Average treatment effects on binary outcomes with stochastic covariates

When evaluating the effect of psychological treatments on a dichotomous outcome variable in a randomized controlled trial (RCT), covariate adjustment using logistic regression models is often applied. In the presence of covariates, average marginal effects (AMEs) are often preferred over odds ratios, as AMEs yield a clearer substantive and causal interpretation. However, standard error computation of AMEs neglects sampling-based uncertainty (i.e., covariate values are assumed to be fixed over repeated sampling), which leads to underestimation of AME standard errors in other generalized linear models (e.g., Poisson regression). In this paper, we present and compare approaches allowing for stochastic (i.e., randomly sampled) covariates in models for binary outcomes. In a simulation study, we investigated the quality of the AME and stochastic-covariate approaches focusing on statistical inference in finite samples. Our results indicate that the fixed-covariate approach provides reliable results only if there is no heterogeneity in interindividual treatment effects (i.e., presence of treatment-covariate interactions), while the stochastic-covariate approaches are preferable in all other simulated conditions. We provide an illustrative example from clinical psychology investigating the effect of a cognitive bias modification training on post-traumatic stress disorder while accounting for patients' anxiety using an RCT.