!if (!more.cores) n.cores = 1if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 8}# step 1 of PRC-LMM: estimate the LMMsy.names = paste('marker', 1:p, sep = '')step1 = fit_lmms(y.names = y.names, fixefs = ~ age, ranefs = ~ age | id, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = n.boots, n.cores = n.cores) # step 2 of PRC-LMM: compute the summaries # of the longitudinal outcomesstep2 = summarize_lmms(object = step1, n.cores = n.cores)# step 3 of PRC-LMM: fit the penalized Cox modelsstep3 = fit_prclmm(object = step2, surv.data = simdata$surv.data, baseline.covs = ~ baseline.age, penalty = 'ridge', n.cores = n.cores)summary(step3)Step 3 of PRC-MLPMM (estimation of the penalized Cox model(s))
Description
This function performs the third step for the estimationof the PRC-MLPMM model proposed in Signorelli et al. (2021)
Usage
fit_prcmlpmm(object, surv.data, baseline.covs = NULL, include.b0s = TRUE, penalty = "ridge", standardize = TRUE, pfac.base.covs = 0, cv.seed = 19920207, n.alpha.elnet = 11, n.folds.elnet = 5, n.cores = 1, verbose = TRUE)Arguments
object | the output of step 2 of the PRC-MLPMM procedure, as produced by the |
surv.data | a data frame with the survival data and (if relevant) additional baseline covariates. |
baseline.covs | a formula specifying the variables (e.g., baseline age) in |
include.b0s | logical. If |
penalty | the type of penalty function used for regularization.Default is |
standardize | logical argument: should the predicted random effectsbe standardized when included in the penalized Cox model? Default is |
pfac.base.covs | a single value, or a vector of values, indicatingwhether the baseline covariates (if any) should be penalized (1) or not (0).Default is |
cv.seed | value of the random seed to use for the cross-validationdone to select the optimal value of the tuning parameter |
n.alpha.elnet | number of alpha values for the two-dimensional grid of tuning parameteres in elasticnet.Only relevant if |
n.folds.elnet | number of folds to be used for the selectionof the tuning parameter in elasticnet. Only relevant if |
n.cores | number of cores to use to parallelize part ofthe computations. If |
verbose | if |
Value
A list containing the following objects:
call: the function callpcox.orig: the penalized Cox model fitted on theoriginal dataset;tuning: the values of the tuning parameter(s) selected through cross-validationsurv.data: the supplied survival data (ordered bysubject id)n.boots: number of bootstrap samples;boot.ids: a list with the ids of bootstrapped subjects (whenn.boots > 0);pcox.boot: a list where each element is a fitted penalizedCox model for a given bootstrap sample (whenn.boots > 0).
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
fit_mlpmms (step 1),summarize_mlpmms (step 2),performance_prc
Examples
# generate example dataset.seed(123)n.items = c(4,2,2,3,4,2)simdata = simulate_prcmlpmm_data(n = 100, p = length(n.items), p.relev = 3, n.items = n.items, type = 'u+b', seed = 1) # specify options for cluster bootstrap optimism correction# procedure and for parallel computing do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to speed computations up!if (!more.cores) n.cores = 2if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 2}# step 1 of PRC-MLPMM: estimate the MLPMMsy.names = vector('list', length(n.items))for (i in 1:length(n.items)) { y.names[[i]] = paste('marker', i, '_', 1:n.items[i], sep = '')}step1 = fit_mlpmms(y.names, fixefs = ~ contrast(age), ranef.time = age, randint.items = TRUE, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = n.boots, n.cores = n.cores)# step 2 of PRC-MLPMM: compute the summaries step2 = summarize_mlpmms(object = step1, n.cores = n.cores)# step 3 of PRC-LMM: fit the penalized Cox modelsstep3 = fit_prcmlpmm(object = step2, surv.data = simdata$surv.data, baseline.covs = ~ baseline.age, include.b0s = TRUE, penalty = 'ridge', n.cores = n.cores)summary(step3)A fitted PRC LMM
Description
This list contains a fitted PRC LMM, where the CBOCP iscomputed using 50 cluster bootstrap samples. It isused to reduce the computing time in the example ofthe functionperformance_prc. The simulated dataset on which the model was fitted was landmarked at t = 2.
