Sensitivity Analysis on the Odds Ratio Scale: Extending Cornfield's Conditions

Two procedures are proposed to assess sensitivity to a binary unobserved confounder for a binary outcome when the causal effect is expressed as a (log) odds ratio, as commonly arises in standard logistic modelling, particularly in case-control studies. The methods are based on graphical tools that visualize the extent to which an unobserved confounder could attenuate, nullify, or even reverse the estimated causal effect. The second procedure relies on a single sensitivity parameter, yielding a naturally bounded assessment that can be translated into an objective measure. Connections with Cornfield's conditions on relative risks are presented, thereby enlarging the circumstances where the proposed procedures can be applied and establishing a link that allows extensions to polytomous confounders.