Cox Model for Interval Censored Data in Breast Cancer Follow-Up Studies.

摘要

The overall objective of this research proposal is semi-parametric inference of the Cox proportional hazards (PH) regression model for a survival function Pr(X > x I Z = z) = S(x I z) = S 0 (x)ezbeta , where X is a time-to- event variable. which is subject to interval censoring, Z represents the covariates, S0 is a baseline survival function, and beta represents the regression coefficients. The main objective of our research is to develop asymptotic inferences of the generalized maximum likelihood estimators (GMLE) of beta and S(. I z). A critical limitation with GMLE under interval censoring is that it is computationally feasible only for a small data set. We therefore propose to also investigate asymptotic properties of a computationally simpler alternative to GMLE, namely two-stage estimators (TSE) of beta and S(. I z) obtained by a two-stage modified Newton-Raphson algorithm involving data grouping. In the four years of our research, we have implemented a foolproof algorithm for obtaining TSE, proved consistency and established asymptotic normality for both GMLE and TSE under both discrete and continuous distributional assumptions, and proposed new diagnostic method for PH assumption. Also, we have successfully applied our asymptotic Cox regression methodology to the analysis of a large-scale, long-term breast cancer relapse follow-up study. Our results will be useful to data analysis of breast cancer relapse follow-up studies, chemoprevention intervention trials and genetic studies on familial aggregation of breast cancer and related cancers.