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Semiparametric estimation of treatment effects given base-line covariates on an outcome measured after a post-randomization event occurs

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  • Yannis Jemiai
  • Andrea Rotnitzky
  • Bryan E. Shepherd
  • Peter B. Gilbert

Abstract

We consider estimation, from a double-blind randomized trial, of treatment effect within levels of base-line covariates on an outcome that is measured after a post-treatment event E has occurred in the subpopulation P E,E that would experience event E regardless of treatment. Specifically, we consider estimation of the parameters "&ggr;" indexing models for the outcome mean conditional on treatment and base-line covariates in the subpopulation P E,E . Such parameters are not identified from randomized trial data but become identified if additionally it is assumed that the subpopulation P E , E of subjects that would experience event E under the second treatment but not under the first is empty and a parametric model for the conditional probability that a subject experiences event E if assigned to the first treatment given that the subject would experience the event if assigned to the second treatment, his or her outcome under the second treatment and his or her pretreatment covariates. We develop a class of estimating equations whose solutions comprise, up to asymptotic equivalence, all consistent and asymptotically normal estimators of "&ggr;" under these two assumptions. In addition, we derive a locally semiparametric efficient estimator of "&ggr;". We apply our methods to estimate the effect on mean viral load of vaccine "versus" placebo after infection with human immunodeficiency virus (the event E ) in a placebo-controlled randomized acquired immune deficiency syndrome vaccine trial. Copyright 2007 Royal Statistical Society.

Suggested Citation

  • Yannis Jemiai & Andrea Rotnitzky & Bryan E. Shepherd & Peter B. Gilbert, 2007. "Semiparametric estimation of treatment effects given base-line covariates on an outcome measured after a post-randomization event occurs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 879-901.
  • Handle: RePEc:bla:jorssb:v:69:y:2007:i:5:p:879-901
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    References listed on IDEAS

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    1. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    2. Peter B. Gilbert & Ronald J. Bosch & Michael G. Hudgens, 2003. "Sensitivity Analysis for the Assessment of Causal Vaccine Effects on Viral Load in HIV Vaccine Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 531-541, September.
    3. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    4. Junni L. Zhang & Donald B. Rubin, 2003. "Estimation of Causal Effects via Principal Stratification When Some Outcomes are Truncated by “Deathâ€," Journal of Educational and Behavioral Statistics, , vol. 28(4), pages 353-368, December.
    5. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    6. Douglas Hayden & Donna K. Pauler & David Schoenfeld, 2005. "An Estimator for Treatment Comparisons among Survivors in Randomized Trials," Biometrics, The International Biometric Society, vol. 61(1), pages 305-310, March.
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    Cited by:

    1. Gilbert Peter B. & Hudgens Michael G. & Wolfson Julian, 2011. "Commentary on "Principal Stratification -- a Goal or a Tool?" by Judea Pearl," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-15, September.
    2. Halloran M. Elizabeth & Hudgens Michael G., 2012. "Causal Inference for Vaccine Effects on Infectiousness," The International Journal of Biostatistics, De Gruyter, vol. 8(2), pages 1-40, January.
    3. Arvid Sjölander & Keith Humphreys & Stijn Vansteelandt & Rino Bellocco & Juni Palmgren, 2009. "Sensitivity Analysis for Principal Stratum Direct Effects, with an Application to a Study of Physical Activity and Coronary Heart Disease," Biometrics, The International Biometric Society, vol. 65(2), pages 514-520, June.
    4. Sjolander Arvid & Vansteelandt Stijn & Humphreys Keith, 2010. "A Principal Stratification Approach to Assess the Differences in Prognosis between Cancers Caused by Hormone Replacement Therapy and by Other Factors," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-37, June.
    5. VanderWeele Tyler J, 2011. "Principal Stratification -- Uses and Limitations," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-14, July.
    6. Sandra García & Jennifer Hill, 2009. "The Impact of Conditional Cash Transfers on Children´s School Achievement: Evidence from Colombia," DOCUMENTOS CEDE 005403, UNIVERSIDAD DE LOS ANDES-CEDE.

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