Semiparametric approaches for joint modeling of longitudinal and survival data with time-varying coefficients.

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. However, simulation studies indicate that the conditional score estimator outperforms the corrected score estimator for finite samples, especially in the case of relatively large measurement error. The approaches are demonstrated by an application to data from an HIV clinical trial.