Estimating the variance of covariate-adjusted estimators of average treatment effects in clinical trials with binary endpoints

Covariate-adjusted estimators of average treatment effects in clinical trials are typically more efficient than unadjusted estimators. Recent guidance from the FDA is highly detailed regarding the appropriate use of covariate adjustment for point estimation. Less direction is provided, however, on how to estimate the variance of such estimators. In this paper, we demonstrate that a precise description of the estimand is necessary to avoid ambiguity when comparing variance estimators for average treatment effects involving binary endpoints. When considering the suitability of a proposed estimand, together with a corresponding variance estimator, it is important to consider that the patients enrolled in clinical trials are typically a convenience sample. Since there is no unique way to map this process into formal statistical assumptions, it follows that a range of estimands, and therefore a range of variance estimators, may be acceptable. We aim to highlight through simulation results how the properties of proposed variance estimators differ, as well as the underlying reasons.