Simple, efficient estimators of treatment effects in randomized trials using generalized linear models to leverage...

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Statistical Modeling

Background:

• Regression models like logistic and Poisson regression are common for estimating treatment effects in randomized trials.
• These models utilize pre-randomization variables to enhance the precision of treatment effect estimates.
• A significant risk in using these models is potential bias arising from model misspecification.

Purpose of the Study:

• To demonstrate that specific model-based estimators are asymptotically unbiased, even with arbitrary model misspecification.
• To highlight the local efficiency of these robust estimators.
• To present a special case involving a Poisson working model, analogous to ANCOVA in linear models.

Main Methods:

• The study focuses on developing and analyzing model-based estimators.
• Asymptotic properties of these estimators are investigated under conditions of model misspecification.
• Targeted maximum likelihood estimation (TMLE) principles are applied.

Main Results:

• Certain easily computable, model-based estimators are shown to be asymptotically unbiased regardless of model misspecification.
• These estimators are also demonstrated to be locally efficient.
• For a simple Poisson model, the maximum likelihood estimate of the treatment coefficient is proven to be an asymptotically unbiased estimator of the marginal log rate ratio, even if the model is misspecified.

Conclusions:

• The findings offer a method for obtaining reliable treatment effect estimates in randomized trials, mitigating concerns about model misspecification.
• This work showcases a practical application of targeted maximum likelihood estimation in biostatistics.
• The results provide a robust statistical framework for analyzing trial data where model assumptions may not hold perfectly.