Hering-Breuer reflex and respiratory rate: a biased association

The Hering-Breuer reflex (HBR) plays an important role in the regulation of respiratory timing in infancy. Some investigators have noted that HBR is stronger when the respiratory rate (RR) is faster. However, this finding may be due to a spurious correlation, since one of the variables (expiratory time) used to calculate both HBR and RR is the same. We investigated this hypothesis with Monte Carlo (simulation) studies by using uncorrelated random numbers to calculate RR and HBR and found a strong spurious correlation (r = 0.7) between HBR and RR, i.e., subjects with higher RR had a stronger HBR. These results were confirmed algebraically, and the formula for the expected value of the correlation coefficient [E(r)] was derived. E(r) was always >0; it was 0.707 when no prolongation of inspiration occurred and was larger in the presence of a prolongation; when HBR strength was 100%, E(r) = 0.89, and when it was 200%, E(r) = 0.94. The expected value of the slope of the regression line of HBR on RR was found to be directly proportional to expiratory time during occlusion. As faster RRs produce stronger HBRs, any variable associated with RR, i.e., age, length, and weight, may influence HBR. This can lead to inconclusive or biased results in studies of the maturation of HBR with age and can confound comparisons across groups that do not have the same RR.