In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields, and can also apply to survival data. In survival analysis, most existing methods compare two treatment groups for the entirety of the study period. Some treatments may take a length of time to show effects in subjects. This has been called the time-lag effect in the literature, and in cases where time-lag effect is considerable, such methods may not be appropriate to detect significant differences between two groups. In this paper, we propose a novel non-parametric approach for estimating the point of treatment time-lag effect by using an empirical divergence measure. Theoretical properties of the estimator are studied. The results from the simulated data and the applications to real data examples support our proposed method.
Keywords: Change point analysis; lag effect; non-parametric statistics; survival analysis; treatment time-lag effect.