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The International Journal of Biostatistics

Ed. by Chambaz, Antoine / Hubbard, Alan E. / van der Laan, Mark J.

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

Michael Rosenblum / Mark J. van der Laan
Published Online: 2010-04-01 | DOI: https://doi.org/10.2202/1557-4679.1138

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: misspecified model; targeted maximum likelihood; generalized linear model; Poisson regression

About the article

Published Online: 2010-04-01

Citation Information: The International Journal of Biostatistics, Volume 6, Issue 1, ISSN (Online) 1557-4679, DOI: https://doi.org/10.2202/1557-4679.1138.

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