Usage
data(fitted_prclmm)Format
A list comprising step 2 and step 3 as obtainedduring the estimation of a PRC LMM
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
See Also
Examples
data(fitted_prclmm)ls(fitted_prclmm)A fitted PRC MLPMM
Description
This list contains a fitted PRC MLPMM. It isused to reduce the computing time in the example ofthe functionsurvpred_prcmlpmm. The simulated dataset on which the model was fitted was landmarked at t = 2.
Usage
data(fitted_prclmm)Format
A list comprising step 2 and step 3 as obtainedduring the estimation of a PRC MLPMM
Author(s)
Mirko Signorelli
References
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Examples
data(fitted_prcmlpmm)ls(fitted_prcmlpmm)pbc2 dataset
Description
This list contains data from the Mayo Clinic primary biliary cirrhosis (PBC)study (1974-1984). It comprises two datasets, one with the survival and baseline covariatesand the other with the longitudinal measurements. The datasets are a rearrangement of the 'pbc2' dataframe from the 'joineRML' package that makesthem more suitable for analysis within 'pencal'
Usage
data(pbc2data)Format
The list contains two data frames:
baselineInfocontains the subject indicator 'id', information aboutthe survival outcome ('time' and 'event') and the covariates 'baselineAge', 'sex'and 'treatment';longitudinalInfocontains the subject 'id' and the repeated measurement data: 'age' is the age of the individual at each visit, 'fuptime' the follow-up time(time on study), and 'serBilir', 'serChol', 'albumin', 'alkaline', 'SGOT','platelets' and 'prothrombin' contain the value of each covariate at the corresponding visit
Author(s)
Mirko Signorelli
Examples
data(pbc2data)head(pbc2data$baselineInfo)head(pbc2data$longitudinalInfo)Estimation of a penalized Cox model with time-independent covariates
Description
This function estimates a penalized Cox model where onlytime-independent covariates are included as predictors, and thencomputes a bootstrap optimism correction procedure that is used to validate the predictive performance of the model
Usage
pencox(data, formula, penalty = "ridge", standardize = TRUE, penalty.factor = 1, n.alpha.elnet = 11, n.folds.elnet = 5, n.boots = 0, n.cores = 1, verbose = TRUE)Arguments
data | a data frame with one row for each subject.Itshould at least contain a subject id (called |
formula | a formula specifying the variables in |
penalty | the type of penalty function used for regularization.Default is |
standardize | logical argument: should the covariatesbe standardized when included in the penalized Cox model? Default is |
penalty.factor | a single value, or a vector of values, indicatingwhether the covariates (if any) should be penalized (1) or not (0).Default is |
n.alpha.elnet | number of alpha values for the two-dimensional grid of tuning parameteres in elasticnet.Only relevant if |
n.folds.elnet | number of folds to be used for the selectionof the tuning parameter in elasticnet. Only relevant if |
n.boots | number of bootstrap samples to be used in the bootstrap optimism correction procedure. If 0, nobootstrapping is performed |
n.cores | number of cores to use to parallelize the computationof the CBOCP. If |
verbose | if |
Value
A list containing the following objects:
call: the function callpcox.orig: the penalized Cox model fitted on theoriginal dataset;surv.data: a data frame with the survival dataX.orig: a data frame with the design matrix usedto estimate the Cox modeln.boots: number of bootstrap samples;boot.ids: a list with the ids of bootstrapped subjects (whenn.boots > 0);pcox.boot: a list where each element is a fitted penalizedCox model for a given bootstrap sample (whenn.boots > 0).
