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arXiv 2602.09145stat.ME
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利用修改的功能治疗政策估计因果效应

Estimating causal effects of functional treatments with modified functional treatment policies

University of Minnesota(明尼苏达大学)

Ziren Jiang, Erjia Cui, Jared D. Huling

AI总结:

本文提出一种新的因果估计量MFTP,通过功能主成分分析分解解决无限维对象平均问题,用于估计个体治疗轨迹微调后的潜在结果,通过模拟和实证研究验证了其有效性。

摘要:

功能数据在生物医学研究中日益普遍。尽管功能数据分析已有数十年的历史,但使用功能治疗进行因果推断仍鲜有探索。现有方法通常集中在估计因果平均剂量响应函数(ADRF),这需要强正性假设且可解释性有限。在本工作中,我们针对一个新的因果估计量,即修改的功能治疗政策(MFTP),该估计量旨在估计当每个个体略微修改其治疗轨迹时的平均潜在结果。这一新估计量的主要挑战在于需要对无限维对象进行平均,而该对象没有密度。通过提出一种新的基于功能主成分分析(FPCA)分解来定义功能变量总体平均的方法,我们建立了MFTP估计量的因果可识别性。我们进一步推导了MFTP的结局回归、逆概率加权和双重稳健估计量,并在温和的正则条件下提供了理论保证。所提出的估计量通过广泛的模拟研究进行了验证。将我们的MFTP框架应用于国家健康和营养调查(NHANES)加速计数据,我们估计了减少干扰夜间活动和低活动持续时间对所有原因死亡率的因果效应。

英文摘要:

Functional data are increasingly prevalent in biomedical research. While functional data analysis has been established for decades, causal inference with functional treatments remains largely unexplored. Existing methods typically focus on estimating the causal average dose response functional (ADRF), which requires strong positivity assumptions and offers limited interpretability. In this work, we target a new causal estimand, the modified functional treatment policy (MFTP), which focuses on estimating the average potential outcome when each individual slightly modifies their treatment trajectory from the observed one. A major challenge for this new estimand is the need to define an average over an infinite-dimensional object with no density. By proposing a novel definition of the population average over a functional variable using a functional principal component analysis (FPCA) decomposition, we establish the causal identifiability of the MFTP estimand. We further derive outcome regression, inverse probability weighting, and doubly robust estimators for the MFTP, and provide theoretical guarantees under mild regularity conditions. The proposed estimators are validated through extensive simulation studies. Applying our MFTP framework to the National Health and Nutrition Examination Survey (NHANES) accelerometer data, we estimate the causal effects of reducing disruptive nighttime activity and low-activity duration on all-cause mortality.

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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