On Instrumental Variables Estimation of Causal Odds Ratios

TL;DR

This paper reviews and proposes methods for instrumental variables estimation of causal odds ratios for dichotomous outcomes, including both conditional and marginal effects, supported by simulations and real data applications.

Contribution

It introduces new IV estimators for marginal causal odds ratios and explores their connections with existing methods, enhancing causal inference for binary outcomes.

Findings

Proposed IV estimators for marginal causal odds ratios.

Extensive simulation studies validate the estimators.

Applications demonstrate practical relevance.

Abstract

Inference for causal effects can benefit from the availability of an instrumental variable (IV) which, by definition, is associated with the given exposure, but not with the outcome of interest other than through a causal exposure effect. Estimation methods for instrumental variables are now well established for continuous outcomes, but much less so for dichotomous outcomes. In this article we review IV estimation of so-called conditional causal odds ratios which express the effect of an arbitrary exposure on a dichotomous outcome conditional on the exposure level, instrumental variable and measured covariates. In addition, we propose IV estimators of so-called marginal causal odds ratios which express the effect of an arbitrary exposure on a dichotomous outcome at the population level, and are therefore of greater public health relevance. We explore interconnections between the different estimators and support the results with extensive simulation studies and three applications.