Computing an E-value

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. Note that for outcome types other than relative risks, assumptions are involved with the approximate conversions used. See citation (2) for details.

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.

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.
Please use the following citations:

(1) Mathur MB, Ding P, Riddell CA, VanderWeele TJ. (2018). Website and R package for computing E-values. Epidemiology, 29(5), e45-e47.

(2) VanderWeele TJ, & Ding P. (2017). Sensitivity analysis in observational research: introducing the E-value. Annals of Internal Medicine, 167(4), 268-274.

Bug reports

Submit any bug reports to: mmathur [AT] stanford [DOT] edu or open an issue on Github.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: You are calculating a "non-null" E-value, i.e., an E-value for the minimum amount of unmeasured confounding needed to move the estimate and confidence interval to your specified true value rather than to the null value.
Note: Using the standard deviation of the outcome yields a conservative approximation of the standardized mean difference. For a non-conservative estimate, you could instead use the estimated residual standard deviation from your linear regression model. Regardless, the reported E-value for the confidence interval treats the standard deviation as known, not estimated.

Each point along the curve defines a joint relationship between the two sensitivity parameters that could potentially explain away the estimated effect. If one of the two parameters is smaller than the E-value, the other must be larger, as defined by the plotted curve.


More resources for E-values for unmeasured confounding

In addition to using this website, you can alternatively compute E-values (VanderWeele & Ding, 2017) using the R package EValue (Mathur et al., 2018) or the Stata module EVALUE (Linden et al., 2020).

For more information on the interpretation of the E-value and further technical details, see Ding & VanderWeele (2016), Haneuse et al. (2019), VanderWeele et al. (2019a), and VanderWeele et al. (2019b).

More resources for other biases and study designs

Methods and tools are also available to conduct analogous sensitivity analyses for other types of biases, including: An analog of the E-value is also available to address unmeasured mediator-outcome confounding when carrying out mediation analysis for direct and indirect effects (Smith & VanderWeele, 2019b).

Finally, similar approaches are also available to assess biases in meta-analyses including: Developers

This website was created by Maya Mathur, Peng Ding, Corinne Riddell, Louisa Smith, and Tyler VanderWeele.

References