  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.
