Additive hazards regression with incomplete covariate data

Abstract

This dissertation addresses two incomplete covariate data problems in the additive hazards (AH) regression model for failure time data. Both are examples of two-phase designs where some covariate is measured only on a subset of the total sample. The first is the case-cohort design, where the covariates are ascertained on all the failures and on a randomly selected subcohort. We propose an estimator for the AH regression parameter under the case-cohort design, prove its consistency and asymptotic normality and discuss its practical use. The other case we consider is the errors-in-variables design, where the true covariate is observed only on a validation set selected by independent Bernoulli sampling, but a surrogate covariate is available for all subjects. Under these circumstances, we define the corrected score (CS) estimator for the AH regression parameter and show that it is consistent and asymptotically normal. Our approach works under mild regularity conditions, does not impose any parametric distributional assumptions on the covariates and allows for surrogates that are biased for the true covariate of interest. The CS estimator is easily generalized to multiple covariates. We describe its application in several situations involving both discrete and continuous covariates, investigate its behavior by simulation studies and illustrate its use on a real-life example.