Joint analysis of informatively interval-censored failure time and panel count data

Interval-censored failure time and panel count data, which frequently arise in medical studies and social sciences, are two types of important incomplete data. Although methods for their joint analysis have been available in the literature, they did not consider the observation process, which may depend on the failure time and/or panel count of interest. This study considers a three-component joint model to analyze interval-censored failure time, panel counts, and the observation process within a unique framework. Gamma and distribution-free frailties are introduced to jointly model the interdependency among the interval-censored data, panel count data, and the observation process. We propose a sieve maximum likelihood approach coupled with Bernstein polynomial approximation to estimate the unknown parameters and baseline hazard function. The asymptotic properties of the resulting estimators are established. An extensive simulation study suggests that the proposed procedure works well for practical situations. An application of the method to a real-life dataset collected from a cardiac allograft vasculopathy study is presented.