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.
Developers

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

Other software for E-values

You can alternatively compute E-values using the R package EValue or the Stata module EVALUE.

Analogous sensitivity analyses for other settings and biases

If you are concerned about unmeasured confounding in a meta-analysis rather than a single study, you can conduct sensitivity analyses analogous to the E-value using the R package EValue or this website. If you are concerned about selection bias instead of (or in addition to) confounding, you can conduct analogous sensitivity analyses using the R package EValue.

Additional references

For more on the technical details and the interpretation of the E-value, see:

(1) Ding P & VanderWeele TJ. (2017). Sensitivity analysis without assumptions. Epidemiology, 27(3): 368–377.

(2) VanderWeele TJ, Ding P, Mathur MB. (in press). Technical considerations in the use of the E-value. Journal of Causal Inference.

(3) VanderWeele TJ, Mathur MB, Ding P. (2019). Correcting misinterpretations of the E-value. Annals of Internal Medicine, 170(2):131-132.