Handling unobserved confounding for continuous sequential data via extracting key sub-intervals

Existing methods for addressing unobserved confounding (UC) face practical limitations. Instrumental variable (IV) methods require additional variables, while “instrument-free” (IF) methods rely on specific model assumptions. This paper introduces a novel causal effect estimation method, CanKeSie (Causal Analysis based on Key Sub-interval Extraction), based on key sub-interval extraction to suppress UC in continuous sequential data. The key steps of CanKeSie for estimating fixed causal effects include: (1) extracting sub-intervals centered on change-points of the target variable (i.e., the explanatory variable of interest), (2) performing window regression to obtain a sub-estimator of the regression coefficient for the target variable within each sub-interval, and (3) combining these sub-estimators with appropriate weights to obtain an overall estimator. Among these steps, change-point detection is a core component of CanKeSie. To improve its accuracy, this paper proposes a novel algorithm, WASCC-CCPR (Cutting and Clustering combined with Peak Recognition based on Weighted Adjustment for Shape Context Cost), which incorporates three key techniques: data denoising, data-driven thresholding, and the construction of WASCC statistic. Furthermore, we enhance CanKeSie with spline fitting to enable time-varying causal estimation. Simulations confirm its effectiveness and highlight the superior performance of WASCC-CCPR. Two empirical studies show that CanKeSie's findings align with real-world survey data.