Comparison between probabilistic and Wiener–Granger causality in assessing modifications of the cardiac baroreflex control with age

Abstract

Background: Probabilistic causality (PC) is a framework for checking that the occurrence of a cause raises the probability of the effect by comparing the probability of the effect conditioned and unconditioned to the cause. Even though it is less frequently utilized with respect to the more traditional model-based Wiener–Granger causality (WGC) that is based on the predictability improvement of an effect resulting from the inclusion of the presumed cause in the multivariate linear regression model, PC has the advantage of being model-free. Objective: The aim of the study is to apply the PC framework to assess the evolution of cardiac baroreflex control with age from spontaneous fluctuations of heart period (HP) and systolic arterial pressure (SAP) and to compare it to the more common WGC approach. Approach: We studied 100 healthy humans (54 males, age: 21–70 years, 20 subjects for each 10 years bin). HP and SAP were extracted on a beat-to-beat basis from 5 min recordings of electrocardiogram and plethysmographic arterial pressure at rest in supine position (REST) and during active standing (STAND) under spontaneous breathing. The WGC ratio (WGCR) was computed as the log ratio of the prediction error variance of the autoregressive model on HP to that on HP with exogenous SAP. The PC ratio (PCR) was computed as the probability of observing an HP ramp given an associated parallel SAP variation divided by the probability of observing an HP ramp. Main results: The WGCR and PCR suggested the gradual impairment of cardiac baroreflex with age, especially during STAND. Moreover, they were significantly associated both at REST and during STAND but the degree of the PCR-WGCR association was weak. Significance: PC can be effectively exploited to assess modification of the cardiovascular control during senescence even though a limited agreement was observed with WGC.