[论文解读] Variance stabilization of targeted estimators of causal parameters in high-dimensional settings

Nima S. Hejazi, Sara Kherad-Pajouh+2 more|arXiv (Cornell University)|Oct 16, 2017

Statistical Methods and Inference被引用 4

一句话总结

该论文提出了一种稳健、数据自适应的方法，用于在小样本的高维生物数据中估计变量重要性，结合目标最小损失估计（TMLE）与基于影响曲线的校正t统计量。该方法可稳定方差，并在不依赖参数假设的前提下实现精确推断，即使在调整年龄、种族和吸烟等多重混杂因素时亦然。

ABSTRACT

Exploratory analysis of high-dimensional biological sequencing data has received much attention for its ability to allow the simultaneous screening of numerous biological characteristics. While there has been an increase in the dimensionality of such data sets in studies of environmental exposure and biomarkers, two important questions have received less interest than deserved: (1) how can independent estimates of associations be derived in the context of many competing causes while avoiding model misspecification, and (2) how can accurate small-sample inference be obtained when data-adaptive techniques are employed in such contexts. The central focus of this paper is on variable importance analysis in high-dimensional biological data sets with modest sample sizes, using semiparametric statistical models. We present a method that is robust in small samples, but does not rely on arbitrary parametric assumptions, in the context of studies of gene expression and environmental exposures. Such analyses are faced with not only issues of multiple testing, but also the problem of teasing out the associations of biological expression measures with exposure, among confounds such as age, race, and smoking. Specifically, we propose the use of targeted minimum loss-based estimation (TMLE), along with a generalization of the moderated t-statistic of Smyth, relying on the influence curve representation of a statistical target parameter to obtain estimates of variable importance measures (VIM) of biomarkers. The result is a data-adaptive approach that can estimate individual associations in high-dimensional data, even with relatively small sample sizes.

研究动机与目标

• 解决在样本量适中的高维生物数据中估计变量重要性的挑战。
• 开发一种在存在多个竞争原因时避免模型误设的方法。
• 在使用数据自适应估计技术时，实现精确的小样本推断。
• 提高调整年龄、种族和吸烟等混杂因素后，生物标志物与环境暴露之间关联估计的可靠性。
• 为基因表达和暴露研究中的变量重要性分析提供一种稳健的参数假设替代方案。

提出的方法

• 该方法采用目标最小损失估计（TMLE）在高维设置中生成高效、半参数的因果参数估计。
• 利用统计目标参数的影响曲线表示，以在小样本中稳定方差。
• 应用Smyth校正t统计量的推广形式，利用影响曲线提升估计精度。
• 该方法允许在调整多个混杂因素的同时，对个体生物标志物关联进行数据自适应估计。
• 该方法设计为对模型误设具有鲁棒性，且无需任意的参数假设。

实验结果

研究问题

• RQ1 在存在大量竞争原因的高维数据中，如何在不发生模型误设的情况下获得独立的关联估计？
• RQ2 在高维设置中使用数据自适应技术时，如何实现精确的小样本推断？
• RQ3 TMLE结合校正t统计量在估计小样本、高维生物研究中生物标志物的变量重要性方面表现如何？
• RQ4 与传统方法相比，该方法在方差稳定性和鲁棒性方面表现如何？

主要发现

• 所提出的方法在小样本量的高维生物数据中，为变量重要性度量提供了稳定的方差估计。
• 在校正t统计量中使用影响曲线可提高小样本推断的精度和鲁棒性。
• 该方法在不依赖参数假设的前提下，有效调整了年龄、种族和吸烟等混杂因素。
• 即使变量数量远超样本量，该方法也能可靠检测生物标志物与暴露的关联。