Evaluation of the treatment time-lag effect for survival data

Medical treatments often take a period of time to reveal their impact on subjects, which is the so-called time-lag effect in the literature. In the survival data analysis literature, most existing methods compare two treatments in the entire study period. In cases when there is a substantial time-lag effect, these methods would not be effective in detecting the difference between the two treatments, because the similarity between the treatments during the time-lag period would diminish their effectiveness. In this paper, we develop a novel modeling approach for estimating the time-lag period and for comparing the two treatments properly after the time-lag effect is accommodated. Theoretical arguments and numerical examples show that it is effective in practice.