基于秩回归的多阈值变平面模型研究

Research on Multi-Threshold Variable Plane Model Based on Rank Regression

摘要: 为了更好地应用个性化医疗技术，识别出导致治疗效果出现异质性的亚组人群，进而为这些特定的患者群体提供更加精准有效的治疗方法，文章介绍了一种多阈值的变平面模型，该模型将研究对象划分为具有不同协变量效应的亚组。针对此模型，文章提出了一种新的基于秩回归的两阶段估计方法来确定亚组数量、阈值的位置以及其他的回归参数。在第一阶段，采用分组选择原则，一致地识别亚组的数量；在第二阶段，采用惩罚诱导平滑技术来精确估计变点位置和模型的其他参数。通过将该方法应用到艾滋病临床试验组研究175所得数据中，并对比其他的模型方法，可以发现基于秩回归的估计方法结果更好，同时该方法具有很好的鲁棒性。

Abstract: In order to better apply personalized medical technology, identify subgroups that cause heterogeneity in treatment outcomes, and provide more accurate and effective treatment methods for these specific patient groups, this paper introduces a multi-threshold variable plane model, which divides the research subjects into subgroups with different covariate effects. This article proposes a new two-stage estimation method based on rank regression to determine the number of subgroups, the position of thresholds, and other regression parameters for this model. In the first stage, the principle of grouping selection is adopted to consistently identify the number of subgroups. In the second stage, the penalty-induced smoothing technique is used to accurately estimate the position of the inflection point and other parameters of the model. By applying the method proposed in this paper to the data obtained from the AIDS clinical trial group study 175, compared with other model methods, we can find that the estimation method based on rank regression has better results, and this method has good robustness.