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Examples
# generate example dataset.seed(1234)p = 4 # number of longitudinal predictorssimdata = simulate_prclmm_data(n = 100, p = p, p.relev = 2, seed = 123, t.values = c(0, 0.2, 0.5, 1, 1.5, 2))#create dataframe with baseline measurements onlybaseline.visits = simdata$long.data[which(!duplicated(simdata$long.data$id)),]df = merge(simdata$surv.data, baseline.visits, by = 'id')df = df[ , -c(5:6)]do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to speed computations up!if (!more.cores) n.cores = 2if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 2}form = as.formula(~ baseline.age + marker1 + marker2 + marker3 + marker4)base.pcox = pencox(data = df, formula = form, n.boots = n.boots, n.cores = n.cores) ls(base.pcox)Predictive performance of the penalized Cox modelwith time-independent covariates
Description
This function computes the naive and optimism-correctedmeasures of performance (C index, time-dependent AUC and time-dependent Brier score) for a penalized Cox model with time-independent covariates. The optimism correction is computed based on a cluster bootstrapoptimism correction procedure (CBOCP, Signorelli et al., 2021)
Usage
performance_pencox(fitted_pencox, metric = c("tdauc", "c", "brier"), times = c(2, 3), n.cores = 1, verbose = TRUE)Arguments
fitted_pencox | the output of |
metric | the desired performance measure(s). Options include: 'tdauc','c' and 'brier' |
times | numeric vector with the time points at whichto estimate the time-dependent AUC and time-dependent Brier score |
n.cores | number of cores to use to parallelize part ofthe computations. If |
verbose | if |
Value
A list containing the following objects:
call: the function call;concordance: a data frame with the naive andoptimism-corrected estimates of the concordance (C) index;tdAUC: a data frame with the naive andoptimism-corrected estimates of the time-dependent AUCat the desired time points.
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Examples
# generate example dataset.seed(1234)p = 4 # number of longitudinal predictorssimdata = simulate_prclmm_data(n = 100, p = p, p.relev = 2, seed = 123, t.values = c(0, 0.5, 1, 1.5, 2))# create dataframe with baseline measurements onlybaseline.visits = simdata$long.data[which(!duplicated(simdata$long.data$id)),]df = merge(simdata$surv.data, baseline.visits, by = 'id')df = df[ , -c(5:6)]do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to speed computations up!if (!more.cores) n.cores = 2if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 2}form = as.formula(~ baseline.age + marker1 + marker2 + marker3 + marker4)base.pcox = pencox(data = df, formula = form, n.boots = n.boots, n.cores = n.cores) ls(base.pcox) # compute the performance measuresperf = performance_pencox(fitted_pencox = base.pcox, metric = 'tdauc', times = 3:5, n.cores = n.cores) # use metric = 'brier' for the Brier score and metric = 'c' for the # concordance index# time-dependent AUC estimates:ls(perf)perf$tdAUCPredictive performance of the PRC-LMM and PRC-MLPMM models
Description
This function computes the naive and optimism-correctedmeasures of performance (C index, time-dependent AUC and time-dependent Brier score) for the PRC models proposed in Signorelli et al. (2021). The optimismcorrection is computed based on a cluster bootstrapoptimism correction procedure (CBOCP)
Usage
performance_prc(step2, step3, metric = c("tdauc", "c", "brier"), times = c(2, 3), n.cores = 1, verbose = TRUE)Arguments
step2 | the output of either |
step3 | the output of |
metric | the desired performance measure(s). Options include: 'tdauc','c' and 'brier' |
times | numeric vector with the time points at whichto estimate the time-dependent AUC and time-dependent Brier score |
n.cores | number of cores to use to parallelize part ofthe computations. If |
verbose | if |
Value
A list containing the following objects:
call: the function call;concordance: a data frame with the naive andoptimism-corrected estimates of the concordance (C) index;tdAUC: a data frame with the naive andoptimism-corrected estimates of the time-dependent AUCat the desired time points;Brier: a data frame with the naive andoptimism-corrected estimates of the time-dependent Brier scoreat the desired time points;
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
for the PRC-LMM model:fit_lmms (step 1),summarize_lmms (step 2) andfit_prclmm (step 3);for the PRC-MLPMM model:fit_mlpmms (step 1),summarize_mlpmms (step 2) andfit_prcmlpmm (step 3).
