Resources

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).

Further papers provide more information on the use and interpretation of E-values (Haneuse et al., 2019; VanderWeele et al. 2019b; VanderWeele, 2021), technical details concerning E-values (Ding & VanderWeele, 2016; VanderWeele et al., 2019a) and reporting guidelines for E-values (VanderWeele and Mathur, 2020).

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:

  • Unmeasured confounding of effect heterogeneity or causal interaction estimates (Mathur et al., 2021; R package EValue)
  • Selection bias (Smith & VanderWeele, 2019a; online tool or R package EValue)
  • Missing data or selection bias (Mathur, 2023; 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)

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)

Developers

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

References

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

VanderWeele TJ (2021). Are Greenland, Ioannidis and Poole opposed to the Cornfield conditions? A defence of the E-value. International Journal of Epidemiology, dyab218. 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

Mathur MB (2023). The M-value: A simple sensitivity analysis for bias due to missing data in treatment effect estimates. American Journal of Epidemiology, 192(4), 612-620. Link