Mathematical Sciences: Weighted Empiricals in Regression with Survival Data

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Proposal: DMS 9504918 PI: Song Yang Institution: Texas A&M Title: Weighted Empiricals in Regression with Survival Data Abstract: This research involves various semiparametric regression models, with right, double or interval censoring. These models include the commonly used multiplicative hazard model and the log transform of accelerated life model, the relatively new frailty model, and the rarely studied multiplicative odds ratio model. In all these models, the covariates are allowed to be time-dependent. The weighted Nelson-Aalen hazard function and Kaplan-Meier survival function are defined via weighted empirical processes and some self consistency equations. Various estimating equations and estimating functions are established using these weighted functions. Some classes of the regression estimators, including the rank, minimum distance and M-estimators, are then obtained and analyzed. The efficiency and robustness of the estimators and some goodness-of-fit tests of the models is studies, as well as the practical issues on computing these estimators. The models and related statistical problems studied in this research have applications in areas such as medical follow-up studies and industrial reliability tests. In situations involved in those areas, the available data are often incomplete due to various censoring. The censoring is attributed to the conditions of the patients or machine operating systems and is influenced by factors such as treatment, age, stress, and load. These influences can be formulated by some of the models in this research. Through studies of these models and related statistical problems, the conditions of the patients or operating systems can be better understood, predicted, and controlled. Compared with the existing research literature, the new methods in this research will require different or more sophisticated computing algorithms. Implementations of these methods provide a background to, and are facilitated by, efficient coding and high performance computing.