Dongsheng Tu, Queen's University
Nonparametric Inferences on the Time-Dependent Hazard Ratios with Censored Data
Hazard ratio is one of the most used statistical measures in clinical trials with survival endpoints to quantify the differences between two treatment regimens. It is usually estimated from the Cox¡¯s proportional hazard model based on the assumption that the hazard ratios between two treatment groups are constant over time. In some applications, hazard ratios are time dependent and it is of interest to make statistical inference on the hazard ratios at different time points. In this talk, I will first present an example from a recent clinical trial on earlier breast cancer we conducted and then introduce some estimation and confidence intervals procedures based directly on the ratio of nonparametric kernel estimates for the hazard rates. A new method of bandwidth selection for the kernel hazard estimate is derived based on the asymptotic expansion for the coverage of the confidence intervals and some empirical studies. The proposed methods are evaluated through Monte-Carlo simulations and applied to the analysis of data from the clinical trial mentioned above. Part of this talk is based on joint work with Drs. Ming-Yen Cheng of the National Taiwan University and Peter Hall of the Australian National University.