Overestimation of Mean Heart Rate by the Arithmetic Average of Beat-By-Beat Sampled Heart Rate Values

The arithmetic average of beat-by-beat sampled heart rate (HR) values overestimates true HR defined as number of heart beats per time unit. The aims of this study were to (1) estimate the magnitude of overestimation; (2) illustrate the significance of this issue using data from patients with congestive heart failure (CHF) and control subjects; and (3) outline approaches to correctly calculate mean HR. Linear regression analysis of computer-generated time series, representing beat-by-beat HR values in humans, rats, and mice, revealed that the difference between the arithmetic average of beat-by-beat sampled HR values and the true mean HR (error e) can be approximated by the variance (σ 2 ) divided by the arithmetic average (µ) of the beat-by-beat HR values (e = σ 2 /µ). True mean HR was higher in patients with CHF (92.9±4.3 bpm) than in control subjects (82.6±2.1 bpm, P=0.045). However, if mean HR was calculated as arithmetic average of the beat-by-beat HR values the difference in mean HR was no longer significant (93.4±4.4 bpm in CHF vs. 83.8±2.1 bpm in controls, P=0.059). In conclusion, the arithmetic average of beat-by-beat sampled HR values overestimates true HR by approximately the ratio of σ 2 to µ of the beat-by-beat HR values. Thus, the error (e) is largest in subjects with high HR variability and low average HR and may affect interpretation of mean HR values in studies investigating populations of subjects with differing HR variability, such as CHF patients vs. healthy subject or old vs. young subjects.