CAREER: Semiparametric Regression Models for Censored Data

Semiparametric regression methods for censored data currently used by empirical researchers rarely extend beyond the well-known Cox proportional hazards regression model. The Cox model assumes that covariate-specific hazard functions are proportional, an assumption often not satisfied in practice. The proposed research investigates the accelerated failure time regression and the family of semiparametric linear transformation models, of which the Cox model is a member. Existing methods for these models are complicated by their numerical difficulties and stringent assumptions. To circumvent these complications, the investigator proposes a number of new approaches, including modified least squares method, the M-estimation and a minimization-based rank-type estimation for the accelerated failure time model and a general counting process-based score equations for the transformation models. An important feature of the new approaches is that their inference procedures can be readily implemented with numerically stable algorithms.

Results from the proposed project will be relevant and directly applicable to many scientific disciplines. They will provide methodologic tools for analysis of data across many important fields, including economics, business administration, industrial engineering, medicine, biology and public health. Examples of the scientific research problems that the methods can deal with are as diverse as identification of factors associated with the duration of unemployment, determination of major risk factors for cancer, testing of new drugs to combat AIDS, examination of factors associated with the lifespan of system components, evaluation of potential confounding factors in crime prevention and drug abuse. The research touches many important areas in statistical science: linear regression, survival analysis, semiparametrics, robust statistics, nonparametric statistics and statistical computing. In this connection, it will generate excellent opportunities for graduate students to have exposures to a broad spectrum of modern statistics as well as to learn vital skills in conducting independent researches. A research topic/reading course and a journal club will be developed to facilitate these exposures and enhance the educational experience.