Individuals differ in how they respond to a given treatment. In an effort to predict the treatment response and analyze the heterogeneity of treatment effect, we propose a general modeling framework by identifying treatment-covariate interactions honoring a hierarchical condition. We construct a single-step $l_1$ norm penalty procedure that maintains the hierarchical structure of interactions in the sense that a treatment-covariate interaction term is included in the model only when either the covariate or both the covariate and treatment have nonzero main effects. We developed a constrained Lasso approach with two parameterization schemes that enforce the hierarchical interaction restriction differently. We solved the resulting constrained optimization problem using a spectral projected gradient method. We compared our methods to the unstructured Lasso using simulation studies including a scenario that violates the hierarchical condition (misspecified model). The simulations showed that our methods yielded more parsimonious models and outperformed the unstructured Lasso for correctly identifying nonzero treatment-covariate interactions. The superior performance of our methods are also corroborated by an application to a large randomized clinical trial data investigating a drug for treating congestive heart failure (N = 2569). Our methods provide a well-suited approach for doing secondary analysis in clinical trials to analyze heterogeneous treatment effects and to identify predictive biomarkers.

中文翻译：

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用于分析治疗效果异质性的分层相互作用的套索估计

个体对给定治疗的反应不同。为了预测治疗反应并分析治疗效果的异质性，我们通过识别符合分层条件的治疗-协变量相互作用，提出了一个通用建模框架。我们构建一个单步${升}_1$规范惩罚程序维护交互的层次结构，因为只有当协变量或协变量和处理具有非零主效应时，模型中才包含处理-协变量交互项。我们开发了一种约束套索方法，它具有两个参数化方案，以不同的方式强制执行分层交互限制。我们使用谱投影梯度法解决了由此产生的约束优化问题。我们使用模拟研究将我们的方法与非结构化套索进行了比较，其中包括违反分层条件（错误指定的模型）的场景。模拟表明，我们的方法产生了更简约的模型，并且在正确识别非零治疗协变量相互作用方面优于非结构化套索。我们方法的卓越性能也得到了对研究治疗充血性心力衰竭药物的大型随机临床试验数据的应用 (N = 2569) 的证实。我们的方法提供了一种非常适合在临床试验中进行二次分析的方法，以分析异质性治疗效果并确定预测性生物标志物。