Sensitivity analysis for causal effects measured on the Odds Ratio scale

E. Stanghellini ${}^a$, S. Geneletti ${}^b$

${}^a$ Dipartimento di Economia, Università di Perugia (IT) ${}^b$ Department of Statistics, London School of Economics and Political Science (U.K.)

Causal conclusions drawn from observational studies necessarily rely on the unverifiable assumption that there are no unobserved confounders. With reference to the context of a binary treatment and a binary outcome, we propose two different - though related - strategies to assess sensitivity to a binary unobserved confounder when the causal effect is expressed as a (log) odds ratio, a situation commonly arising in standard logistic modelling, particularly in case-control studies.

Existing methods tipically rely on the rare outcome approximation. Using the exact formula linking marginal and conditional odds ratios in Stanghellini and Doretti (2019), we propose two graphical tools that visualize the extent to which the unobserved confounder could attenuate, nullify, or even reverse the estimated causal effect. Connections with Cornfield’s conditions on relative risks are presented, thereby enlarging the circumstances where the proposed procedures can be applied.

The talk is based on a paper to appear (Stanghellini and Geneletti, 2026) and complements work for a continuous unobserved confounder (Gasparin et al., 2025).

Keywords: Cornfield’s conditions, relative risk, visualization.