We study joint modeling of survival and longitudinal data. There are two regression models of interest. The primary model is for survival outcomes, which are assumed to follow a time varying coefficient proportional hazards model. The second model is for longitudinal data, which are assumed to follow a random effects model. Based on the trajectory of a subject's longitudinal data, some covariates in the survival model are functions of the unobserved random effects. Estimated random effects are generally different from the unobserved random effects and hence this leads to covariate measurement error. To deal with covariate measurement error, we propose a local corrected score estimator and a local conditional score estimator. Both approaches are semiparametric methods in the sense that there is no distributional assumption needed for the underlying true covariates. The estimators are shown to be consistent and asymptotically normal. Finite sample properties are assessed via simulation. The approaches are demonstrated by an application to data from an HIV clinical trial.
Song, Xiao and Wang, C.Y., "Semiparametric Approaches for Joint modeling of Longitudinal and Survival Data with Time Varying Coefficients" (December 2005). UW Biostatistics Working Paper Series. Working Paper 273.