Examples
data(fitted_prclmm)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to speed computations up!if (!more.cores) n.cores = 2if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 2} # compute the time-dependent AUCperf = performance_prc(fitted_prclmm$step2, fitted_prclmm$step3, metric = 'tdauc', times = c(3, 3.5, 4), n.cores = n.cores) # use metric = 'brier' for the Brier score and metric = 'c' for the # concordance index# time-dependent AUC estimates:ls(perf)perf$tdAUCPrepare longitudinal data for PRC
Description
This function removes from a longitudinal dataframeall measurements taken after the occurence of the event or after censoring. It is used internally byfit_lmmsand it assumes thatdf is sorted bysubj.id,with survival times given in the same order by subject id(fit_lmms automatically performs this sorting whenneeded)
Usage
prepare_longdata(df, t.from.base, subj.id, survtime, verbose = TRUE)Arguments
df | dataframe with the longitudinal measurements |
t.from.base | name (as character) of the variable containingtime from baseline in |
subj.id | name of the subject id variable in |
survtime | vector containing the survival time or censoring time |
verbose | if |
Value
A list containing: a reduced dataframe calleddf.sanitized, where only measurements taken beforet are retained; the number ofmeasurements retained (n.kept) and removed (n.removed)from the input data frame
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Print method for PRC-LMM model fits
Description
Print method for PRC-LMM model fits
Usage
## S3 method for class 'prclmm'print(x, digits = 4, ...)Arguments
x | an object of class |
digits | number of digits at which the printed estimated regressioncoefficients should be rounded (default is 4) |
... | additional arguments |
Value
Summary information about the fitted PRC-LMM model
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Print method for PRC-MLPMM model fits
Description
Print method for PRC-MLPMM model fits
Usage
## S3 method for class 'prcmlpmm'print(x, digits = 4, ...)Arguments
x | an object of class |
digits | number of digits at which the printed estimated regressioncoefficients should be rounded (default is 4) |
... | additional arguments |
Value
Summary information about the fitted PRC-MLPMM model
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Simulate data that can be used to fit the PRC-LMM model
Description
This function allows to simulate a survival outcomefrom longitudinal predictors following the PRC LMM model(see references for details). Specifically, the longitudinalpredictors are simulated from linear mixed models (LMMs), and the survival outcome from a Weibull model where the timeto event depends linearly on the baseline age and on the random effects from the LMMs.
Usage
simulate_prclmm_data(n = 100, p = 10, p.relev = 4, t.values = c(0, 0.5, 1, 2), landmark = max(t.values), seed = 1, lambda = 0.2, nu = 2, cens.range = c(landmark, 10), base.age.range = c(3, 5), tau.age = 0.2)Arguments
n | sample size |
p | number of longitudinal outcomes |
p.relev | number of longitudinal outcomes thatare associated with the survival outcome (min: 1, max: p) |
t.values | vector specifying the time points at which longitudinal measurements are collected(NB: for simplicity, this function assumes a balanced designed; however, |
landmark | the landmark time up until which all individuals survived.Default is equal to |
seed | random seed (defaults to 1) |
lambda | Weibull location parameter, positive |
nu | Weibull scale parameter, positive |
cens.range | range for censoring times. By default, the minimumof this range is equal to the |
base.age.range | range for age at baseline (set itequal to c(0, 0) if you want all subjects to enterthe study at the same age) |
tau.age | the coefficient that multiplies baseline agein the linear predictor (like in formula (6) from Signorelli et al. (2021)) |
Value
A list containing the following elements:
a dataframe
long.datawith data on the longitudinal predictors, comprehensive of a subject id (id),baseline age (base.age), time from baseline(t.from.base) and the longitudinal biomarkers;a dataframe
surv.datawith the survival data: a subject id (id), baseline age (baseline.age),the time to event outcome (time) and a binary vector(event) that is 1 if the eventis observed, and 0 in case of right-censoring;perc.censthe proportion of censored individuals in the simulated dataset;theta.truea list containing the true parameter valuesused to simulate data from the mixed model (beta0 and beta1) andfrom the Weibull model (tau.age, gamma, delta)
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
Examples
# generate example datasimdata = simulate_prclmm_data(n = 20, p = 10, p.relev = 4, t.values = c(0, 0.5, 1, 2), landmark = 2, seed = 19931101)# view the longitudinal markers:if(requireNamespace("ptmixed")) { ptmixed::make.spaghetti(x = age, y = marker1, id = id, group = id, data = simdata$long.data, legend.inset = - 1) }# proportion of censored subjectssimdata$censoring.prop# visualize KM estimate of survivallibrary(survival)surv.obj = Surv(time = simdata$surv.data$time, event = simdata$surv.data$event)kaplan <- survfit(surv.obj ~ 1, type="kaplan-meier")plot(kaplan)Simulate data that can be used to fit the PRC-LMM model
Description
This function allows to simulate a survival outcomefrom longitudinal predictors following the PRC MLPMM modelpresented in Signorelli et al. (2021). Specifically, the longitudinal predictors are simulated from multivariate latent process mixed models (MLPMMs), and the survival outcome from a Weibull model where the timeto event depends on the random effects from the MLPMMs.
