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Understanding the influence of cardiovascular diseases (CVD) on human regulatory functions is a major challenge in modern healthcare. This study explores whether the autonomic response to sleep arousals can serve as a diagnostic marker of the health of physiological networks. We introduce a novel method for the robust calculation of information transfer, based on the optimization of embedding parameters for transfer entropy (TE) calculation. Using this approach, we analyzed the information transfer dynamics of 8,136 sleep arousals from 1,956 subjects from the SHHS follow-up visit. Compared to three state-of-the-art approaches, our newly introduced method, max. TE, achieved a 17.9% more stable TE estimate than the second-best approach. Our results indicate a significantly ( p < 0.001 ) lower TE in patients with CVD ( 85.4 ± 0.8  mnats) than that in healthy controls ( 87.9 ± 0.5  mnats), indicating an impairment of regulatory control mechanisms. Furthermore, the TE decreases linearly with increasing age and shows significant differences between sleep stages, with the highest TE occurring during REM sleep ( p < 0.001 ) . These findings demonstrate that sleep arousals, as a physiological stimulus, can reveal sleep stage- and disease-related changes in cardiovascular networks and that our approach provides a robust group-level embedding strategy for physiological information-transfer analysis.