How to use this website


Please use the following citations when using this website:

  1. Mathur MB, Ding P, Riddell CA, VanderWeele TJ (2018). Website and R package for computing E-values. Epidemiology, 29(5), e45-e47. Link
  2. VanderWeele TJ & Ding P (2017). Sensitivity analysis in observational research: introducing the E-value. Annals of Internal Medicine, 167(4), 268-274. Link

Computing an E-value

Default E-values: The tab Compute an E-value computes the E-value, defined as the minimum strength of association on the risk ratio scale that an unmeasured confounder would need to have with both the exposure and the outcome, conditional on the measured covariates, to fully explain away a specific exposure-outcome association. Stated otherwise, confounding associations that were jointly weaker than the E-value could not explain away the association. Note that for outcome types other than relative risks, assumptions are involved with the approximate conversions used (VanderWeele & Ding, 2017).

Non-null E-values: Alternatively, you can consider the confounding strength capable of moving the observed association to any other value (e.g. attenuating the observed association to a true causal effect that is no longer scientifically important, or alternatively increasing a near-null observed association to a value that is of scientific importance). For this purpose, simply type a non-null effect size into the box “True causal effect to which to shift estimate” when computing the E-value.

E-values for effect-measure modification: Standard E-values apply to the main effect of one exposure on an outcome. If instead your point estimate is a statistical interaction term representing effect-measure modification of one exposure across strata of another exposure, then the E-values this website calculates for ratio measures can still be used to assess sensitivity of the effect-measure modification estimate to uncontrolled confounding (Mathur, et al., 2021). The E-values then represent the minimum severity of confounding (defined as above) in least one stratum of the second exposure in order to explain away the effect-measure modification. This assumes that confounding operates in the same direction in each stratum of the second exposure. To avoid that assumption, you would take the square-root of your estimate on the risk ratio scale before using this calculator. For estimates on the difference scale (i.e., the interaction contrast), use the function evalues.IC in the R package EValue.

Computing a bias factor

Additionally, if you have substantive knowledge on the strength of the relationships between the unmeasured confounder(s) and the exposure and outcome, you can use these numbers to calculate the bias factor.

Bug reports

Submit any bug reports by opening an issue on GitHub.