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E-value analogs for bias due to missing data in treatment effect estimates

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  • Mathur, Maya B

Abstract

Background: Complete-case analyses can be biased if missing data are not missing completely at random. Methods: We propose simple sensitivity analyses that apply to complete-case estimates of treatment effects; these analyses use only simple summary data and obviate specifying the mechanism of missingness and making distributional assumptions. Bias arises when: (1) treatment effects differ between retained and non-retained participants; or (2) among non-retained participants, the estimate is biased because conditioning on retention has induced a backdoor path. We thus bound the overall treatment effect on the difference scale by specifying: (1) the unobserved treatment effect among non-retained participants; (2) the strengths of association that unobserved variables have with the exposure and with the outcome among retained participants (``induced confounding associations''). Working with the former sensitivity parameter subsumes certain existing methods of worst-case imputation, while also accommodating less conservative assumptions (e.g., that the treatment is not detrimental even among non-retained participants). We propose analogs to the E-value for confounding that represent, for a specified treatment effect among non-retained participants, the strength of induced confounding associations required to reduce the treatment effect to the null or to any other value. Results: We apply the methods to a published randomized trial on financial incentives for smoking cessation. Conclusion: These methods could help characterize the robustness of complete-case analyses to potential bias due to missing data. The methods can also be used for general selection bias when the probability of selection is known.

Suggested Citation

  • Mathur, Maya B, 2022. "E-value analogs for bias due to missing data in treatment effect estimates," OSF Preprints e9bzc, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:e9bzc
    DOI: 10.31219/osf.io/e9bzc
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    1. Thompson Jr., R.G. & Wall, M.M. & Greenstein, E. & Grant, B.F. & Hasin, D.S., 2013. "Substance-use disorders and poverty as prospective predictors of first-time homelessness in the United States," American Journal of Public Health, American Public Health Association, vol. 103(S2), pages 282-288.
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