Powering RCTs for marginal effects with GLMs using prognostic score adjustment

In randomized clinical trials (RCTs), the accurate estimation of marginal treatment effects is crucial for determining the efficacy of interventions. Enhancing the statistical power of these analyses is a key objective for statisticians. The increasing availability of historical data from registries, prior trials, and health records presents an opportunity to improve trial efficiency. However, many methods for historical borrowing compromise strict type-I error rate control. Building on the work by Schuler et al. [2022] on prognostic score adjustment for linear models, this paper extends the methodology to the plug-in analysis proposed by Rosenblum et al. [2010] using generalized linear models (GLMs) to further enhance the efficiency of RCT analyses without introducing bias. Specifically, we train a prognostic model on historical control data and incorporate the resulting prognostic scores as covariates in the plug-in GLM analysis of the trial data. This approach leverages the predictive power of historical data to improve the precision of marginal treatment effect estimates. We demonstrate that this method achieves local semi-parametric efficiency under the assumption of an additive treatment effect on the link scale. We expand the GLM plug-in method to include negative binomial regression. Additionally, we provide a straightforward formula for conservatively estimating the asymptotic variance, facilitating power calculations that reflect these efficiency gains. Our simulation study supports the theory. Even without an additive treatment effect, we observe increased power or reduced standard error. While population shifts from historical to trial data may dilute benefits, they do not introduce bias.

💡 Research Summary

This paper develops a practical method for improving the efficiency of randomized clinical trials (RCTs) when estimating marginal treatment effects, by incorporating a prognostic score derived from historical control data into the generalized linear model (GLM) plug‑in estimator originally proposed by Rosenblum and van der Laan (2010). The authors build on Schuler et al. (2022), who showed that adjusting for a prognostic score in linear models yields locally semiparametric efficiency for the average treatment effect (ATE). Here, the same idea is extended to the broader class of GLMs—including logistic, Poisson, and, importantly, negative‑binomial regression—so that a wide range of clinical endpoints (binary, count, continuous) can benefit.

The methodological workflow is as follows. First, a prognostic model is trained on external control data to predict the conditional mean outcome under control, ( \mu_0(W)=E