Sensitivity Analysis in Observational Research: Introducing the E-Value

TLDR

Sensitivity analysis is useful in assessing how robust an association is to potential unmeasured or uncontrolled confounding. This article introduces the E‑value, a measure of evidence for causality in observational studies, and proposes that it be reported in all such studies to assess robustness to confounding. The E‑value is defined as the minimum risk‑ratio strength an unmeasured confounder must have with both treatment and outcome to explain away an association, and the authors suggest calculating it for the adjusted estimate and the confidence‑interval limit nearest the null. A large E‑value indicates that substantial unmeasured confounding would be required to explain away an effect estimate, whereas a small E‑value suggests only minimal confounding is needed, implying that widespread use of the E‑value would markedly improve the assessment of causal evidence in observational studies.

Abstract

Sensitivity analysis is useful in assessing how robust an association is to potential unmeasured or uncontrolled confounding. This article introduces a new measure called the "E-value," which is related to the evidence for causality in observational studies that are potentially subject to confounding. The E-value is defined as the minimum strength of association, on the risk ratio scale, that an unmeasured confounder would need to have with both the treatment and the outcome to fully explain away a specific treatment–outcome association, conditional on the measured covariates. A large E-value implies that considerable unmeasured confounding would be needed to explain away an effect estimate. A small E-value implies little unmeasured confounding would be needed to explain away an effect estimate. The authors propose that in all observational studies intended to produce evidence for causality, the E-value be reported or some other sensitivity analysis be used. They suggest calculating the E-value for both the observed association estimate (after adjustments for measured confounders) and the limit of the confidence interval closest to the null. If this were to become standard practice, the ability of the scientific community to assess evidence from observational studies would improve considerably, and ultimately, science would be strengthened.