Variance estimation for logistic regression in case-cohort studies

The logistic regression analysis proposed by Schouten et al. (Stat Med. 1993;12:1733-1745) has been one of the standard methods in current statistical analysis of case-cohort studies, and it enables effective estimation of risk ratios from the selected subsamples with adjusting potential confounding factors. A remarkable advantage of their method is that the computation can be easily implemented using statistical packages for logistic regression analysis (e.g., glm in R). In this article, however, we show that their robust variance estimator does not account for the duplications of case and subcohort samples, and has generally overestimation bias. We also provide an alternative bootstrap-based consistent variance estimator. Through simulation studies, the bootstrap method provided more precise confidence intervals compared with the robust variance method with retaining the adequate coverage probabilities, consistently.