ISSN 2385-2275 No. 14 - October 2015
A joint model for longitudinal and survival data based on an AR(1) latent process
Silvia BACCI
University of Perugia, Department of Economics, Perugia, Italy
Francesco BARTOLUCCI
University of Perugia, Department of Economics, Perugia, Italy
Silvia PANDOLFI
University of Perugia, Department of Economics, Perugia, Italy
Abstract:
A critical problem in repeated measurement studies is the occurrence of non-
ignorable 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 eect that is usually assumed to be time constant. We relax this
hypothesis by introducing time-varying subject-specific random eects that follow a
first-order autoregressive process, AR(1). We also adopt a generalized linear model
formulation to accommodate for dierent types of longitudinal response (i.e., con-
tinuous, 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 maximization of the likelihood
computed by a recursion developed in the hidden Markov literature. The maximiza-
tion 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 pro-
posed approach is illustrated through a Monte Carlo simulation study and through
the analysis of certain medical datasets.
Keywords: generalized linear models; informative dropout; nonignorable missing mechanism; sequential quadrature; shared-parameter models
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