Usage
simulate_prcmlpmm_data(n = 100, p = 5, p.relev = 2, n.items = c(3, 2, 3, 4, 1), type = "u", t.values = c(0, 0.5, 1, 2), landmark = max(t.values), seed = 1, lambda = 0.2, nu = 2, cens.range = c(landmark, 10), base.age.range = c(3, 5), tau.age = 0.2)Arguments
n | sample size |
p | number of longitudinal latent processes |
p.relev | number of latent processes thatare associated with the survival outcome (min: 1, max: p) |
n.items | number of items that are observed for each latent process of interest. It must be either a scalar, ora vector of length |
type | the type of relation between the longitudinaloutcomes and survival time. Two values can be used: 'u' refers to the PRC-MLPMM(U) model, and 'u+b' to the PRC-MLPMM(U+B)model presented in Section 2.3 of Signorelli et al. (2021).See the article for the mathematical details |
t.values | vector specifying the time points at which longitudinal measurements are collected(NB: for simplicity, this function assumes a balanced designed; however, |
landmark | the landmark time up until which all individuals survived.Default is equal to |
seed | random seed (defaults to 1) |
lambda | Weibull location parameter, positive |
nu | Weibull scale parameter, positive |
cens.range | range for censoring times. By default, the minimumof this range is equal to the |
base.age.range | range for age at baseline (set itequal to c(0, 0) if you want all subjects to enterthe study at the same age) |
tau.age | the coefficient that multiplies baseline agein the linear predictor (like in formulas (7) and (8) from Signorelli et al. (2021)) |
Value
A list containing the following elements:
a dataframe
long.datawith data on the longitudinal predictors, comprehensive of a subject id (id),baseline age (base.age), time from baseline(t.from.base) and the longitudinal biomarkers;a dataframe
surv.datawith the survival data: a subject id (id), baseline age (baseline.age),the time to event outcome (time) and a binary vector(event) that is 1 if the eventis observed, and 0 in case of right-censoring;perc.censthe proportion of censored individuals in the simulated dataset.
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
Examples
# generate example datasimdata = simulate_prcmlpmm_data(n = 40, p = 6, p.relev = 3, n.items = c(3,4,2,5,4,2), type = 'u+b', t.values = c(0, 0.5, 1, 2), landmark = 2, seed = 19931101)# names of the longitudinal outcomes:names(simdata$long.data)# markerx_y is the y-th item for latent process (LP) x# we have 6 latent processes of interest, and for LP1 # we measure 3 items, for LP2 4, for LP3 2 items, and so on# visualize trajectories of marker1_1if(requireNamespace("ptmixed")) { ptmixed::make.spaghetti(x = age, y = marker1_1, id = id, group = id, data = simdata$long.data, legend.inset = - 1) }# proportion of censored subjectssimdata$censoring.prop# visualize KM estimate of survivallibrary(survival)surv.obj = Surv(time = simdata$surv.data$time, event = simdata$surv.data$event)kaplan <- survfit(surv.obj ~ 1, type="kaplan-meier")plot(kaplan)Generate survival data from a Weibull model
Description
This function implements the algorithm proposed byBender et al. (2005) to simulate survival times from a Weibull model. In essence, this is simply an implementationof the Inverse Transformation Method.
