Robust variance estimators for risk ratio estimators from logistic regression in cohort and case-cohort studies

Logistic regression with augmented pseudo-observations provides a simple and effective estimator of the log–risk ratio. Logistic regression based on the same principle has also been widely used in case–cohort designs. However, the commonly used White-type robust variance estimator treats their duplicated records as independent and is therefore asymptotically biased. In this article, we clarify the estimating-equation structure underlying such logistic regression and show that the valid sandwich variance must be constructed at the individual (cluster) level. Using Godambe’s estimating-equation theory, we derive a consistent closed-form variance estimator and analytically demonstrate the upward bias of the naïve estimator. We further provide three finite-sample–corrected estimators for the sandwich variance.