An extended hazard model with longitudinal covariates

In clinical trials and other medical studies, it has become increasingly common to observe simultaneously an event time of interest and longitudinal covariates. In the literature, joint modelling approaches have been employed to analyse both survival and longitudinal processes and to investigate their association. However, these approaches focus mostly on developing adaptive and flexible longitudinal processes based on a prespecified survival model, most commonly the Cox proportional hazards model. In this paper, we propose a general class of semiparametric hazard regression models, referred to as the extended hazard model, for the survival component. This class includes two popular survival models, the Cox proportional hazards model and the accelerated failure time model, as special cases. The proposed model is flexible for modelling event data, and its nested structure facilitates model selection for the survival component through likelihood ratio tests. A pseudo joint likelihood approach is proposed for estimating the unknown parameters and components via a Monte Carlo EM algorithm. Asymptotic theory for the estimators is developed together with theory for the semiparametric likelihood ratio tests. The performance of the procedure is demonstrated through simulation studies. A case study featuring data from a Taiwanese HIV/AIDS cohort study further illustrates the usefulness of the extended hazard model.