Exploration of Heterogeneous Treatment Effects via Concave Fusion

IF 1.2 4区 数学
Shujie Ma, Jian Huang, Zhiwei Zhang, Mingming Liu
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引用次数: 33

Abstract

Abstract Understanding treatment heterogeneity is essential to the development of precision medicine, which seeks to tailor medical treatments to subgroups of patients with similar characteristics. One of the challenges of achieving this goal is that we usually do not have a priori knowledge of the grouping information of patients with respect to treatment effect. To address this problem, we consider a heterogeneous regression model which allows the coefficients for treatment variables to be subject-dependent with unknown grouping information. We develop a concave fusion penalized method for estimating the grouping structure and the subgroup-specific treatment effects, and derive an alternating direction method of multipliers algorithm for its implementation. We also study the theoretical properties of the proposed method and show that under suitable conditions there exists a local minimizer that equals the oracle least squares estimator based on a priori knowledge of the true grouping information with high probability. This provides theoretical support for making statistical inference about the subgroup-specific treatment effects using the proposed method. The proposed method is illustrated in simulation studies and illustrated with real data from an AIDS Clinical Trials Group Study.
凹形融合异质治疗效果探讨
了解治疗异质性对于精准医学的发展至关重要,精准医学旨在为具有相似特征的患者亚组量身定制医疗治疗。实现这一目标的挑战之一是,我们通常没有关于治疗效果的患者分组信息的先验知识。为了解决这个问题,我们考虑了一个异构回归模型,该模型允许处理变量的系数与未知的分组信息相关。我们提出了一种凹融合惩罚方法来估计分组结构和子组特定的处理效果,并推导了一种乘法算法的交替方向方法来实现它。我们还研究了该方法的理论性质,并证明了在适当的条件下存在一个局部极小器,该极小器等于基于高概率的真实分组信息的先验知识的预估最小二乘估计。这为使用所提出的方法对亚组特异性治疗效果进行统计推断提供了理论支持。该方法在模拟研究和艾滋病临床试验组研究的真实数据中得到了说明。
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来源期刊
International Journal of Biostatistics
International Journal of Biostatistics Mathematics-Statistics and Probability
CiteScore
2.30
自引率
8.30%
发文量
28
期刊介绍: The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.
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