Statistical Methods for Analyzing Time-Dependent Events in Breast Cancer Chemoprevention Studies

摘要

The overall aim of the research proposal is the statistical nonparametric inferences of the redistribution-to- the-center estimator (RTCE) and the generalized maximum likelihood estimator (GMLE) for the survival function of a time-to-event variable that is subject to interval censoring. The RTCE, proposed by the Strang Center, has a closed-form expression and is equal to GMLE under a homogeneous condition. The GMLE is the standard estimator in survival analysis. However, it cannot be expressed in a closed-form expression, and asymptotic distribution theory for it has been limited. From the study of the asymptotic properties of RTCE, we have gained important insight into proofs of asymptotic properties of GMLE. Specifically, we have established consistency, asymptotic normality and efficiency of GMLE under different conditions. Also, we have derived an asymptotic nonparametric two-sample distance test for comparing two populations. Under finite distributional assumptions on the survival and censoring distributions, we have established consistency, asymptotic normality for both the regression coefficients and the survival function of the Cox regression model. We point out major computational limitations associated with the Newton-Raphson algorithm for computing the asymptotic estimates of the Cox regression parameters, and suggest a simpler two-step estimation alternative.