Statistical Methods for Analyzing Time-Dependent Events in Breast CancerChemoprevention Studies

摘要

The overall aim of our research proposal is the statistical inference ofnonparametric estimates, the restribution-to-the-inside estimator (RTIE) and the generalized maximum likelihood estimator (GMLE),for the survival function of a time-to-event variable that is subject to interval censoring. The RTIE, which is proposed by us, has a closed-form expression and is equal to the GMLE under a homogeneous condition. The GMLE is the standard optimal procedure in survival analysis. However, no closed-form expression for the GMLE is available, and asymptotic distribution theory for it has been limited. Our research efforts in the third year have focused on the asymptotic inference of the GMLE under conditions more general than the discrete distribution assumption that we previously imposed on the censoring variables. Additionally, we have derived an asymptotic nonparametric the sample test procedure for comparing two populations. Finally, we have begun investigating the asymptotic inference of Cox regression model for interval-censored data by establishing consistency of the GMLE of the model parameters under finite assumptions on both the survival and censoring distributions.