Semiparametric Models, Methodologies and Related Theory for Analysis of Censored Survival Data

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This project addresses issues related to semi-parametric regression models, methods and theories with censored survival data. The investigator and his collaborators aim to develop semi-parametric efficient estimators of the regression parameters for the proportional hazards mixture cure model. The approach is extended to another class of semi-parametric cure models. They propose a general class of mixture transformation models, which are common in medical and econometrics literature, and study them via estimating equations as well as some nonparametric smoothing techniques. In addition, they plan to develop estimating equations for multivariate failure time data based on marginal linear transformation models and propose a class of independence tests for multivariate failure time data with the adjustment of covariates. They also derive relatively simple method for analysis of survival data from case-cohort design and discuss more efficient parameter estimation via the projection method. The statistical problems studied here are motivated by applications in biomedical sciences, engineering sciences, sociology, economics and genetics. The project develops appropriate statistical models, inferential methods and mathematical theory. The results can be used to facilitate design of clinical trials and epidemiological studies, particularly in studies of cancer, cardiovascular diseases, to analyze engineering reliability and market penetration data, to assess the association among failure times due to unmeasured effects, such as familial genetic effects, after adjusting some environmental factors.