Commentary: Interpretation and sensitivity analysis for the localized average causal effect curve.

Burgess, Davies, and thompson have presented a method for using instrumental variables (IVs) to investigate whether an exposure-outcome relation is nonlinear and for estimating its shape. as noted by Burgess et al, most methods for estimating causal effects using IVs have assumed that the exposure-outcome relation is linear. I congratulate Burgess and colleagues for focusing attention on the important problem of estimating nonlinear exposure-outcome relations using IV methods and contributing an interesting and stimulating paper. In this commentary, I make 2 points. First, the localized average causal effect curve estimated by Burgess et al reflects a combination of how the exposure’s effect varies across the range of the exposure for a specific subject and how the effect of the exposure varies among groups of subjects with different IV-free exposure levels. this curve can provide insight into the linearity vs. nonlinearity of the subject-specific exposure-outcome relation, but it is different and needs to be interpreted carefully. Second, the localized average causal effect curve estimation method proposed by Burgess et al is sensitive to the assumption that the effect of the IV on exposure is not correlated with potential outcomes; sensitivity analysis methods that allow for violations of this assumption are available. Following the notation of Burgess et al, let Y i be the observed outcome, X i the observed exposure, and G i the observed IV for subject i. Let Y i (x) be the potential outcome that subject i would have if she were to have exposure level x and let X i (g) be the potential exposure level that subject i would have if she were to have IV level g. Consider the simple setting that G is a binary IV and that there is no heterogeneity in the effect of the IV on the exposure,