Arvid Sjölander: Are E-values too optimistic or too pessimistic? Both and neither!

Abstract

The E-value is a popular tool to assess the sensitivity to unmeasured confounding; the higher the E-value, the stronger the unmeasured confounding must be to “explain away” an observed association. However, despite its popularity, the E-value has also been heavily debated and criticized. Ioannidis et al (2019) argued that a high E-value may give an unwarranted optimistic impression, since the accumulated effect of many unmeasured confounders may be large and “trump” even a high E-value, even though the effect of each separate cofounder is small. In contrast, Greenland (2020) argued that a small E-value may give an unnecessarily pessimistic impression, since bias by unmeasured confounders may be weakened considerably due to their associations with measured confounders. These criticisms may appear contradictory, and leave the analyst wondering whether E-values should be interpreted as being too optimistic or too pessimistic. In this presentation we will attempt to reconcile these criticisms, and use a real data example to argue that both interpretations are valid. The presentation will be largely non-technical, and focus on fundamental conceptual issues.