In clinical or social studies and aging research, it has become increasingly common to observe an event time of interest, usually referred to as a survival time, along with baseline and longitudinal covariates. Both the survival and covariate processes are of interest, so is the relationship between them. Due to several complications, traditional approaches, including the partial likelihood approach for the Cox proportional hazards model and rank based approaches for the accelerated failure time model, encounter difficulties when longitudinal covariates are involved in the modeling of survival times. Moreover, the longitudinal processes are often subject to informative dropout. Jointly modeling the survival and longitudinal data emerges as an effective way to overcome these difficulties, and we will first briefly review such an approach.
So far, attention has focused on Cox models for the survival data. The accelerated failure time (AFT) model is an attractive alternative to the Cox model when the proportionality assumption fails to capture the relation between the survival time and its longitudinal covariates. This occurs for the medfly fecundity data in Carey et al. (1998), where the interest is to explore the relation between longevity and reproductive history of females medflies. We illustrate how to implement the joint modeling approach for the AFT survival model and study the fecundity data with such an approach. The procedure is based on maximizing the joint likelihood function where random effects are treated as missing data. A Monte Carlo EM algorithm is employed to estimate the unknown parameters, including the unknown baseline hazard function. We will also discuss the robustness of the procedure against departure from the assumption of normal random effects.
Both the proportional hazards and AFT models are special cases of a broader class, termed "extended hazard survival model". In the second part of the talk, we will extend the joint modeling approaches to this more general setting, which facilitates model checking and model selection. The is is part of an ongoing research.
* The talk is based on joint work with Yi-Kuan Tseng (National Central University) and Fushing Hsieh (University of California at Davis).
