Alternative sensitivity analyses for regression estimates of treatment effects to unobserved confounding in binary and survival data

Byeong Yeob Choi, Jason P. Fine, Roman Fernandez, M. Alan Brookhart

Research output: Contribution to journalArticlepeer-review


Estimates of treatment effects in non-experimental studies are subject to bias owing to unobserved confounding. It is desirable to assess the sensitivity of an estimated treatment effect to a hypothetical unmeasured confounder, U. A commonly used approach to sensitivity analysis requires two parameters: one parameter relates U to the treatment and the other relates it to the outcome. The method uses a simple algebraic formula with these two parameters to relate the true treatment effect to the apparent treatment effect, obtained from a reduced model without U. This formula approximately holds for logistic and proportional hazards models, which are frequently used to model binary and survival outcomes. This approximation works with an assumption that the absolute regression coefficient for the unmeasured confounder is small. Therefore, when the unmeasured confounding is relatively large, the formula will not perform well. In this article, we propose alternative sensitivity analysis methods for binary and survival outcomes. We develop sensitivity analysis formulas for treatment effect estimates under probit and additive hazard models, which are alternatives to the logistic and proportional hazards models, respectively. The proposed formulae hold without any approximations. We also discuss a method to postulate reasonable values of the sensitivity parameters using the observed covariates. Simulation studies demonstrate that the proposed formulae perform well for moderate and severe unmeasured confounding even when the model used for the sensitivity analysis is moderately mis-specified. The practical utility of the approach is illustrated in two example studies.

Original languageEnglish (US)
Pages (from-to)637-659
Number of pages23
JournalStatistical Methods and Applications
Issue number3
StatePublished - Sep 2022


  • Additive hazard model
  • Probit regression
  • Sensitivity analysis
  • Treatment effect
  • Unmeasured confounding

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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