Exploratory analysis of the accuracy of age-based maximal heart rate equations across cardiorespiratory fitness levels

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