On the validity of single regression strategy for Granger causality assessment in cardiovascular and cardiorespiratory control studies

Granger causality (GC) analysis is based on the comparison between prediction error variances computed over the full and restricted models after identifying the coefficients of appropriate vector regressions. GC markers can be computed via a double regression (DR) approach identifying two separate, independent models and a single regression (SR) strategy optimizing the description of the dynamics of the target over the full model and, then, reusing some parts of it in the restricted model. The present study compares the SR and DR strategies over heart period (HP), systolic arterial pressure (SAP) and respiration (R) beat-to-beat series collected during a graded orthostatic challenge induced by head-up tilt in 17 healthy individuals (age: 21-36 yrs; median: 29 yrs; 9 females and 8 males). We found that the DR approach was more powerful than the SR one in detecting the expected stronger involvement of the baroreflex during the challenge, while the expected weaker cardiorespiratory coupling was identified by both SR and DR strategies. The less powerful ability of the SR approach was the result of the greater variance of GC markers compared to the DR strategy. We conclude that, contrary to the suggestions present in literature, the SR approach is not necessarily associated with a smaller dispersion of GC markers. Moreover, we suggest that additional factors, such as the strategy utilized to build embedding spaces and metric utilized to compare prediction error variances, might play an important role in differentiating SR and DR approaches.