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An instrumental variable procedure for estimating Cox models with non‐proportional hazards in the presence of unmeasured confounding

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  • Pablo Martínez‐Camblor
  • Todd A. MacKenzie
  • Douglas O. Staiger
  • Phillip P. Goodney
  • A. James O’Malley

Abstract

Two‐stage instrumental variable methods are commonly used for estimating average causal effects in the presence of an unmeasured confounder. In the context of the proportional hazard Cox regression models, this problem has recently received attention with several methods being proposed. Previously, we developed an improved estimator under the incumbent two‐stage residual inclusion procedure called ‘2SRI’ by adding a Gaussian frailty in the second stage. We now consider the more complex situation in which the treatment and the unmeasured confounders can have time varying effects, illustrating the method with the case of a step function with one prespecified change point. We prove that, in situations where the effects of the unmeasured confounder or the treatment change during the follow‐up, the first stage of the 2SRI algorithm induces a frailty with time varying coefficients in the second stage, which enables incumbent methods and our previously developed procedure to be improved on. A Monte Carlo simulation study demonstrates the superior performance of the proposed extension of 2SRI that we develop. We apply the new procedure to estimate the effect of endarterectomy versus carotid artery stenting on the time to death of patients suffering from carotid artery disease by using linked vascular quality initiative registry–Medicare data.

Suggested Citation

  • Pablo Martínez‐Camblor & Todd A. MacKenzie & Douglas O. Staiger & Phillip P. Goodney & A. James O’Malley, 2019. "An instrumental variable procedure for estimating Cox models with non‐proportional hazards in the presence of unmeasured confounding," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(4), pages 985-1005, August.
  • Handle: RePEc:bla:jorssc:v:68:y:2019:i:4:p:985-1005
    DOI: 10.1111/rssc.12341
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    Cited by:

    1. Pablo Martínez-Camblor, 2022. "Learning the Treatment Impact on Time-to-Event Outcomes: The Transcarotid Artery Revascularization Simulated Cohort," IJERPH, MDPI, vol. 19(19), pages 1-12, September.
    2. Linbo Wang & Eric Tchetgen Tchetgen & Torben Martinussen & Stijn Vansteelandt, 2023. "Instrumental variable estimation of the causal hazard ratio," Biometrics, The International Biometric Society, vol. 79(2), pages 539-550, June.
    3. Gruber, Jonathan & Lin, Mengyun & Yi, Junjian, 2023. "The largest insurance program in history: Saving one million lives per year in China," Journal of Public Economics, Elsevier, vol. 226(C).

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