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arXiv 1903.04367stat.ME
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个性化决策规则的鲁棒性研究

On Robustness of Individualized Decision Rules

Zhengling Qi, Jong-Shi Pang, Yufeng Liu

摘要:

随着精准医疗的出现,估计最优个体化决策规则(IDR)在许多科学领域引起了极大的关注。大多数现有的文献都集中在寻找最佳的IDR,可以最大限度地提高每个人的预期结果。基于复杂的个体化决策过程和流行的条件风险价值(CVaR)度量,我们提出了一个新的稳健准则来估计最优IDR,以控制个体结果的平均下尾。除了改善个体化预期结局外,我们提出的标准还考虑了风险,因此产生的IDR可以预防不良事件。我们的标准下的最优IDR可以解释为决策规则,最大限度地提高了“最坏情况”的情况下,个性化的结果时,潜在的分布在一个约束集内扰动。提出了一种有效的非凸优化算法,并给出了收敛保证。我们调查的理论性质,我们估计的最佳IDR下所提出的标准,如一致性和有限样本误差界。仿真研究和实际数据的应用,以进一步证明我们的方法的鲁棒性能。文中还讨论了该方法的几个推广。

英文摘要:

With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize the expected outcome for each individual. Motivated by complex individualized decision making procedures and the popular conditional value at risk (CVaR) measure, we propose a new robust criterion to estimate optimal IDRs in order to control the average lower tail of the individuals' outcomes. In addition to improving the individualized expected outcome, our proposed criterion takes risks into consideration, and thus the resulting IDRs can prevent adverse events. The optimal IDR under our criterion can be interpreted as the decision rule that maximizes the ``worst-case" scenario of the individualized outcome when the underlying distribution is perturbed within a constrained set. An efficient non-convex optimization algorithm is proposed with convergence guarantees. We investigate theoretical properties for our estimated optimal IDRs under the proposed criterion such as consistency and finite sample error bounds. Simulation studies and a real data application are used to further demonstrate the robust performance of our methods. Several extensions of the proposed method are also discussed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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