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Ensuring valid inference for Cox hazard ratios after variable selection

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  • Kelly Van Lancker
  • Oliver Dukes
  • Stijn Vansteelandt

Abstract

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference. A major drawback of routine procedures is that there is no finite sample size at which they are guaranteed to deliver exposure effect estimators and associated confidence intervals with adequate performance. In this work, we will consider this problem when inferring conditional causal hazard ratios from observational studies under the assumption of no unmeasured confounding. The major complication that we face with survival data is that the key confounding variables may not be those that explain the censoring mechanism. In this paper, we overcome this problem using a novel and simple procedure that can be implemented using off‐the‐shelf software for penalized Cox regression. In particular, we will propose tests of the null hypothesis that the exposure has no effect on the considered survival endpoint, which are uniformly valid under standard sparsity conditions. Simulation results show that the proposed methods yield valid inferences even when covariates are high‐dimensional.

Suggested Citation

  • Kelly Van Lancker & Oliver Dukes & Stijn Vansteelandt, 2023. "Ensuring valid inference for Cox hazard ratios after variable selection," Biometrics, The International Biometric Society, vol. 79(4), pages 3096-3110, December.
  • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3096-3110
    DOI: 10.1111/biom.13889
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    References listed on IDEAS

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    1. Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2016. "Post-Selection Inference for Generalized Linear Models With Many Controls," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 606-619, October.
    2. Ethan X. Fang & Yang Ning & Han Liu, 2017. "Testing and confidence intervals for high dimensional proportional hazards models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1415-1437, November.
    3. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    4. Stijn Vansteelandt & Oliver Dukes, 2022. "Assumption‐lean inference for generalised linear model parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 657-685, July.
    5. Wenjiang J. Fu, 2003. "Penalized Estimating Equations," Biometrics, The International Biometric Society, vol. 59(1), pages 126-132, March.
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