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Robust Covariate Adjustment in Multi-Center Randomized Trials

Muluneh Alene, Stijn Vansteelandt, Kelly Van Lancker

Abstract

Augmented inverse probability weighting and G-computation with canonical generalized linear models have become increasingly popular for estimating average treatment effects (ATEs) in randomized experiments. These methods leverage outcome prediction models to adjust for imbalances in baseline covariates across treatment arms, improving power compared to unadjusted analyses, while controlling Type I error, even when models are misspecified. In multi-center trials they are often implemented without accounting for clustering by centers. We investigate how ignoring center-level correlation can impair estimation, degrade coverage of confidence intervals, and obscure interpretation. We find these issues to be especially acute for estimators of counterfactual means, as shown through simulations and clarified via theoretical arguments. To address these challenges, we develop semiparametric efficient estimators of counterfactual means and ATE defined for a randomly sampled center and patient. These estimators leverage outcome prediction models to improve efficiency yet retain large-sample unbiasedness under model misspecification. We further introduce an inference framework, inspired by random-effects meta-analysis, tailored to settings with many small centers. Incorporating center effects into the prediction models yields substantial efficiency gains, particularly when treatment effects vary across centers. Simulations and application to the WASH Benefits Bangladesh trial illustrate strong finite-sample performance of the proposed methods.

Robust Covariate Adjustment in Multi-Center Randomized Trials

Abstract

Augmented inverse probability weighting and G-computation with canonical generalized linear models have become increasingly popular for estimating average treatment effects (ATEs) in randomized experiments. These methods leverage outcome prediction models to adjust for imbalances in baseline covariates across treatment arms, improving power compared to unadjusted analyses, while controlling Type I error, even when models are misspecified. In multi-center trials they are often implemented without accounting for clustering by centers. We investigate how ignoring center-level correlation can impair estimation, degrade coverage of confidence intervals, and obscure interpretation. We find these issues to be especially acute for estimators of counterfactual means, as shown through simulations and clarified via theoretical arguments. To address these challenges, we develop semiparametric efficient estimators of counterfactual means and ATE defined for a randomly sampled center and patient. These estimators leverage outcome prediction models to improve efficiency yet retain large-sample unbiasedness under model misspecification. We further introduce an inference framework, inspired by random-effects meta-analysis, tailored to settings with many small centers. Incorporating center effects into the prediction models yields substantial efficiency gains, particularly when treatment effects vary across centers. Simulations and application to the WASH Benefits Bangladesh trial illustrate strong finite-sample performance of the proposed methods.

Paper Structure

This paper contains 28 sections, 79 equations, 2 figures, 30 tables.

Table of Contents

  1. Introduction
  2. Estimation
  3. Notation
  4. "Naïve" approach
  5. Proposed approach
  6. Inference
  7. Simulation studies
  8. Data-generating mechanisms
  9. Estimators
  10. Results
  11. Data analysis
  12. Data description
  13. Estimators
  14. Results
  15. Discussion
  16. ...and 13 more sections

Figures (2)

  • Figure B.1.1: Distribution of the number of patients per center across simulation settings.
  • Figure B.2.2: Number of children per center in each intervention group for each outcome. A: WSH intervention with length-for-age Z-score outcome; B: WSH+N intervention with length-for-age Z-score outcome; C: WSH intervention with diarrhoea prevalence outcome, and D: WSH+N intervention with diarrhoea prevalence outcome.