An individualized decision rule (IDR) is a decision function that assigns each individual a given treatment based on his/her observed characteristics. Most of the existing works in the literature consider settings with binary or finitely many treatment options. In this paper, we focus on the continuous treatment setting and propose a jump interval-learning to develop an individualized interval-valued decision rule (I2DR) that maximizes the expected outcome. Unlike IDRs that recommend a single treatment, the proposed I2DR yields an interval of treatment options for each individual, making it more flexible to implement in practice. To derive an optimal I2DR, our jump interval-learning method estimates the conditional mean of the outcome given the treatment and the covariates via jump penalized regression, and derives the corresponding optimal I2DR based on the estimated outcome regression function. The regressor is allowed to be either linear for clear interpretation or deep neural network to model complex treatment-covariates interactions. To implement jump interval-learning, we develop a searching algorithm based on dynamic programming that efficiently computes the outcome regression function. Statistical properties of the resulting I2DR are established when the outcome regression function is either a piecewise or continuous function over the treatment space. We further develop a procedure to infer the mean outcome under the (estimated) optimal policy. Extensive simulations and a real data application to a warfarin study are conducted to demonstrate the empirical validity of the proposed I2DR.
翻译:个性化决定规则( IDR) 是一个基于个人观察到的特性指定特定治疗方法的决定函数。文献中的大多数现有作品都考虑二进制或有限的多种治疗选项。在本文中,我们侧重于连续治疗设置,并提议跳跃间学习,以制定个体化间隔估值决定规则( I2DR) 以最大限度地实现预期结果。与建议单一治疗的IDR不同,拟议的 I2DR 产生对每个人的治疗选择间隔,使其更灵活地在实践中实施。为获得最佳的 I2DR,我们跳跃间学习方法以二进制回归法来估算结果的有条件值,并基于估计结果回归功能得出相应的最佳I2DR 。允许递减者为直线解释或深神经网络,以模拟复杂的治疗-变异相互作用。为了实施跳跃间学习,我们根据动态程序开发一种搜索算算算算算算法,因此产生的 I2DR 的统计属性是在结果回归功能下建立的,当结果回归后,我们根据一个持续或持续地模拟进行一个结果回归分析的模型分析程序。