Goodness of Fit of a joint model for event time and nonignorable missing Longitudinal Quality of Life data

In many survival studies one is interested not only in the duration time to some terminal event, but also in repeated measurements made on a time-dependent covariate. In these studies, subjects often drop out of the study before the occurrence of the terminal event and the problem of interest then becomes modelling the relationship between the time to dropout and the internal covariate. Dupuy and Mesbah (2002) (DM) proposed a model that described this relationship when the value of the covariate at the dropout time is unobserved. This model combined a first-order Markov model for the longitudinally measured covariate with a time-dependent Cox model for the dropout process. Parameters were estimated using the EM algorithm and shown to be consistent and asymptotically normal. In this paper, we propose a test statistic to test the validity of Dupuy and Mesbah’s model. Using the techniques developed by Lin (1991), we develop a class of estimators of the regression parameters using weight functions. The test statistic is a function of the standard maximum likelihood estimators and the estimators based on the weight function. Its asymptotic distribution and some related results are presented. 1.