The Magnitude and Direction of Potential Bias in Instrumental Variable Analyses when Treatment Effects are Heterogeneous

INTRODUCTION: Investigators often estimate an average treatment effect using instrumental variable (IV) methods without acknowledging a critical assumption implicit in their analyses: additive effect homogeneity. Without this assumption, the average treatment effect can only be partially identified with generally wide bounds. However, a reliance on this assumption in the presence of effect heterogeneity to obtain a point estimate may lead to ill-placed conclusions. We sought to clarify the direction and magnitude of potential bias in the presence of effect heterogeneity.  

METHODS: We simulated a dichotomous instrument (Z), treatment (X), unmeasured confounder (U), and outcome (Y) under the IV assumptions with outcomes generated from a structural mean modeling framework. Parameters were set to emulate the distribution of variables in a study of the effects of statin initiation. Simulations primarily varied the strength of effect modification by the instrument. 

RESULTS: As expected, under no effect modification the standard IV estimate was unbiased. In the presence of effect modification, the direction of bias  depended on whether E[Y(1)-Y(0)|Z=1] was greater or less than E[Y(1)-Y(0)|Z=0], with more effect heterogeneity leading to more bias. The magnitude and direction of bias will be discussed under various circumstances, including: qualitative effect modification, additive and/or multiplicative effect modification, when using surrogate instruments, and in conjunction with violations of other requisite assumptions. 

CONCLUSIONS: The standard IV estimate may be substantially biased in the presence of effect heterogeneity.