The Annals of Applied Statistics

The sensitivity of linear regression coefficients’ confidence limits to the omission of a confounder

Carrie A. Hosman, Ben B. Hansen, and Paul W. Holland

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Omitted variable bias can affect treatment effect estimates obtained from observational data due to the lack of random assignment to treatment groups. Sensitivity analyses adjust these estimates to quantify the impact of potential omitted variables. This paper presents methods of sensitivity analysis to adjust interval estimates of treatment effect—both the point estimate and standard error—obtained using multiple linear regression. Central to our approach is what we term benchmarking, the use of data to establish reference points for speculation about omitted confounders. The method adapts to treatment effects that may differ by subgroup, to scenarios involving omission of multiple variables, and to combinations of covariance adjustment with propensity score stratification. We illustrate it using data from an influential study of health outcomes of patients admitted to critical care.

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Ann. Appl. Stat., Volume 4, Number 2 (2010), 849-870.

First available in Project Euclid: 3 August 2010

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Causal inference hidden bias observational study


Hosman, Carrie A.; Hansen, Ben B.; Holland, Paul W. The sensitivity of linear regression coefficients’ confidence limits to the omission of a confounder. Ann. Appl. Stat. 4 (2010), no. 2, 849--870. doi:10.1214/09-AOAS315.

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Supplemental materials

  • Supplementary material: Code for computations discussed in the article. Zip archive containing our documented R code and instructions for obtaining Connors et al.’s data, in the form of a Sweave and a corresponding PDF file.