摘要: 目的：对比分析六种常用的年龄预测最大心率公式(Fox, Tanaka, Gellish, Fairbarn, Arena, Nes)在运动员群体中的有效性和预测精度。方法：以Physionet上马拉加大学2008~2018年间992次跑步机最大分级运动测试数据为基础，对实测最大心率和基于Fox、Tanaka、Arena、Gellish、Nes、Fairbarn六个常用年龄预测公式的预测最大心率采用配对Wilcoxon秩和检验、Bland-Altman一致性分析、平均绝对百分比误差(Mean Absolute Percentage Error, MAPE)和均方根误差(Root Mean Square Error, RMSE)进行评估。结果：配对Wilcoxon秩和检验显示，Fox、Tanaka、Arena、Nes、Fairbarn公式预测的最大心率与实测值均存在显著差异，而Gellish公式则无。Gellish公式偏差最小(0.26 bpm)，MAPE (3.49)和RMSE (8.22 bpm)最低，整体预测误差最小；Nes公式预测值正向偏差最大(6.01 bpm)，Fox公式和Nes公式预测精度较差；所有公式预测值95%一致性界限宽泛(平均范围 ± 10~15 bpm)。结论：六个公式在运动员群体中预测准确性存在差异且均有局限性。Gellish公式整体表现最优，但个体误差仍显著；Fox、Nes因系统性偏差大，不推荐用于运动员。

Abstract: Objective: To comparatively analyze the validity and prediction accuracy of six commonly used age-predicted maximum heart rate equations (Fox, Tanaka, Gellish, Fairbarn, Arena, Nes) in the athlete population. Methods: Based on 992 treadmill maximal graded exercise test data from the University of Malaga on Physionet during 2008~2018, the measured maximum heart rate and the predicted maximum heart rate based on six commonly used age-predicted equations of Fox, Tanaka, Arena, Gellish, Nes, and Fairbarn were evaluated using paired Wilcoxon rank sum test, Bland-Altman consistency analysis, mean absolute percentage error, and root mean square error. Results: Paired Wilcoxon rank sum test showed that there were significant differences between the HRmax predicted by Fox, Tanaka, Arena, Nes, and Fairbarn equations and the measured values, while there was no such difference for the Gellish equation. The Gellish equation had the smallest deviation (0.26 bpm), the lowest MAPE (3.49) and RMSE (8.22 bpm), and the smallest overall prediction error; the Nes equation had the largest positive deviation in the predicted value (6.01 bpm), and the prediction accuracy of the Fox equation and the Nes equation was poor; the 95% consistency limits of the predicted values of all equations were wide (average range ± 10~15 bpm). Conclusion: The prediction accuracy of the six equations varies and all have limitations in the athlete population. The Gellish equation has the best overall performance, but the individual error is still significant; Fox and Nes are not recommended for athletes due to large systematic deviations.