Usage
simulate_t_weibull(n, lambda, nu, X, beta, seed = 1)Arguments
n | sample size |
lambda | Weibull location parameter, positive |
nu | Weibull scale parameter, positive |
X | design matrix (n rows, p columns) |
beta | p-dimensional vector of regression coefficientsassociated to X |
seed | random seed (defaults to 1) |
Value
A vector of survival times
Author(s)
Mirko Signorelli
References
Bender, R., Augustin, T., & Blettner, M. (2005). Generating survival times to simulate Cox proportional hazards models. Statistics in medicine, 24(11), 1713-1723.
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
Examples
# generate example dataset.seed(1)n = 50X = cbind(matrix(1, n, 1), matrix(rnorm(n*9, sd = 0.7), n, 9))beta = rnorm(10, sd = 0.7)times = simulate_t_weibull(n = n, lambda = 1, nu = 2, X = X, beta = beta)hist(times, 20)Step 2 of PRC-LMM (computation of the predicted random effects)
Description
This function performs the second step for the estimationof the PRC-LMM model (see references for methodological details).
Usage
summarize_lmms(object, n.cores = 1, verbose = TRUE)Arguments
object | a list of objects as produced by |
n.cores | number of cores to use to parallelize part ofthe computations. If |
verbose | if |
Value
A list containing the following objects:
call: the function callranef.orig: a matrix with the predicted random effectscomputed for the original data;n.boots: number of bootstrap samples;boot.ids: a list with the ids of bootstrapped subjects (whenn.boots > 0);ranef.boot.train: a list where each element is a matrix that contains the predicted random effects for each bootstrap sample (whenn.boots > 0);ranef.boot.valid: a list where each element is a matrix that contains the predicted random effects on the original data, based on the lmms fitted on the cluster bootstrap samples (whenn.boots > 0);
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
fit_lmms (step 1),fit_prclmm (step 3),performance_prc
Examples
# generate example dataset.seed(1234)p = 4 # number of longitudinal predictorssimdata = simulate_prclmm_data(n = 100, p = p, p.relev = 2, seed = 123, t.values = c(0, 0.2, 0.5, 1, 1.5, 2)) # specify options for cluster bootstrap optimism correction# procedure and for parallel computing do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to parallelize and speed computations up!if (!more.cores) n.cores = 1if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 8}# step 1 of PRC-LMM: estimate the LMMsy.names = paste('marker', 1:p, sep = '')step1 = fit_lmms(y.names = y.names, fixefs = ~ age, ranefs = ~ age | id, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = n.boots, n.cores = n.cores) # step 2 of PRC-LMM: compute the summaries # of the longitudinal outcomesstep2 = summarize_lmms(object = step1, n.cores = n.cores)summary(step2)Step 2 of PRC-MLPMM (computation of the predicted random effects)
Description
This function performs the second step for the estimationof the PRC-MLPMM model proposed in Signorelli et al. (2021)
Usage
summarize_mlpmms(object, n.cores = 1, verbose = TRUE)Arguments
object | a list of objects as produced by |
n.cores | number of cores to use to parallelize part ofthe computations. If |
verbose | if |
Value
A list containing the following objects:
call: the function callranef.orig: a matrix with the predicted random effectscomputed for the original data;n.boots: number of bootstrap samples;boot.ids: a list with the ids of bootstrapped subjects (whenn.boots > 0);ranef.boot.train: a list where each element is a matrix that contains the predicted random effects for each bootstrap sample (whenn.boots > 0);ranef.boot.valid: a list where each element is a matrix that contains the predicted random effects on the original data, based on the mlpmms fitted on the cluster bootstrap samples (whenn.boots > 0);
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
fit_mlpmms (step 1),fit_prcmlpmm (step 3),performance_prc
Examples
