A Counting Process Approach To The Cox Proportional Hazards Regression Model With Covariate Errors (survival, Martingale).

Abstract

The Cox (1972) regression model was a major advancement in the analysis of survival data because it is nonparametric (with respect to the hazard function), can incorporate censored data, and can be used to relate many types of covariates to survival. Cox's basic model has been put to various applications and modifications. Some of the asymptotic statistical properties of the Cox model when the covariates are measured with error are investigated using the martingale techniques of Andersen and Gill (1982). Maximum partial likelihood estimates (MPLE) for the regression coefficients (beta)(,x) are not in general consistent when the covariates are measured with error, but are deflated and have smaller variance relative to the estimates based on the true covariate values. A consistent estimator (beta)(,x)* is developed in this dissertation by adjusting the logarithm of the partial likelihood to account for covariate errors. The adjustment requires specification of the error moment generating function. Techniques for implementing the adjustment are discussed. The estimator (beta)(,x)* has full asymptotic efficiency relative to the usual MPLE without covariate errors. A consistent estimator of the variance-covariance matrix of (beta)(,x)* is also developed.