Variable importance measures for heterogeneous causal effects

The recognition that personalised treatment decisions lead to better clinical outcomes has sparked recent research activity in the following two domains. Policy learning focuses on finding optimal treatment rules (OTRs), which express whether an individual would be better off with or without treatment, given their measured characteristics. OTRs optimize a pre-set population criterion, but do not provide insight into the extent to which treatment benefits or harms individual subjects. Estimates of conditional average treatment effects (CATEs) do offer such insights, but valid inference is currently difficult to obtain when data-adaptive methods are used. Moreover, clinicians are (rightly) hesitant to blindly adopt OTR or CATE estimates, not least since both may represent complicated functions of patient characteristics that provide little insight into the key drivers of heterogeneity. To address these limitations, we introduce novel nonparametric treatment effect variable importance measures (TE-VIMs). TE-VIMs extend recent regression-VIMs, viewed as nonparametric analogues to ANOVA statistics. By not being tied to a particular model, they are amenable to data-adaptive (machine learning) estimation of the CATE, itself an active area of research. Estimators for the proposed statistics are derived from their efficient influence curves and these are illustrated through a simulation study and an applied example.