Analysis of case-cohort designs with binary outcomes: Improving efficiency using whole-cohort auxiliary information

The case-cohort design has been widely adopted for reducing the cost of covariate measurements in large prospective cohort studies. Under the case-cohort design, complete covariate data are collected only on randomly sampled cases and a subcohort randomly selected from the whole cohort. For the analysis of case-cohort studies with binary outcomes, logistic regression analysis has been routinely used. However, in many applications, certain covariates are readily measured on all samples from the whole cohort, and the case-cohort design may be regarded as a two-phase sampling design. Using this auxiliary covariate information, estimators for the regression parameters can be substantially improved. In this article, we discuss the theoretical basis of the case-cohort design derived from the formulation of the two-phase design and the improved estimators using whole-cohort auxiliary variable information. In particular, we show that the sampling scheme of the case-cohort design is substantially equivalent to that of conventional two-phase case-control studies (also known as two-stage case-control studies for epidemiologists), i.e., the methodologies of two-phase case-control studies can be directly applied to case-cohort data. Under this framework, we review and apply the following improved estimators to the case-cohort design with binary outcomes: (i) weighted estimators, (ii) a semiparametric maximum likelihood estimator, and (iii) a multiple imputation estimator. In addition, based on the framework of the two-phase design, we can obtain risk ratio and risk difference estimators without the rare-disease assumption. We illustrate these methodologies via simulations and the National Wilms Tumor Study data.