Key result
Age-based maximal heart rate equations show wide prediction errors of ~±20 bpm regardless of fitness.
Why the study?
Maximal heart rate prediction equations may vary by cardiorespiratory fitness, but limited research has evaluated predictive accuracy across fitness levels.
Does cardiorespiratory fitness influence the prediction error of age-based maximal heart rate equations in healthy adults?
Cross-Sectional (n=230)
No
Does cardiorespiratory fitness influence the prediction error of age-based maximal heart rate equations in healthy adults?
p-value: p=0.015
Cardiorespiratory fitness has minimal influence on the accuracy of age-based maximum heart rate equations, and while Tanaka, Gellish, and Arena performed best, all equations exhibit wide individual variability limiting precision for exercise prescription.
Wide limits of agreement caution against relying on age-based equations for precise individual prescriptions; leaves open whether direct measurement improves outcomes.
INTRODUCTION: Maximal heart rate (MHR) is a key measure for cardiorespiratory exercise prescription yet is often estimated using age-based prediction equations. The accuracy of these equations may vary by individual characteristics, including cardiorespiratory fitness (CRF), but limited research has examined predictive accuracy across CRF levels. Therefore, we evaluated the accuracy of seven commonly used MHR prediction equations in adults with varying CRF to assess whether prediction error differs by fitness level. MATERIALS AND METHODS: Data from 230 healthy adults (76% male, mean age 38.5 ± 12.3 years) who completed maximal graded exercise tests between 2019 and 2024 were analyzed retrospectively. Predicted MHR values were calculated using the Fox, Tanaka, Gellish, Arena, Åstrand, Nes, and Fairbairn equations. Linear mixed-effects models (LMM) tested the influence of VO₂max and its interaction with prediction equation on error, with sex included as a covariate. Estimated marginal means and slopes were extracted, with pairwise contrasts adjusted by the Tukey method. Prediction equation accuracy was evaluated by comparing predicted and measured MHR using Bland-Altman analyses, and metrics including mean absolute error (MAE), root mean square error (RMSE), and intraclass correlation coefficients (ICC). RESULTS: LMM indicated a significant main effect of prediction equation on error (p < 0.001) and a significant equation × VO₂max interaction (p = 0.015), though neither sex (p = 0.49) nor VO₂max (p = 0.18) alone influenced error. The conditional R2 for the LME model was 0.70, with a marginal R2 of 0.02. Post-hoc linear regressions showed higher VO₂max was associated with greater prediction error for several equations in males, but not females, with a small amount of variance explained (R2 ≤ 0.06). Agreement analyses indicated small mean biases across equations (-3 to +6 bpm) but wide limits of agreement (~±18-24 bpm). Arena, Tanaka and Gellish equations showed the lowest MAE and RMSE. Among the equations, Fox showed the most stable performance across MHR ranges, being the only formula without proportional bias across the sample. DISCUSSION: The findings indicate that CRF had only a limited influence on MHR prediction error, with small associations observed in males but not females, reinforcing age as the primary determinant of MHR. Although some equations (e.g., Tanaka, Gellish, Arena, Fox) performed better than others across agreement metrics, none demonstrated high individual level accuracy, which highlights a lack of precision when estimating MHR for exercise prescription and monitoring purposes. Future work should explore more individualized modeling approaches, though adjusting for CRF alone may not substantially improve prediction accuracy in healthy adults.
No takes yet. Share an insight, caveat, or question.
Martin et al. (2025) conducted a cross-sectional in Healthy adults (n=230). Cardiorespiratory fitness (VO2max) vs. Directly measured maximal heart rate was evaluated on Influence of VO2max and its interaction with prediction equation on maximal heart rate prediction error (p=0.015). Cardiorespiratory fitness had minimal influence on maximal heart rate prediction error, while all seven age-based equations demonstrated wide limits of agreement (~±18-24 bpm).
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: