Enhancing Causal Inference in Functional Data: a Method for Estimating Time-Varying Causal Treatment Effects

Functional data analysis has emerged as a powerful statistical tool with applications across various scientific domains, yet its integration with causal inference remains underdeveloped despite the fundamental importance of causation in scientific investigations. A central challenge in causal analyses is the lack of random treatment assignment, which complicates the chance of drawing valid conclusions from observational data. This study focuses on evaluating the causal effect of a binary treatment on functional outcomes, addressing the additional complexity of sparse and irregularly measured data. To overcome non-randomized treatment assignments, we employed a weighting approach to mitigate confounding and constructed a pseudo-population for unbiased causal effect estimation. We effectively test and estimate the causal association between treatment and functional outcomes by applying intervalwise testing procedure and weighted functional-on-scalar modelling. The proposed method is applied for drug repurposing by estimating the causal effect of metformin, a diabetes medication, on kidney function using a real-world biobank.