postcard: An R Package for Marginal Effect Estimation with or without Prognostic Score Adjustment

Abstract: Covariate adjustment is a widely used technique in randomized clinical trials (RCTs) for improving the efficiency of treatment effect estimators. By adjusting for predictive baseline covariates, variance can be reduced, enhancing statistical precision and study power. Rosenblum and van der Laan [2010] use the framework of generalized linear models (GLMs) in a plug-in analysis to show efficiency gains using covariate adjustment for marginal effect estimation. Recently the use of prognostic scores as adjustment covariates has gained popularity. Schuler et al. [2022] introduce and validate the method for continuous endpoints using linear models. Building on this work H{\o}jbjerre-Frandsen et al. [2025] extends the method proposed by Schuler et al. [2022] to be used in combination with the GLM plug-in procedure [Rosenblum and van der Laan, 2010]. This method achieves semi-parametric efficiency under assumptions of additive treatment effects on the link scale. Additionally, H{\o}jbjerre-Frandsen et al. [2025] provide a formula for power approximation which is valid even under model misspecification, enabling realistic sample size estimation. This article introduces an R package, which implements the GLM plug-in method with or without PrOgnoSTic CovARiate aDjustment, postcard. The package has two core features: (1) estimating marginal effects and the variance hereof (with or without prognostic adjustment) and (2) approximating statistical power. Functionalities also include integration of the Discrete Super Learner for constructing prognostic scores and simulation capabilities for exploring the methods in practice. Through examples and simulations, we demonstrate postcard as a practical toolkit for statisticians.