Joint Modeling of Survival and Nonignorable Missing Longitudinal Quality-of-Life Data
A problem that frequently arises in clinical trials where quality-of-life values are repeatedly measured on each individual under study, is that of dropout. In some settings, dropout may depend on unobserved components of the longitudinal process. Dropout is then termed nonignorable. Recently, several approaches have been proposed that accommodate nonignorable dropout in the modeling of a longitudinal process. However, most of these approaches rest upon the assumption that dropout can only occur at one of the pre-specified measurement times of quality-of-life. In this paper, we review some of these approaches and we propose a new joint model for longitudinal data with nonignorable dropout and time to dropout, which allows dropout to occur at any point in time. This model combines a first-order Markov model for the longitudinal quality-of-life data with a time-dependent Cox model for the dropout process. We discuss nonparametric maximum likelihood estimation in the suggested joint model and rely on an EM algorithm to calculate estimates of the parameters. The method is illustrated through analysis of quality-of-life data among patients involved in a cancer clinical trial. Comparison of its results to the ones obtained by fitting Diggle and Kenward’s model for nonignorable dropout to the same data is provided.
KeywordsFrailty Model Nonparametric Maximum Likelihood Longitudinal Process Nonparametric Maximum Likelihood Estimator Dropout Model
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