Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies

Abstract

The case-cohort design is a common means of reducing the cost of covariate measurements in large failure-time studies. Under this design, complete covariate data are collected only on the cases (i. e., the subjects whose failure times are uncensored) and on a subcohort randomly selected from the whole cohort. In many applications, certain covariates are readily measured on all cohort members, and surrogate measurements of the expensive covariates also may be available. The existing relative-risk estimators for the case-cohort design disregard the covariate data collected outside the case-cohort sample and thus incur loss of efficiency. To make better use of the available data, we develop a class of weighted estimators with general time-varying weights that are related to a class of estimators proposed by Robins, Rotnitzky, and Zhao. The estimators are shown to be consistent and asymptotically normal under appropriate conditions. We identify the estimator within this class that maximizes efficiency, numerical studies demonstrate that the efficiency gains of the proposed estimator over the existing ones can be substantial in realistic settings. We also study the estimation of the cumulative hazard function. An illustration with data taken from Wilms' tumor studies is provided.