E-value Calculator

How strong would unmeasured confounding have to be to explain away an observed association?

The E-value is 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, above and beyond the measured confounders, to fully explain away the observed association.

Input Parameters

Adjusted for the measured confounders
Optional. The calculator uses whichever limit is closer to 1.

Calculated E-values

E-value for the estimate --
E-value for the CI --
E-value = RR + √(RR × (RR − 1))

Interpretation

Enter an estimate to see the interpretation.

How it is calculated

  • Risk ratio: E-value = RR + √(RR × (RR − 1)). For a risk ratio below 1, use 1/RR first.
  • Odds ratio: with a rare outcome (under 15% at the end of follow-up), RR ≈ OR. With a common outcome, RR ≈ √OR.
  • Hazard ratio: with a rare outcome, RR ≈ HR. With a common outcome, RR ≈ (1 − 0.5√HR) / (1 − 0.5√(1/HR)).
  • Confidence interval: apply the same steps to the limit closest to 1. If the interval already includes 1, its E-value is 1: no confounding is needed to move it to the null.
  • Reading it: a large E-value means considerable unmeasured confounding would be needed to explain away the effect. The E-value says nothing about other biases, such as selection or measurement error.

References

  • VanderWeele TJ, Ding P. Sensitivity analysis in observational research: introducing the E-value. Ann Intern Med. 2017;167(4):268-274. doi:10.7326/M16-2607
  • VanderWeele TJ. Optimal approximate conversions of odds ratios and hazard ratios to risk ratios. Biometrics. 2020;76(3):746-752. doi:10.1111/biom.13197

For education and research use. The E-value is one sensitivity analysis; it does not replace subject-matter judgment about confounding.