Functional data is a powerful tool for capturing and analyzing complex patterns and relationships in a variety of fields, allowing for more precise modeling, visualization, and decision-making. For example, in healthcare, functional data such as medical images can help doctors make more accurate diagnoses and develop more effective treatment plans. However, understanding the causal relationships between functional predictors and time-to-event outcomes remains a challenge. To address this, we propose a functional causal framework including a functional accelerated failure time (FAFT) model and three causal approaches. The regression adjustment approach is based on conditional FAFT with subsequent confounding marginalization, while the functional-inverse-probability-weighting approach is based on marginal FAFT with well-defined functional propensity scores. The double robust approach combines the strengths of both methods and achieves a balance condition through the weighted residuals between imputed observations and regression adjustment outcomes. Our approach can accurately estimate causality, predict outcomes, and is robust to different censoring rates. We demonstrate the power of our framework with simulations and real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. Our findings provide more precise subregions of the hippocampus that align with medical research, highlighting the power of this work for improving healthcare outcomes.

翻译：功能数据是捕捉和分析各领域复杂模式与关系的强大工具，可实现更精确的建模、可视化及决策制定。例如在医疗领域，医学影像等功能数据能辅助医生做出更准确的诊断并制定更有效的治疗方案。然而，理解功能预测变量与时间-事件结局之间的因果关系仍具挑战性。为此，我们提出包含功能加速失效时间模型及三种因果方法的功能性因果框架。回归调整方法基于条件FAFT模型结合后续混杂变量边缘化，功能逆概率加权方法则基于边缘FAFT模型配合定义明确的功能倾向性评分。双重稳健方法融合两者优势，通过插补观测值与回归调整结果之间的加权残差实现平衡条件。本方法能准确估计因果效应、预测结局，并对不同删失率具有稳健性。我们通过阿尔茨海默病神经影像学倡议研究中的模拟数据与真实数据展示了该框架的能力。研究发现定位出与医学研究更精准匹配的海马体子区域，凸显了该工作改善医疗结局的潜力。