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On doubly robust estimation of the hazard difference

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  • Oliver Dukes
  • Torben Martinussen
  • Eric J. Tchetgen Tchetgen
  • Stijn Vansteelandt

Abstract

The estimation of conditional treatment effects in an observational study with a survival outcome typically involves fitting a hazards regression model adjusted for a high‐dimensional covariate. Standard estimation of the treatment effect is then not entirely satisfactory, as the misspecification of the effect of this covariate may induce a large bias. Such misspecification is a particular concern when inferring the hazard difference, because it is difficult to postulate additive hazards models that guarantee non‐negative hazards over the entire observed covariate range. We therefore consider a novel class of semiparametric additive hazards models which leave the effects of covariates unspecified. The efficient score under this model is derived. We then propose two different estimation approaches for the hazard difference (and hence also the relative chance of survival), both of which yield estimators that are doubly robust. The approaches are illustrated using simulation studies and data on right heart catheterization and mortality from the SUPPORT study.

Suggested Citation

  • Oliver Dukes & Torben Martinussen & Eric J. Tchetgen Tchetgen & Stijn Vansteelandt, 2019. "On doubly robust estimation of the hazard difference," Biometrics, The International Biometric Society, vol. 75(1), pages 100-109, March.
    • Handle: RePEc:bla:biomet:v:75:y:2019:i:1:p:100-109
    DOI: 10.1111/biom.12943
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    References listed on IDEAS

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    1. Daniel O. Scharfstein, 2002. "Estimation of the failure time distribution in the presence of informative censoring," Biometrika, Biometrika Trust, vol. 89(3), pages 617-634, August.
    2. Sally Picciotto & Miguel A. Hernán & John H. Page & Jessica G. Young & James M. Robins, 2012. "Structural Nested Cumulative Failure Time Models to Estimate the Effects of Interventions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 886-900, September.
    3. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    4. Eric J. Tchetgen Tchetgen & James M. Robins & Andrea Rotnitzky, 2010. "On doubly robust estimation in a semiparametric odds ratio model," Biometrika, Biometrika Trust, vol. 97(1), pages 171-180.
    5. S. Vansteelandt & T. Martinussen & E. J. Tchetgen Tchetgen, 2014. "On adjustment for auxiliary covariates in additive hazard models for the analysis of randomized experiments," Biometrika, Biometrika Trust, vol. 101(1), pages 237-244.
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    Cited by:

    1. Shaun Seaman & Oliver Dukes & Ruth Keogh & Stijn Vansteelandt, 2020. "Adjusting for time‐varying confounders in survival analysis using structural nested cumulative survival time models," Biometrics, The International Biometric Society, vol. 76(2), pages 472-483, June.
    2. Kara E. Rudolph & Nicholas Williams & Iván Díaz, 2023. "Efficient and flexible estimation of natural direct and indirect effects under intermediate confounding and monotonicity constraints," Biometrics, The International Biometric Society, vol. 79(4), pages 3126-3139, December.

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