AI 中文总结
研究个性化治疗规则，基于结果加权学习，将单隐藏层神经网络OWL从岭型正则化扩展到非线性变量选择和核近似，建立估计器收敛率，扩展到残差加权学习，模拟研究和数据应用验证了方法。
AI 中文摘要
个性化治疗规则（ITRs）通过根据患者协变量分配治疗来规范精准医学，旨在最大化预期临床结果。当治疗效果因患者而异时，此类规则尤为重要，如在慢性病中，人口统计学、临床、基因、影像或生物标志物信息可能改变可用疗法的相对益处。结果加权学习（OWL）通过将治疗分配重铸为直接针对临床价值的加权分类问题来估计ITRs。受现代神经网络灵活性的启发，我们将单隐藏层神经网络OWL（NNOWL）从岭型正则化扩展到非线性变量选择和基于核的近似。我们建立了这些估计器的非渐近收敛率，并研究了NNOWL梯度下降的全局收敛和隐式偏差。最后，我们将神经网络方法从OWL扩展到残差加权学习。模拟研究说明了过参数化、核近似和非线性变量选择的作用，阿尔茨海默病的数据应用证明了所提出的方法。
英文摘要
Individualized treatment rules (ITRs) formalize precision medicine by assigning treatments according to patient covariates, with the goal of maximizing expected clinical outcomes. Such rules are especially important when treatment effects vary across patients, as in chronic diseases where demographic, clinical, genetic, imaging, or biomarker information may modify the relative benefits of available therapies. Individualized treatment rules (ITRs) formalize precision medicine by assigning treatments according to patient covariates, with the goal of maximizing expected clinical outcomes. Such rules are especially important when treatment effects vary across patients, as in chronic diseases where demographic, clinical, genetic, imaging, or biomarker information may modify the relative benefits of available therapies. Outcome weighted learning (OWL) estimates ITRs by recasting treatment assignment as a weighted classification problem that directly targets clinical value. Motivated by the flexibility of modern neural networks, we extend single hidden-layer neural-network OWL (NNOWL) from ridge-type regularization to nonlinear variable selection and kernel-based approximation. We establish non-asymptotic convergence rates for these estimators, and study the global convergence and implicit bias of gradient descent for NNOWL. Finally, we extend the neural-network methods from OWL to residual weighted learning. Simulation studies illustrate the roles of over-parameterization, kernel approximation, and nonlinear variable selection, and a data application in Alzheimer's disease demonstrates the proposed methods.
