Jointly Modelling Longitudinal and Survival Data

Abstract

In many clinical and epidemiologic studies, disease markers are measured periodically and used to monitor progression to the onset of disease. Examples of this are CD4 counts and viral load measures in AIDS and PSA values in prostate cancer. We develop a joint model for analysis of both longitudinal and survival data. We use a longitudinal model for continuous data which incorporates a mean structure dependent on covariates, a random intercept, a correlated stochastic process and measurement error. The model is based on an integrated Ornstein-Uhlenbeck (IOU) stochastic process, which is an underlying AR(1) process for the derivatives of the observations. This stochastic process represents a family of covariance structures with a random effects model as one special case and Brownian motion as another. The regression model for the event time data is a time-dependent proportional hazards model, in which the longitudinal marker is a time-dependent variable and includes other covariates as well. An algorithm using Gibbs sampling and Metropolis-Hastings steps is developed for fitting the model. The algorithm requires drawing a value for the IOU stochastic process at every time point for each individual. Judicious choice of parametrisation and prior distributions is needed for an efficient algorithm. The approach is tested in a simulation study and applied to AIDS data.