Hazard Model with Random Treatment Time-Lag Effect

In clinical studies, it is often that the medical treatments take a period of time before having an effect on patients and the delayed time may vary from person to person. Even though there exists a rich literature developing methods to estimate the time-lag period and treatment effects after lag time, most of these existing studies assume a fixed lag time. In this paper, we propose a hazard model incorporating a random treatment time-lag effect to describe the heterogeneous treatment effect among subjects. The EM algorithm is used to obtain the maximum likelihood estimator. We give the asymptotic properties of the proposed estimator and evaluate its performance via simulation studies. An application of the proposed method to real data is provided.