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

TL;DR

This paper introduces sensitivity analysis methods for linear regression that quantify how omitted confounders can bias treatment effect estimates, using benchmarking to set reference points based on observed data.

Contribution

It develops a flexible framework for sensitivity analysis of treatment effects in linear regression, incorporating benchmarking, subgroup analysis, multiple omitted variables, and combined adjustment methods.

Findings

Benchmarking provides realistic bounds for confounder effects.

The methods adapt to subgroup-specific treatment effects.

Application to health data demonstrates practical utility.

Abstract

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.