Understanding the causal effects of organ-specific features from medical imaging on clinical outcomes is essential for biomedical research and patient care. We propose a novel Functional Linear Structural Equation Model (FLSEM) to capture the relationships among clinical outcomes, functional imaging exposures, and scalar covariates like genetics, sex, and age. Traditional methods struggle with the infinite-dimensional nature of exposures and complex covariates. Our FLSEM overcomes these challenges by establishing identifiable conditions using scalar instrumental variables. We develop the Functional Group Support Detection and Root Finding (FGS-DAR) algorithm for efficient variable selection, supported by rigorous theoretical guarantees, including selection consistency and accurate parameter estimation. We further propose a test statistic to test the nullity of the functional coefficient, establishing its null limit distribution. Our approach is validated through extensive simulations and applied to UK Biobank data, demonstrating robust performance in detecting causal relationships from medical imaging.

翻译：理解医学影像中器官特异性特征对临床结果的因果效应，对于生物医学研究和患者诊疗至关重要。本文提出一种新颖的函数线性结构方程模型，用以刻画临床结果、功能性影像暴露变量以及遗传学特征、性别、年龄等标量协变量之间的关联关系。传统方法难以处理暴露变量的无限维特性及复杂协变量结构。本研究通过引入标量工具变量建立可识别条件，克服了这些挑战。我们开发了函数组支持检测与求根算法，以实现高效的变量选择，该算法具有严格的理论保证，包括选择一致性和参数估计准确性。进一步提出用于检验函数系数零假设的检验统计量，并确立了其零假设极限分布。通过大量模拟实验及在英国生物银行数据中的应用，验证了本方法的有效性，证明其在医学影像因果关联检测中具有稳健性能。