Getting to Know Worst-Case Confounders

Since Cornfield, Haenszel, Hammond, Lilienfeld, Shimkin, and Wynder (1959)'s seminal contribution, many sensitivity analyses have been introduced. Modern-day approaches to sensitivity analysis aim to impose relatively little structure on the unobserved confounder. However, while a sensitivity analysis may not rely on many assumptions on the unobserved confounder, the worst-case bounds that are solved for within a sensitivity analysis are often only realized when a hypothetical confounder takes on a specific form, which is not always made explicit. In the following commentary, we consider several leading sensitivity analysis approaches and review what is known about the structure of the confounder at which the worst-case bounds are realized. We show that the type of sensitivity model used can induce different data generating processes for the worst-case confounders. We argue that understanding the structure of the omitted confounder implied by the worst-case bounds is crucial for more transparent sensitivity analysis, and we suggest directions for future work.