Robustness of ANCOVA in randomized trials with unequal randomization

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Analysis of covariance (ANCOVA) is frequently employed in randomized trials to analyze continuous outcomes, adjusting for baseline covariates.
• The ANCOVA estimator for treatment effects is known to be consistent, even with model misspecification.
• Previous work suggested that model-based variance estimators are also consistent under outcome model misspecification when randomization probability is 1/2.

Purpose of the Study:

• To investigate the validity of model-based variance estimators in the presence of unequal randomization probabilities.
• To compare the performance of model-based variance estimators with robust sandwich variance estimators under model misspecification.

Main Methods:

• Derivation of explicit mathematical expressions to analyze the bias of model-based variance estimators.
• Theoretical comparison of model-based and robust sandwich variance estimators.
• Focus on scenarios with unequal randomization probabilities in continuous outcome trials.

Main Results:

• Model-based variance estimators can exhibit upward or downward bias when randomization probabilities are unequal.
• This bias contrasts with the consistency of the ANCOVA treatment effect estimator itself.
• Robust sandwich variance estimators demonstrate asymptotic validity irrespective of randomization probabilities or model misspecification.

Conclusions:

• Reliance on model-based variance estimators in ANCOVA may lead to inaccurate inferences when randomization is unequal.
• Robust sandwich variance estimators offer a more reliable approach for variance estimation in such settings.
• Researchers should consider using robust variance estimators to ensure valid statistical inferences in randomized trials with unequal randomization.