Bias factor, maximum bias and the E-value: insight and extended applications. (30th September 2020)

• Record Type: Journal Article
• Authors: Cusson, Alexandre; Infante-Rivard, Claire
• Is Part Of: International journal of epidemiology. Volume 49:Number 5(2020)
• Page Start: 1509
• Page End: 1516
• Publication Date: 2020-09-30
• Subjects: Unmeasured confounding -- E-value -- bias factor -- sensitivity analysis; Epidemiology -- Periodicals; 614.4
• DOI: 10.1093/ije/dyaa127
• Languages: English
• ISSNs: 0300-5771

Abstract

Abstract: Background: Unmeasured confounding can bias the relationship between exposure and outcome. Sensitivity analyses generate bias-adjusted measures but these are not much used; this may change with the availability of the E-value (for evidence for causality in observational studies), appealing for its ease of calculation. However, as currently proposed, the E-value has some practical limitations that may reduce its use. Methods: We first provide some insight into the relationship between two established measures for unmeasured confounding: 'the bias factor' and the maximum value this bias factor can take ('the B bias'). These measures are the statistical foundation for the E-value. We use them to develop new E-value formulas for situations when it is not currently applicable such as e.g. when, not unusually, a negative relation between unmeasured confounder and outcome and a positive one with exposure are postulated. We also provide E-values on the odds ratio scale because, currently, even when using the odds ratio as the study measure in the calculation of E-value, the result is to be interpreted as a relative risk, which is somewhat inconvenient. Results: The additional formulas for the E-value measure make it applicable in all possible scenarios defined by the combined directions between unmeasured confounder and both the exposure and outcome. In addition, E-value measures can now be interpreted as odds ratios if the observed results are reported on the same scale. Conclusions: The E-value is part of newer sensitivity analyses methods for unmeasured confounding. We provide insight into its structure, underscoring its advantages and limitations, and expand its applications.