A Shrinkage Likelihood Ratio Test for High-Dimensional Subgroup Analysis with a Logistic-Normal Mixture Model
A Shrinkage Likelihood Ratio Test for High-Dimensional Subgroup Analysis with a Logistic-Normal Mixture Model
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发表时间：
2023-07
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通讯作者：
Shota Takeishi
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作者：
Shota Takeishi
在亚组分析中，检验具有差异治疗效应的亚组的存在可防止虚假亚组发现。尽管它的重要性，这种假设检验具有复杂的性质：参数表征的亚组分类是不确定的零假设下没有亚组。由于这种不规则性，现有方法具有以下两个局限性。首先，检验统计量的渐近零分布往往具有一种难以处理的形式，这就需要计算量要求很高的重构方法来计算临界值。第二，表征子群成员的个人属性维度不允许是高维度的。为了同时解决这两个问题，本研究开发了一种新的收缩似然比检验的存在一个子群使用逻辑正态混合模型。建议的检验统计量是建立在一个修改后的似然函数，收缩可能高维不明参数向零下的零假设，同时保留电源下的替代。这种收缩有助于处理的不规则性和恢复简单的卡方型渐近，即使在高维制度。
In subgroup analysis, testing the existence of a subgroup with a differential treatment effect serves as protection against spurious subgroup discovery. Despite its importance, this hypothesis testing possesses a complicated nature: parameter characterizing subgroup classification is not identified under the null hypothesis of no subgroup. Due to this irregularity, the existing methods have the following two limitations. First, the asymptotic null distribution of test statistics often takes an intractable form, which necessitates computationally demanding resampling methods to calculate the critical value. Second, the dimension of personal attributes characterizing subgroup membership is not allowed to be of high dimension. To solve these two problems simultaneously, this study develops a novel shrinkage likelihood ratio test for the existence of a subgroup using a logistic-normal mixture model. The proposed test statistics are built on a modified likelihood function that shrinks possibly high-dimensional unidentified parameters toward zero under the null hypothesis while retaining power under the alternative. This shrinkage helps handle the irregularity and restore the simple chi-square-type asymptotics even under the high-dimensional regime.