Semiparametric Analysis of Interval-Censored Survival Data with Median Regression Model

Analysis of interval censored survival data has become increasingly popular and important in many areas including clinical trials and biomedical research. Generally, right censored survival data can be seen as a special case of interval censored data. However, due to the fundamentally special and complex nature of interval censoring, most of the commonly used survival analysis methods for right censored data, including methods based on martingale-theory (Andersen et al., Statistical models based on counting processes. Springer, New York, 1992), can not be used for analyzing interval censored survival data. Most of the popular semiparametric models for interval censored survival data focus on modeling the hazard function. In this chapter, we develop a semiparametric model dealing with the median regression function for interval censored survival data, which introduce many practical advantages in real applications. Both semiparametric maximum likelihood estimator (MLE) and the Markov chain Monte Carlo (MCMC) based semiparametric Bayesian estimator, including how to incorporate the historical information, have been proposed and presented. We illustrate the case study through a real breast cancer data example and make a comparison between different models. Key findings and recommendations are also discussed to provide further guidance on application in clinical trials.