More resources for E-values for unmeasured confounding

In addition to using this online tool, 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:

  • Selection bias (Smith & VanderWeele, 2019a; online tool or R package EValue)
  • Measurement error (VanderWeele & Li, 2019; R package EValue)
  • A combination of unmeasured confounding, selection bias, and measurement error simultaneously (Smith et al, 2021; R package EValue)
  • Unmeasured mediator-outcome confounding in mediation analysis for direct and indirect effects (Smith & VanderWeele, 2019b)
  • Unmeasured confounding of effect heterogeneity or causal interaction estimates (Mathur et al., 2021; R package EValue)

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

  • Unmeasured confounding in meta-analyses (Mathur & VanderWeele, 2020a; online tool or R package EValue)
  • Publication bias in meta-analyses (Mathur & VanderWeele, 2020b; R package PublicationBias)


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


Ding P & VanderWeele TJ (2016). Sensitivity analysis without assumptions. Epidemiology, 27(3), 368–377. Link

Haneuse S, VanderWeele TJ, & Arterburn D (2019). Using the E-value to assess the potential effect of unmeasured confounding in observational studies. Journal of the American Medical Association, 321(6), 602-603. Link

Linden A, Mathur MB, & VanderWeele TJ (2020). Conducting sensitivity analysis for unmeasured confounding in observational studies using E-values: The evalue package. The Stata Journal, 20(1), 162-175. Link

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

Mathur MB & VanderWeele TJ (2020a). Sensitivity analysis for unmeasured confounding in meta-analyses. Journal of the American Statistical Association 115(529), 163-170. Link; online tool

Mathur MB & VanderWeele TJ (2020b). Sensitivity analysis for publication bias in meta-analyses. Journal of the Royal Statistical Society: Series C, 69(5), 1091-1119. Link

Mathur MB, Smith LH, Yoshida K, Ding P, VanderWeele TJ (2021). E-values for effect heterogeneity and conservative approximations for causal interaction. Under review. Link.

Smith LH & VanderWeele TJ (2019a). Bounding bias due to selection. Epidemiology 30(4), 509-516. Link; online tool

Smith LH & VanderWeele TJ (2019b). Mediational E-values: Approximate sensitivity analysis for mediator-outcome confounding. Epidemiology 30(6), 835-837. Link

Smith LH, Mathur MB, VanderWeele TJ (2021). Multiple-bias sensitivity analysis using bounds. Epidemiology (in press). Link

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

VanderWeele TJ, Ding P, & Mathur MB (2019a). Technical considerations in the use of the E-value. Journal of Causal Inference, 7(2). Link

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

VanderWeele TJ & Li Y (2019). Simple sensitivity analysis for differential measurement error. American Journal of Epidemiology, 188(10), 1823-1829. Link

VanderWeele, TJ & Mathur MB. (2020). Commentary: developing best-practice guidelines for the reporting of E-values. International Journal of Epidemiology, 49(5), 1495-1497. Link

Zhang X, Stamey JD, Mathur MB (2020). Assessing the impact of unmeasured confounders for credible and reliable real-world evidence. Pharmacoepidemiology and Drug Safety, 29:1219–1227. Link