Package JM fits shared parameter models for the joint modelling of normal longitudinal responses and event times under a maximum likelihood approach. Various options for the survival model and optimization/integration algorithms are provided.

The package has a single model-fitting function named jointModel(), which accepts as main arguments a linear mixed effects object fit returned by function lme() of package nlme, and a survival object fit returned by either function coxph() or function survreg() of package survival. For the longitudinal process only linear mixed effects models are currently available. For the event process, the method argument of jointModel() specifies the type survival model to be fitted and the type of the numerical integration method. Available options are:

• method = ‘Cox-PH-GH’: the time-dependent version of a proportional hazards model with unspecified baseline hazard function. The Gauss-Hermite integration rule is used to approximate the required integrals. This option corresponds to the joint model proposed by Wulfsohn and Tsiatis (1997, Biometrics).

• method = ‘piecewise-PH-GH’: a relative risk model with a piecewise-constant baseline risk function. The Gauss-Hermite integration rule is used to approximate the required integrals.

• method = ‘weibull-AFT-GH’: a time-dependent accelerated failure time model with Weibull or Exponential (by setting argument scaleWB of jointModel() to 1) baseline risk function. The Gauss-Hermite integration rule is used to approximate the required integrals.

• method = ‘weibull-PH-GH’: a relative risk model with a Weibull or Exponential (by setting argument scaleWB of jointModel() to 1) baseline risk function. The Gauss-Hermite integration rule is used to approximate the required integrals.

• method = ‘spline-PH-GH’: a relative risk model with a B-spline approximation for the baseline risk function. The Gauss-Hermite integration rule is used to approximate the required integrals.

• method = ‘ch-Laplace’: an additive log cumulative risk model, in which the log cumulative baseline risk function is approximated using B-splines. A fully exponential Laplace approximation method is used to approximate the required integrals.

Current Version: 0.6-2

Author: Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

Maintainer: Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

Depends: R (>= 2.7.0), MASS, nlme, splines, survival

License: GPL (>= 2)

• Methods for Basic Generics: the function jointModel() return objects of class jointModel, for which the following methods are available: print(), coef(), fixef(), ranef(), fitted(), residuals(), summary(), plot(), vcov(), and logLik(). A detailed description of these functions is available at the on-line help files.

• Stratification: joint models with method = “spline-PH-GH” also allow for stratification factors, i.e., different coefficients for the B-spline approximation of the log baseline risk function are assumed for different levels of categorical variable. To fit such a stratified joint model the user needs to include the stratification factors in the definition of the survival model, which must only be a Cox model. The supporting function wald.strata() can be used to test for equality of the spline coefficients across strata with a Wald test.

• Optimization Algorithms: for all survival models (except for the time-dependent proportional hazards model), the optimization algorithm starts with EM iterations, and if convergence is not achieved, it switches to quasi-Newton iterations until convergence.

• MI Residuals: a new method for calculating residuals and producing diagnostics plots in joint models. This is based on the idea of multiply imputing the missing longitudinal responses under the fitted joint model, creating thus random versions of the complete data set. These complete data sets can then be used to extract conclusions regarding the modelling assumptions, and how these assumptions are affected by the nonrandom dropout.

• Dynamic Prediction: function survfitJM() can be used to provide predictions and dynamic predictions of survival probabilities for new subjects in the study, taking into account their longitudinal history and baseline covariates.

• Dynamic Discrimination Index: function dync() can be used to provide a dynamic discrimination index for joint models using ROC methodology. In particular, this function computes time-dependent AUCs, and their weighted average over the follow-up period.

• Download latest version from CRAN.

• The Reference manual of the package.

• The changes in the current and previous versions of the package can be found in the NEWS file.

• A paper presenting the main features of the package has been published in the Journal of Statistical Software.

• Sample Analysis of the AIDS data set

• Sample Analysis of the PBC data set

• Detailed Joint Modelling Analysis

• Conditional Survival Probabilities & the Dynamic Discrimination Index

• Joint Modelling Analysis with Stratificat­ion Factors

• Joint Modelling Analysis with Lagged Effects

• MI Residuals for the AIDS data set

• MI Residuals for the PBC data set