Plan an E-Value Analysis Without Treating It as Proof of Causality

Identify the bias question first

Sensitivity analysis asks how conclusions depend on assumptions that cannot be fully checked with the observed data. Start by naming the unmeasured-confounding concern, the effect scale and the contrast whose robustness matters. An association can also be distorted by selection, measurement error or model misspecification, which require their own assessments.

VanderWeele and Ding’s E-value paper defines a sensitivity measure on a risk-ratio scale. Its interpretation concerns the strength of confounder associations needed to explain an observed association under the stated framework; it is not a probability that the effect is causal.

Preserve the analysis scale and interval

Record whether the original estimate is a risk ratio, odds ratio, hazard ratio or another measure. Do not silently apply a risk-ratio formula to every ratio-shaped estimate. Use a justified conversion or the appropriate method, and retain assumptions about outcome frequency and the underlying effect measure.

Compute sensitivity for the point estimate and, where relevant, the confidence limit closest to the null. Describe which result answers the question of explaining away the estimated association and which concerns moving the uncertainty interval to include the null. Keep measured covariates and the adjustment set visible in the interpretation.

Work through a hypothetical risk ratio

For a harmful risk ratio RR at least 1, the familiar point-estimate expression is RR + √[RR(RR−1)]. If a fictional adjusted risk ratio is 2, the E-value is 2 + √2, approximately 3.4142.

If the lower confidence limit is 1.2, the corresponding value is 1.2 + √0.24, approximately 1.6899. The interval is therefore less robust to the specified confounding sensitivity than the point estimate alone might suggest. If the interval already includes the null, the relevant confidence-limit E-value is 1 under this convention.

Put the number in substantive context

Discuss plausible omitted factors, their measurement and how strongly they could relate to exposure and outcome after the measured adjustments. Comparisons with measured covariates can be informative but are not automatic calibrations of all unmeasured bias.

Report the method, effect-scale assumptions and both sensitivity values with the original estimate and interval. Avoid labels such as confounding-proof or causally confirmed. Preserve other sensitivity analyses and design limitations in the same discussion. A useful E-value analysis narrows one question about robustness while making clear which threats it does not address and which scientific judgments remain unresolved.

Source verification: 6 November 2026. Examples are hypothetical.