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

Michael Aaron Rosenblum, Mark J. Van Der Laan

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number13
JournalThe international journal of biostatistics
Volume6
Issue number1
DOIs
StatePublished - 2010

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Likelihood Functions
Randomized Trial
Efficient Estimator
Generalized Linear Model
Treatment Effects
Random Allocation
Leverage
Baseline
Linear Models
Logistic Models
Estimator
Analysis of Covariance
Poisson Regression
Model Misspecification
Model
Unbiased estimator
Poisson Model
Logistic Regression
Randomisation
Maximum Likelihood Estimate

Keywords

  • Generalized linear model
  • Misspecified model
  • Poisson regression
  • Targeted maximum likelihood

ASJC Scopus subject areas

  • Medicine(all)
  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

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