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：个体化决策规则（IDR）是一种决策函数，根据个体观测特征为其分配特定治疗。现有文献大多考虑二元或有限治疗选项的场景。本文聚焦连续治疗场景，提出跳跃区间学习方法以构建最大化期望结果的个体化区间值决策规则（I2DR）。与推荐单一治疗的IDR不同，所提出的I2DR为每个个体提供治疗选项区间，使其在实践中更具灵活性。为推导最优I2DR，本文的跳跃区间学习方法通过跳跃惩罚回归估计给定治疗和协变量后的结果条件均值，并基于估计的结果回归函数推导相应的最优I2DR。回归器既可采用线性模型以清晰解释，也可采用深度神经网络以建模复杂的治疗-协变量交互作用。为实施跳跃区间学习，我们开发了基于动态规划的搜索算法，高效计算结果回归函数。当结果回归函数在治疗空间中为分段或连续函数时，建立了所得I2DR的统计性质。我们还进一步开发了在（估计的）最优策略下推断均值结果的程序。通过大量仿真实验以及华法林研究的真实数据应用，验证了所提I2DR的经验有效性。