Simple, Efficient Estimators of Treatment Effects in Randomized Trials Using Generalized Linear Models to Leverage Baseline Variables

Michael Rosenblum and Mark J. van der Laan
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Michael Rosenblum: Johns Hopkins University
Mark J. van der Laan: University of California, Berkeley

The International Journal of Biostatistics, 2010, vol. 6, issue 1, pages 13

Abstract:

Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we prove the maximum likelihood estimate of the coefficient corresponding to the treatment variable is an asymptotically unbiased estimator of the marginal log rate ratio, even when the working model is arbitrarily misspecified. This is the log-linear analog of ANCOVA for linear models. Our results demonstrate one application of targeted maximum likelihood estimation.

Keywords: Clinical Trials; General Biostatistics; Statistical Models; Statistical Theory and Methods; misspecified model; targeted maximum likelihood; generalized linear model; Poisson regression (search for similar items in EconPapers)
Date: 2010
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