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

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  • Rosenblum Michael

    (Johns Hopkins University)

  • van der Laan Mark J.

    (University of California, Berkeley)

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.

Suggested Citation

  • Rosenblum Michael & van der Laan Mark J., 2010. "Simple, Efficient Estimators of Treatment Effects in Randomized Trials Using Generalized Linear Models to Leverage Baseline Variables," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-44, April.
    • Handle: RePEc:bpj:ijbist:v:6:y:2010:i:1:n:13
    DOI: 10.2202/1557-4679.1138
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    References listed on IDEAS

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    1. van der Laan Mark J. & Dudoit Sandrine & Keles Sunduz, 2004. "Asymptotic Optimality of Likelihood-Based Cross-Validation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-25, March.
    2. Min Zhang & Anastasios A. Tsiatis & Marie Davidian, 2008. "Improving Efficiency of Inferences in Randomized Clinical Trials Using Auxiliary Covariates," Biometrics, The International Biometric Society, vol. 64(3), pages 707-715, September.
    3. Yang L. & Tsiatis A. A., 2001. "Efficiency Study of Estimators for a Treatment Effect in a Pretest-Posttest Trial," The American Statistician, American Statistical Association, vol. 55, pages 314-321, November.
    4. Rubin Daniel B & van der Laan Mark J., 2008. "Empirical Efficiency Maximization: Improved Locally Efficient Covariate Adjustment in Randomized Experiments and Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-42, May.
    5. Michael Rosenblum & Mark J. van der Laan, 2009. "Using Regression Models to Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models," Biometrics, The International Biometric Society, vol. 65(3), pages 937-945, September.
    6. Selene Leon & Anastasios A. Tsiatis & Marie Davidian, 2003. "Semiparametric Estimation of Treatment Effect in a Pretest-Posttest Study," Biometrics, The International Biometric Society, vol. 59(4), pages 1046-1055, December.
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    Citations

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    Cited by:

    1. Zhenke Wu & Constantine E. Frangakis & Thomas A. Louis & Daniel O. Scharfstein, 2014. "Estimation of treatment effects in matched-pair cluster randomized trials by calibrating covariate imbalance between clusters," Biometrics, The International Biometric Society, vol. 70(4), pages 1014-1022, December.
    2. Wei Zhang & Zhiwei Zhang & Aiyi Liu, 2023. "Optimizing treatment allocation in randomized clinical trials by leveraging baseline covariates," Biometrics, The International Biometric Society, vol. 79(4), pages 2815-2829, December.
    3. Trang Quynh Nguyen & Elizabeth A. Stuart, 2020. "Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 598-636, October.
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    5. Rosenblum Michael & van der Laan Mark J., 2010. "Targeted Maximum Likelihood Estimation of the Parameter of a Marginal Structural Model," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-30, April.

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