Software for the Joint Modelling of Longitudinal and Survival Data

Software for the Joint Modelling of Longitudinal and Survival Data

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.

Description

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.

For all types of joint models fitted by JM (except the last one) there is the option to use a pseudo adaptive Gauss-Hermite rule. This is much faster than the default option and produces results of equal or better quality. It can be invoked via the ‘method’ argument of jointModel() by specifying in the method argument an option with “aGH” instead of “GH”, e.g., “spline-PH-aGH” instead of “spline-PH-GH”.

Package Info

Current Version: 0.9-2

Author: Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

Maintainer: Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

Depends: R (>= 2.11.0), MASS, nlme, splines, survival

License: GPL (>= 2)

Available Features

Methods for Basic Generics: Function jointModel() return objects of class jointModel, for which the following methods are available: print(), coef(), fixef(), ranef(), fitted(), residuals(), summary(), plot(), predict(), 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” or method = “spline-PH-aGH” 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.

Competing risks: Competing risks joint models can be also fitted with options method = “spline-PH-GH” or method = “spline-PH-aGH”. As first step, the survival dataset must be transformed to the competing risks long format using function crLong(). Then in the survival submodel the competing risks indicator must be included as a stratification factor. Finally, the joint model is fitted by providing the stratified survival submodel as second argument, and setting argument CompRisk to TRUE.

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. Function predict() can be analogously used to provide marginal or subject-specific predictions for the longitudinal outcome.

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.

ROC Analysis: function rocJM() calculates sensitivity and specificity, and the corresponding ROC and AUC for joint models.

Export Results: function xtable.jointModel() enhances package xtable and produces a LaTeX table with the results of a joint modeling analysis.