A joint model for longitudinal and survival data based on an AR(1) latent process

A critical problem in repeated measurement studies is the occurrence of nonignorable missing observations. A common approach to deal with this problem is joint modeling the longitudinal and survival processes for each individual on the basis of a random effect that is usually assumed to be time constant. We relax this hypothesis by introducing time-varying subject-specific random effects that follow a first-order autoregressive process, AR(1). We also adopt a generalized linear model formulation to accommodate for different types of longitudinal response (i.e. continuous, binary, count) and we consider some extended cases, such as counts with excess of zeros and multivariate outcomes at each time occasion. Estimation of the parameters of the resulting joint model is based on the maximization of the likelihood computed by a recursion developed in the hidden Markov literature. This maximization is performed on the basis of a quasi-Newton algorithm that also provides the information matrix and then standard errors for the parameter estimates. The proposed approach is illustrated through a Monte Carlo simulation study and the analysis of certain medical datasets.