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Bias formulas for violations of proximal identification assumptions in a linear structural equation model

Author

Listed:
  • Cobzaru Raluca

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, 02142 MA, United States of America)

  • Welsch Roy

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, 02142 MA, United States of America)

  • Finkelstein Stan

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, 02142 MA, United States of America)

  • Ng Kenney

    (MIT-IBM Watson AI Lab, Cambridge, 02142 MA, United States of America)

  • Shahn Zach

    (MIT-IBM Watson AI Lab, Cambridge, 02142 MA, United States of America)

Abstract

Causal inference from observational data often rests on the unverifiable assumption of no unmeasured confounding. Recently, Tchetgen Tchetgen and colleagues have introduced proximal inference to leverage negative control outcomes and exposures as proxies to adjust for bias from unmeasured confounding. However, some of the key assumptions that proximal inference relies on are themselves empirically untestable. In addition, the impact of violations of proximal inference assumptions on the bias of effect estimates is not well understood. In this article, we derive bias formulas for proximal inference estimators under a linear structural equation model. These results are a first step toward sensitivity analysis and quantitative bias analysis of proximal inference estimators. While limited to a particular family of data generating processes, our results may offer some more general insight into the behavior of proximal inference estimators.

Suggested Citation

  • Cobzaru Raluca & Welsch Roy & Finkelstein Stan & Ng Kenney & Shahn Zach, 2024. "Bias formulas for violations of proximal identification assumptions in a linear structural equation model," Journal of Causal Inference, De Gruyter, vol. 12(1), pages 1-34.
    • Handle: RePEc:bpj:causin:v:12:y:2024:i:1:p:34:n:1001
    DOI: 10.1515/jci-2023-0039
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