Quantifying the heterogeneity of treatment effect is important for understanding how a commercial product or medical treatment affects different subgroups in a population. Beyond the overall impact reflected parameters like the average treatment effect, the analysis of treatment effect heterogeneity further reveals details on the importance of different covariates and how they lead to different treatment impacts. One relevant parameter that addresses such heterogeneity is the variance of treatment effect across different covariate groups, however the treatment effect is defined. 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 for a treatment effect variable importance measure. This estimator 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. The simulation results show that this TMLE estimator has competitive performance in terms of lower bias and better confidence interval coverage compared to the simple substitution estimator and the estimating equation estimator. The application of this method also demonstrates the advantage of a substitution estimator, which always respects the global constraints on the data distribution and that the estimand is a particular function of the distribution.

翻译：量化处理效应的异质性对于理解商业产品或医疗干预如何在总体中影响不同亚组具有重要意义。除了平均处理效应等参数所反映的整体影响外，处理效应异质性分析进一步揭示了不同协变量的重要性以及它们如何导致不同的处理效应。针对此类异质性的一个相关参数是不同协变量组间处理效应的方差（无论处理效应如何定义），同时还可推导出变量重要性参数，用以衡量（并排序）特定协变量子集所解释的处理效应异质性程度。本文针对处理效应变量重要性度量提出了一种新的靶向最大似然估计量。该估计量为纯插入式估计量，包含两个步骤：1）对需插入的相关分量进行初始估计；2）通过迭代更新步骤优化偏差-方差权衡。仿真结果表明，与简单替代估计量和估计方程估计量相比，该TMLE估计量在降低偏差和改善置信区间覆盖率方面具有竞争力。该方法的实际应用也凸显了替代估计量的优势，即始终尊重数据分布的全局约束，且估计目标为分布的特定函数。