Targeted Learning on Variable Importance Measure for Heterogeneous Treatment Effect

Quantifying the heterogeneity of treatment effect is important for understanding how a commercial product or medical treatment affects different population subgroups. While much of treatment effect heterogeneity analysis focuses on the conditional average treatment effect, an alternative parameter that captures treatment effect heterogeneity is the variance of treatment effect across different covariate groups. One can also derive variable importance parameters that measure (and rank) how much of treatment effect heterogeneity is explained by a targeted subset of covariates. In this article, we propose a new targeted maximum likelihood estimator (TMLE) for a treatment effect variable importance measure, in the form of the difference of the variances of conditional average treatment effect. This TMLE is a pure plug-in estimator that consists of two steps: 1) the initial estimation of relevant components to plug in and 2) an iterative updating step to optimize the bias-variance tradeoff. Simulation results show that the proposed estimator has competitive performance in terms of lower bias and better confidence interval coverage compared to a simple substitution estimator and an estimating equation estimator. We apply these methods to data from a randomized clinical trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults. We find that the estimating equation estimator and the proposed TMLE suggest similar rankings of variable importance. The application of this method also demonstrates the advantage of a plug-in estimator, which always respects the global constraints on the data distribution and that the estimand is a particular function of the distribution.