Estimation of semiparametric probit model based on case-cohort interval-censored failure time data

The estimation of semiparametric probit model is discussed for the situation where one observes interval-censored failure time data arising from case-cohort studies. The probit model has recently attracted some attention for regression analysis of failure time data partly due to the popularity of the normal distribution and its similarity to linear models. Although some methods have been developed in the literature for its estimation, it does not seem to exist an established approach for the situation of case-cohort interval-censored data. To address this, a pseudo-maximum likelihood method is proposed and furthermore, an EM algorithm is developed for its implementation. The resulting estimators of regression parameters are shown to be consistent and asymptotically follow the normal distribution. To assess the empirical performance of the proposed method, a simulation study is conducted and indicates that it works well in practical situations. In addition, it is applied to a set of real data arising from an AIDS clinical trial that motivated this study.