postcard provides tools for accurately estimating marginal effects using plug-in estimation with GLMs, including increasing precision using prognostic covariate adjustment. See Powering RCTs for marginal effects with GLMs using prognostic score adjustment by Højbjerre-Frandsen et. al (2025).

rctglm() is used to estimate marginal effects. See introductory examples of its usage in vignette("postcard") and more details in vignette("model-fit").

Marginal effects are causal effects of the form $r(\Psi_1, \Psi_0)$, where $\Psi_a=\mathbb{E}[Y(a)]$ are population mean outcomes under exposure $a=0, 1$, respectively, and $r$ is the estimand (function). $\Psi_a$ are sometimes referred to as counterfactual means. The package uses plug-in estimation for robust estimation of any marginal effect estimand as well as influence functions for robust estimation of the variance of the estimand (Rosenblum, M. and M. J. van der Laan, 2010: Simple, efficient estimators of treatment effects in randomized trials using generalized linear models to leverage baseline variables. The International Journal of Biostatistics, 6, no. 1).

rctglm_with_prognosticscore() is used to estimate marginal effects including the use of prognostic covariate adjustment. See introductory examples of its usage in vignette("postcard") and more details in vignette("model-fit").

Prognostic covariate adjustment involves training a prognostic model on historical data to predict the response in that data. Assuming that the historical data is representative of the comparator group in a “new” data set, we can use the prognostic model to predict the comparator counterfactual outcome for all observations (including the ones in the comparator group). This prediction, which is called the prognostic score, is then used as an adjustment covariate in the GLM.

Implementations of sample size/power approximation formulas are available, enabling retrospective power analyses to be performed using the package.

Introductory examples are available in vignette("postcard") and more details in vignette("prospective-power").

A method of estimating power in any case of estimating marginal effects is described in the reference at the top of this page, and the algorithm is implemented in the function power_marginaleffect.

Functionalities available to estimate the power for linear models include functions variance_ancova, power_gs, samplesize_gs, power_nc.

To install the package:

install.packages("postcard")

# Development version:
# install.packages("pak")
pak::pak("NovoNordisk-OpenSource/postcard")