arXiv subjects

Emilie Højbjerre-Frandsen

Publications and source records attributed to Emilie Højbjerre-Frandsen.

5 recordsLinked to original sources

arXiv2026

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.

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arXiv2025

A Non-Parametric Sensitivity Analysis for Bounding Bias in Hybrid Control Trials

We study hybrid control trials (HCTs), in which a randomized controlled trial (RCT) is augmented with external control patients. Existing approaches for HCTs typically assume conditional exchangeability of the concurrent and external controls to identify trial-specific effects. When violated, this can induce substantial unquantified bias, which in turn limits the acceptability of HCTs in regulatory settings. We treat violations of mean exchangeability as omitted variable bias and develop a non-parametric sensitivity analysis that (i) applies to the efficient, doubly robust HCT estimator of the trial-specific ATE, and (ii) delivers sharp bounds on the bias induced by unmeasured covariates. Building on recent work in double machine learning, our approach characterizes the maximal bias in terms of two partial R-squared sensitivity parameters: the additional explanatory power that unmeasured confounders could have for the outcome regression and for trial participation. For any given choice of these parameters, we construct valid confidence bounds for bias-adjusted treatment effects and visualize critical causal gaps via contour plots and robustness values that show how strong unmeasured confounding would need to be to overturn nominally significant HCT findings. Through simulations, we show that the method (i) reliably upper-bounds true bias, (ii) restores type I error control in settings where naïve HCT analysis is anti-conservative, and (iii) can still deliver meaningful power gains and RCT sample-size reductions even under moderate violations of mean exchangeability. We illustrate the approach in a phase III trial on diabetes, supplemented with external controls. We discuss practical guidelines for designing and evaluating HCTs, including external-data selection, sample-size allocation, and interpretation of sensitivity contours.

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arXiv2025

"Within-trial" prognostic score adjustment is targeted maximum likelihood estimation

Adjustment for ``super'' or ``prognostic'' composite covariates has become more popular in randomized trials recently. These prognostic covariates are often constructed from historical data by fitting a predictive model of the outcome on the raw covariates. A natural question that we have been asked by applied researchers is whether this can be done without the historical data: can the prognostic covariate be constructed or derived from the trial data itself, possibly using different folds of the data, before adjusting for it? Here we clarify that such ``within-trial'' prognostic adjustment is nothing more than a form of targeted maximum likelihood estimation (TMLE), a well-studied procedure for optimal inference. We demonstrate the equivalence with a simulation study and discuss the pros and cons of within-trial prognostic adjustment (standard efficient estimation) relative to standard TMLE and standard prognostic adjustment with historical data.

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arXiv2025

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

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 Højbjerre-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, Højbjerre-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.

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arXiv2023

Prognostic Adjustment with Efficient Estimators to Unbiasedly Leverage Historical Data in Randomized Trials

Although randomized controlled trials (RCTs) are a cornerstone of comparative effectiveness, they typically have much smaller sample size than observational studies because of financial and ethical considerations. Therefore there is interest in using plentiful historical data (either observational data or prior trials) to reduce trial sizes. Previous estimators developed for this purpose rely on unrealistic assumptions, without which the added data can bias the treatment effect estimate. Recent work proposed an alternative method (prognostic covariate adjustment) that imposes no additional assumptions and increases efficiency in trial analyses. The idea is to use historical data to learn a prognostic model: a regression of the outcome onto the covariates. The predictions from this model, generated from the RCT subjects' baseline variables, are then used as a covariate in a linear regression analysis of the trial data. In this work, we extend prognostic adjustment to trial analyses with nonparametric efficient estimators, which are more powerful than linear regression. We provide theory that explains why prognostic adjustment improves small-sample point estimation and inference without any possibility of bias. Simulations corroborate the theory: efficient estimators using prognostic adjustment compared to without provides greater power (i.e., smaller standard errors) when the trial is small. Population shifts between historical and trial data attenuate benefits but do not introduce bias. We showcase our estimator using clinical trial data provided by Novo Nordisk A/S that evaluates insulin therapy for individuals with type II diabetes.

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