Predicting the Direction of Causal Effect Based on an Instrumental Variable Analysis: A Cautionary Tale

Abstract An instrumental variable can be used to test the causal null hypothesis that an exposure has no causal effect on the outcome, by assessing the association between the instrumental variable and the outcome. Under additional assumptions, an instrumental variable can be used to estimate the magnitude of causal effect of the exposure on the outcome. In this paper, we investigate whether these additional assumptions are necessary in order to predict the direction of the causal effect, based on the direction of association between the instrumental variable and the outcome, or equivalently based on the standard (Wald) instrumental variable estimate. We demonstrate by counterexample that if these additional assumptions (such as monotonicity of the instrument–exposure association) are not satisfied, then the instrumental variable–outcome association can be in the opposite direction to the causal effect for all individuals in the population. Although such scenarios are unlikely, in most cases, a definite conclusion about the direction of causal effect requires similar assumptions to those required to estimate a causal effect.