Using instrumental variables to estimate a Cox’s proportional hazards regression subject to additive confounding

  • Todd A. MacKenzie
  • Tor D. Tosteson
  • Nancy E. Morden
  • Therese A. Stukel
  • A. James O’Malley


The estimation of treatment effects is one of the primary goals of statistics in medicine. Estimation based on observational studies is subject to confounding. Statistical methods for controlling bias due to confounding include regression adjustment, propensity scores and inverse probability weighted estimators. These methods require that all confounders are recorded in the data. The method of instrumental variables (IVs) can eliminate bias in observational studies even in the absence of information on confounders. We propose a method for integrating IVs within the framework of Cox’s proportional hazards model and demonstrate the conditions under which it recovers the causal effect of treatment. The methodology is based on the approximate orthogonality of an instrument with unobserved confounders among those at risk. We derive an estimator as the solution to an estimating equation that resembles the score equation of the partial likelihood in much the same way as the traditional IV estimator resembles the normal equations. To justify this IV estimator for a Cox model we perform simulations to evaluate its operating characteristics. Finally, we apply the estimator to an observational study of the effect of coronary catheterization on survival.


Cox survival model Hazard ratio IV Comparative effectiveness Method-of-moments Omitted confounder 



A. James O’Malley’s research that contributed to this paper was supported by NIH Grant 1RC4MH092717-01. The authors have no conflicts of interest to report.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Todd A. MacKenzie
    • 1
  • Tor D. Tosteson
    • 1
  • Nancy E. Morden
    • 1
  • Therese A. Stukel
    • 2
  • A. James O’Malley
    • 1
  1. 1.Geisel School of Medicine at DartmouthHanoverUSA
  2. 2.Institute for Clinical Evaluative SciencesTorontoCanada

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