E-value Sensitivity Analysis for Unmeasured Confounding
Observational studies cannot rule out unmeasured confounding. The E-value answers: how strongly would an unmeasured confounder have to be associated with both the exposure and the outcome (on the risk-ratio scale) to fully explain away the observed association? The larger the E-value, the more robust the conclusion is to unmeasured confounding. Based on VanderWeele & Ding (2017).
① Enter the effect size
Choose the effect-size type and enter the point estimate and (optionally) the 95% confidence interval. The CI is used to compute the "E-value at the CI limit".
| Point estimate | 95% CI lower | 95% CI upper |
|---|---|---|
How to use & methodology
How is an E-value interpreted?
It is the minimum confounding strength (expressed as a risk ratio) needed to fully explain away the observed association. For example, E-value=7.26 means an unmeasured confounder would have to be associated with both exposure and outcome at RR≥7.26 to explain the association; when such strong confounding is implausible, the conclusion is fairly robust.
Why also compute the E-value at the CI limit?
The point-estimate E-value measures the difficulty of pushing the point estimate back to the null; the CI-limit (null-side) E-value measures the difficulty of pushing the whole confidence interval to include the null, which is more conservative. The two are usually reported together. If the CI already crosses the null, the CI-limit E-value is 1.
How do I enter OR and HR?
When the outcome is rare (about <15%), OR and HR approximate RR, so choose the 'rare' option. For common outcomes a conversion is needed: common-outcome OR uses RR≈√OR, and common-outcome HR uses VanderWeele's conversion. Choosing the wrong type over- or under-estimates the E-value.
What about a protective effect (RR<1)?
The tool automatically takes 1/RR to convert to the ≥1 scale before computing, and the E-value is then interpreted as 'how strong the confounding must be to explain away the protective effect'.