Estimation and Variable Selection for Interval-censored Failure Time Data with Random Change Point and Application to Breast Cancer Study

Motivated by a breast cancer study, we consider regression analysis of interval-censored failure time data in the presence of a random change point. Although a great deal of literature on interval-censored data has been established, it does not seem to exist an established method that can allow for the existence of random change points. Such data can occur in, for example, clinical trials where the risk of a disease may dramatically change when some biological indexes of the human body exceed certain thresholds. To fill the gap, we will first consider regression analysis of such data under a class of linear transformation models and provide a sieve maximum likelihood estimation procedure. Then a penalized method is proposed for simultaneous estimation and variable selection, and the asymptotic properties of the proposed method are established. An extensive simulation study is conducted and indicates that the proposed methods work well in practical situations. The approaches are applied to the real data from the breast cancer study mentioned above.