In many clinical practices, the goal of medical interventions or therapies is often to maintain clinical measures within a desirable range, rather than maximizing or minimizing their values. To achieve this, it may be more practical to recommend a therapeutic dose interval rather than a single dose for a given patient. Since different patients may respond differently to the same dosage of medication, the therapeutic dose interval needs to be personalized based on each patient's unique characteristics. However, this problem is challenging as it requires jointly learning the lower and upper bound functions for personalized dose intervals. Currently, there are no methods available that are suitable to address this challenge. To fill this gap, we propose a novel loss function that converts the task of learning personalized two-sided dose intervals into a risk minimization problem. The loss function is defined over a tensor product reproducing kernel Hilbert space and is doubly-robust to misspecification of nuisance functions. We establish statistical properties of estimated dose interval functions that directly minimize the empirical risk associated with the loss function. Our simulation and a real-world application of personalized warfarin dose intervals show that our proposed direct estimation method outperforms naive indirect regression-based methods.

翻译：在许多临床实践中，医疗干预或治疗的目标通常是使临床指标维持在理想范围内，而非单纯追求其最大值或最小值。为实现这一目标，针对特定患者推荐治疗剂量区间可能比单一剂量更具实践意义。由于不同患者对相同药物剂量的反应存在差异，治疗剂量区间需要根据每位患者的独特特征进行个性化设置。然而，该问题极具挑战性，因为它要求同时学习个性化剂量区间的下界函数和上界函数。目前尚无方法能够有效应对这一挑战。为填补这一空白，我们提出一种新型损失函数，将个性化双界剂量区间的学习任务转化为风险最小化问题。该损失函数定义于张量积再生核希尔伯特空间，并对干扰函数的错误设定具有双重稳健性。我们建立了直接最小化该损失函数对应经验风险的剂量区间函数的统计性质。模拟实验及个性化华法林剂量区间的实际应用表明，我们提出的直接估计方法优于传统的间接回归方法。