A Hybrid Approach for Exploring Real-World Linear Causality Under Multicollinearity Based on Ischemic Post-Stroke Case Series Treated With Integrated Traditional Chinese and Modern Medicine Therapies

Abstract

Objective: Integration of traditional Chinese and modern medicine (TCM-MM) aids rehabilitation of muscle strength among ischemic stroke (IS) survivors. However, it faces statistical challenges (e.g., multicollinearity, small sample) in the real-world setting. This study tried to provide an analytical framework for investigating linear causality with a retrospective small-sample case series.

Methods: Original data was sourced from hospital information system and processed by many means. Wilcoxon signed-rank test was utilized to execute a self-controlled before-and-after comparison, before multiple linear regression (MLR) models were established for exploring prognostic factors of muscle strength improvement. Afterward, Bayesian networks (BN), mediation analysis and between-subjects effects tests were undertaken the detection of underlying multicollinearity sources progressively. Both clinical interpretability and model performance, containing R² and mean squared error (MSE), served as the indices for modelling comparison.

Results: Muscle strength was significantly improved among 112 post-IS patients after accepting TCM-MM therapies (p < 0.01). Initially, MLR analysis with 11 explanatory variables (EVs) (MLR_1) revealed a probable multicollinearity-driven bias, resulting in reduced interpretability. Consequently, we traced collinearity among EVs using a BN structure that provided clues to mediating and mutual effects for establishing MLR with interactions embracing 11 EVs (MLR_2). Eventually, MLR_2 demonstrated superior model performance (ΔR² = 0.097, ΔMSE = –0.004), and better clinical interpretability. Whereas, we cannot deny a 1/3 probability of diminished statistical efficacy due to the small sample size.

Conclusion: Our study proposed a practically hybrid approach for exploring linear causality under multicollinearity using real-world small-sample data, which suggested that balancing model performance with clinical interpretability can resolve statistical trade-offs in modelling optimization.

Keywords

Bayesian network / interactions / mediation test / multicollinearity / multivariable linear regression / small-sample data

RIGHTS & PERMISSIONS

2025 Chinese Cochrane Center, West China Hospital of Sichuan University and John Wiley & Sons Australia, Ltd.