IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v6y2010i1n13.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1557-4679.1138
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1557-4679.1138?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    4. 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.
    5. Katie Potter & Brittany Masteller & Laura B. Balzer, 2021. "Examining Obedience Training as a Physical Activity Intervention for Dog Owners: Findings from the Stealth Pet Obedience Training (SPOT) Pilot Study," IJERPH, MDPI, vol. 18(3), pages 1-11, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Benkeser & Iván Díaz & Alex Luedtke & Jodi Segal & Daniel Scharfstein & Michael Rosenblum, 2021. "Improving precision and power in randomized trials for COVID‐19 treatments using covariate adjustment, for binary, ordinal, and time‐to‐event outcomes," Biometrics, The International Biometric Society, vol. 77(4), pages 1467-1481, December.
    2. Nicholas Williams & Michael Rosenblum & Iván Díaz, 2022. "Optimising precision and power by machine learning in randomised trials with ordinal and time‐to‐event outcomes with an application to COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2156-2178, October.
    3. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    4. van der Laan Mark J., 2010. "Targeted Maximum Likelihood Based Causal Inference: Part I," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-45, February.
    5. van der Laan Mark J. & Gruber Susan, 2010. "Collaborative Double Robust Targeted Maximum Likelihood Estimation," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-71, May.
    6. Yuanyuan Shen & Tianxi Cai, 2016. "Identifying predictive markers for personalized treatment selection," Biometrics, The International Biometric Society, vol. 72(4), pages 1017-1025, December.
    7. 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.
    8. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 235-260, June.
    9. Jitendra Ganju, 2004. "Some Unexamined Aspects of Analysis of Covariance in Pretest–Posttest Studies," Biometrics, The International Biometric Society, vol. 60(3), pages 829-833, September.
    10. Bruce Desmarais, 2012. "Lessons in disguise: multivariate predictive mistakes in collective choice models," Public Choice, Springer, vol. 151(3), pages 719-737, June.
    11. Undral Byambadalai & Tatsushi Oka & Shota Yasui, 2024. "Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction," Papers 2407.16037, arXiv.org.
    12. Paul Frédéric Blanche & Anders Holt & Thomas Scheike, 2023. "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 441-482, April.
    13. Michael Rosenblum & Mark J. van der Laan, 2013. "Rejoinder to “A Note on Using Regression Models to Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models”," Biometrics, The International Biometric Society, vol. 69(1), pages 290-290, March.
    14. Stitelman Ori M & van der Laan Mark J., 2010. "Collaborative Targeted Maximum Likelihood for Time to Event Data," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-46, June.
    15. Hennessy Jonathan & Dasgupta Tirthankar & Miratrix Luke & Pattanayak Cassandra & Sarkar Pradipta, 2016. "A Conditional Randomization Test to Account for Covariate Imbalance in Randomized Experiments," Journal of Causal Inference, De Gruyter, vol. 4(1), pages 61-80, March.
    16. Pierre Chausse & George Luta, 2017. "Casual Inference using Generalized Empirical Likelihood Methods," Working Papers 1707, University of Waterloo, Department of Economics, revised Dec 2017.
    17. Lola Etievant & Joshua N. Sampson & Mitchell H. Gail, 2023. "Increasing efficiency and reducing bias when assessing HPV vaccination efficacy by using nontargeted HPV strains," Biometrics, The International Biometric Society, vol. 79(2), pages 1534-1545, June.
    18. Jiang, Liang & Phillips, Peter C.B. & Tao, Yubo & Zhang, Yichong, 2023. "Regression-adjusted estimation of quantile treatment effects under covariate-adaptive randomizations," Journal of Econometrics, Elsevier, vol. 234(2), pages 758-776.
    19. Tianchen Qian & Constantine Frangakis & Constantin Yiannoutsos, 2020. "Deductive Semiparametric Estimation in Double-Sampling Designs with Application to PEPFAR," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 417-445, December.
    20. Arafat Tayeb & Aurélie Labbe & Alexandre Bureau & Chantal Mérette, 2011. "Solving genetic heterogeneity in extended families by identifying sub-types of complex diseases," Computational Statistics, Springer, vol. 26(3), pages 539-560, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:ijbist:v:6:y:2010:i:1:n:13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.