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.

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影响不同人群亚组具有重要意义。虽然大部分处理效应异质性分析聚焦于条件平均处理效应，但另一种捕捉处理效应异质性的参数是不同协变量组间处理效应的方差。研究者还可以推导变量重要性参数，用以衡量（并排序）目标协变量子集能够解释多少处理效应异质性。本文针对处理效应变量重要性度量——以条件平均处理效应方差之差的形式——提出了一种新的目标最大似然估计量。该估计量是一种纯插件式估计器，包含两个步骤：1) 对需要插入的相关成分进行初始估计；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，所提出的估计器在较低偏差和更优置信区间覆盖度方面具有竞争性表现。我们将这些方法应用于一项比较核苷单药治疗与联合疗法对HIV感染成人疗效的随机临床试验数据。研究发现估计方程估计量与所提出的目标最大似然估计量给出了相似的变量重要性排序结果。该方法的应用也展示了插件式估计器的优势：其始终遵循数据分布的全局约束，且待估参数是分布的特定函数。