# generate example dataset.seed(123)n.items = c(4,2,2,3,4,2)simdata = simulate_prcmlpmm_data(n = 100, p = length(n.items), p.relev = 3, n.items = n.items, type = 'u+b', seed = 1) # specify options for cluster bootstrap optimism correction# procedure and for parallel computing do.bootstrap = FALSE# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!n.boots = ifelse(do.bootstrap, 100, 0)more.cores = FALSE# IMPORTANT: set more.cores = TRUE to speed computations up!if (!more.cores) n.cores = 2if (more.cores) { # identify number of available cores on your machine n.cores = parallel::detectCores() if (is.na(n.cores)) n.cores = 2}# step 1 of PRC-MLPMM: estimate the MLPMMsy.names = vector('list', length(n.items))for (i in 1:length(n.items)) { y.names[[i]] = paste('marker', i, '_', 1:n.items[i], sep = '')}step1 = fit_mlpmms(y.names, fixefs = ~ contrast(age), ranef.time = age, randint.items = TRUE, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = n.boots, n.cores = n.cores)# step 2 of PRC-MLPMM: compute the summaries step2 = summarize_mlpmms(object = step1, n.cores = n.cores)summary(step2)Extract model fits from step 1 of PRC-LMM
Description
Summary function to extract the estimated fixed effect parameters andvariances of the random effects from an object fitted using 'fit_lmms'
Usage
## S3 method for class 'lmmfit'summary(object, yname, what = "betas", ...)Arguments
object | the output of 'fit_lmms' |
yname | a character giving the name of the longitudinalvariable for which you want to extract information |
what | one of the following: ''betas'' for the estimates of the regression coefficients; ''tTable'' for the usual T tableproduced by ‘nlme'; '’variances'' for the estimates of the variances (and covariances) of the random effects and of thevariance of the error term |
... | additional arguments |
Value
A vector containing the estimated fixed-effect parameters if ‘what = ’betas'‘, the usual T table produced by 'nlme' if 'what = ’tTable'',or the estimated variance-covariance matrix of the randomeffects and the estimated variance of the error if ‘what = ’variances''
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Extract model fits from step 1 of PRC-LMM
Description
Utility function to extract the MLPMM summaries from a model fitobtained through 'fit_mlpmms'
Usage
## S3 method for class 'mlpmmfit'summary(object, yname, ...)Arguments
object | the output of 'fit_lmms' |
yname | a character giving the name of one of the longitudinaloutcomes modelled within one of the MLPMM |
... | additional arguments |
Value
The model summary as returned by 'summary.multlcmm'
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
fit_mlpmms andsummary.multlcmm
Summary method for PRC-LMM model fits
Description
Summary method for PRC-LMM model fits
Usage
## S3 method for class 'prclmm'summary(object, ...)Arguments
object | an object of class |
... | additional arguments |
Value
An object of class 'sprclmm'
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Summary method for PRC-MLPMM model fits
Description
Summary method for PRC-MLPMM model fits
Usage
## S3 method for class 'prcmlpmm'summary(object, ...)Arguments
object | an object of class |
... | additional arguments |
Value
An object of class 'sprcmlpmm'
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
Summary for step 2 of PRC
Description
Summary function to extract basic descriptives from 'summarize_lmms'and 'summarize_mlpmms'
Usage
## S3 method for class 'ranefs'summary(object, ...)Arguments
object | the output of 'summarize_lmms' or 'summarize_mlpmms' |
... | additional arguments |
Value
Information about number of predicted random effects and sample size
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
summarize_lmms,summarize_mlpmms
Visualize survival predictions for a fitted PRC model
Description
Visualize survival predictions for a fitted PRC model
Usage
survplot_prc(step1, step2, step3, ids, tmax = 5, res = 0.01, lwd = 1, lty = 1, legend.title = "Subject", legend.inset = -0.3, legend.space = 1)Arguments
step1 | the output of |
step2 | the output of |
step3 | the output of |
ids | a vector with the identifiers of the subjects to show in the plot |
tmax | maximum prediction time to consider for the chart. Default is 5 |
res | resolution at which to evaluate predictions for the chart. Default is 0.01 |
lwd | line width |
lty | line type |
legend.title | legend title |
legend.inset | moves legend more to the left / right (default is -0.3) |
legend.space | interspace between lines in the legend (default is 1) |
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Examples
