Statistics and Its Interface

Volume 3 (2010)

Number 2

A joint model of longitudinal and competing risks survival data with heterogeneous random effects and outlying longitudinal measurements

Pages: 185 – 195



Robert M. Elashoff (Department of Biomathematics, University of California at Los Angeles)

Xin Huang (Amgen Inc., South San Francisco, Calif., U.S.A.)

Gang Li (Department of Biostatistics, School of Public Health, University of California at Los Angeles)


This article proposes a joint model for longitudinal measurements and competing risks survival data. The model consists of a linear mixed effects sub-model with $t$-distributed measurement errors for the longitudinal outcome, a proportional cause-specific hazards frailty submodel for the survival outcome, and a regression sub-model for the variance-covariance matrix of the multivariate latent random effects based on a modified Cholesky decomposition. A Bayesian MCMC procedure is developed for parameter estimation and inference. Our method is insensitive to outlying longitudinal measurements in the presence of nonignorable missing data due to dropout. Moreover, by modeling the variance-covariance matrix of the latent random effects, our model provides a useful framework for handling high-dimensional heterogeneous random effects and testing the homogeneous random effects assumption which is otherwise untestable in commonly used joint models. Finally, our model enables analysis of a survival outcome with intermittently measured time-dependent covariates and possibly correlated competing risks and dependent censoring, as well as joint analysis of the longitudinal and survival outcomes. Illustrations are given using a real data set from a lung study and simulation.


joint model, competing risks, Bayesian analysis, Cholesky decomposition, mixed effects model, MCMC, modeling random effects covariance matrix, outlier

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