# generate example datasimdata = simulate_prclmm_data(n = 100, p = 4, p.relev = 2, t.values = c(0, 0.2, 0.5, 1, 1.5, 2), landmark = 2, seed = 123) # estimate the PRC-LMM modely.names = paste('marker', 1:4, sep = '')step1 = fit_lmms(y.names = y.names, fixefs = ~ age, ranefs = ~ age | id, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = 0)step2 = summarize_lmms(object = step1)step3 = fit_prclmm(object = step2, surv.data = simdata$surv.data, baseline.covs = ~ baseline.age, penalty = 'ridge')# visualize the predicted survival for subjects 1, 3, 7 and 13 survplot_prc(step1, step2, step3, ids = c(1, 3, 7, 13), tmax = 6)Compute the predicted survival probabilities obtainedfrom the PRC models
Description
This function computes the predicted survival probabilities for the for the PRC-LMM model (see references for methodological details)
Usage
survpred_prclmm(step1, step2, step3, times = 1, new.longdata = NULL, new.basecovs = NULL, keep.ranef = FALSE)Arguments
step1 | the output of |
step2 | the output of |
step3 | the output of |
times | numeric vector with the time points at whichto estimate the time-dependent AUC |
new.longdata | longitudinal data if you want to compute predictions for new subjects on which the model was not trained.It should comprise an identifier variable called 'id'.Default is |
new.basecovs | a dataframe with baseline covariates for thenew subjects for which predictions are to be computed. It should comprise an identifier variable called 'id'.Only needed if baseline covariates were included in step 3 and |
keep.ranef | should a data frame with the predicted random effects be included in the output? Default is |
Value
A list containing the function call (call),a data frame with the predicted survival probabilitiescomputed at the supplied time points (predicted_survival),and ifkeep.ranef = TRUE also the predicted random effectspredicted_ranefs.
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
fit_lmms (step 1),summarize_lmms (step 2) andfit_prclmm (step 3)
Examples
# generate example dataset.seed(1234)p = 4 # number of longitudinal predictorssimdata = simulate_prclmm_data(n = 100, p = p, p.relev = 2, t.values = c(0, 0.2, 0.5, 1, 1.5, 2), landmark = 2, seed = 123) # step 1 of PRC-LMM: estimate the LMMsy.names = paste('marker', 1:p, sep = '')step1 = fit_lmms(y.names = y.names, fixefs = ~ age, ranefs = ~ age | id, long.data = simdata$long.data, surv.data = simdata$surv.data, t.from.base = t.from.base, n.boots = 0) # step 2 of PRC-LMM: compute the summaries # of the longitudinal outcomesstep2 = summarize_lmms(object = step1)# step 3 of PRC-LMM: fit the penalized Cox modelsstep3 = fit_prclmm(object = step2, surv.data = simdata$surv.data, baseline.covs = ~ baseline.age, penalty = 'ridge') # predict survival probabilities at times 3 to 6surv.probs = survpred_prclmm(step1, step2, step3, times = 3:6)head(surv.probs$predicted_survival)# predict survival probabilities for new subjects:temp = simulate_prclmm_data(n = 10, p = p, p.relev = 2, seed = 321, t.values = c(0, 0.2, 0.5, 1, 1.5, 2))new.longdata = temp$long.datanew.basecovs = temp$surv.data[ , 1:2]surv.probs.new = survpred_prclmm(step1, step2, step3, times = 3:6, new.longdata = new.longdata, new.basecovs = new.basecovs)head(surv.probs.new$predicted_survival)Compute the predicted survival probabilities obtainedfrom the PRC models
Description
This function computes the predicted survival probabilities for the for the PRC-MLPMM(U) and PRC-MLPMM(U+B) models proposed in Signorelli et al. (2021)
Usage
survpred_prcmlpmm(step2, step3, times = 1)Arguments
step2 | the output of |
step3 | the output of |
times | numeric vector with the time points at whichto estimate the time-dependent AUC |
Value
A data frame with the predicted survival probabilitiescomputed at the supplied time points
Author(s)
Mirko Signorelli
References
Signorelli, M. (2024). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. The R Journal, 16 (2), 134-153.
Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196.
See Also
fit_mlpmms (step 1),summarize_mlpmms (step 2) andfit_prcmlpmm (step 3).
Examples
data(fitted_prcmlpmm) # predict survival probabilities at times 3 to 6surv.probs = survpred_prcmlpmm(fitted_prcmlpmm$step2, fitted_prcmlpmm$step3, times = 3:6)ls(surv.probs)head(surv.probs$predicted_survival)