Raw data of "Old and new equations for maximal heart rate prediction in patients with heart failure and reduced ejection fraction on beta-blockers treatment: results from the MECKI score data set"

AIMS: Predicting maximal heart rate (MHR) in heart failure with reduced ejection fraction (HFrEF) still remains a major concern. In such a context, the Keteyian equation is the only one derived in a HFrEF cohort on optimized beta-blockers treatment. Therefore, using the Metabolic Exercise combined with Cardiac and Kidney Indexes (MECKI) data set, we looked for a possible MHR equation, for an external validation of Keteyien formula and, contextually, for accuracy of the historical MHR formulas and their relationship with the HR measured at the anaerobic threshold (AT). METHODS AND RESULTS: Data from 3487 HFrEF outpatients on optimized beta-blockers treatment from the MECKI data set were analyzed. Besides excluding all possible confounders, the new equation was derived by using HR data coming from maximal cardiopulmonary exercise test. The simplified derived equation was [109-(0.5*age) + (0.5*HR rest) + (0.2*LVEF)-(5 if haemoglobin <11 g/dL)]. The R2 and the standard error of the estimate were 0.24 and 17.5 beats min-1 with a mean absolute percentage error (MAPE) = 11.9%. The Keteyian equation had a slightly higher MAPE = 12.3%. Conversely, the Fox and Tanaka equations showed extremely higher MAPE values. The range 75-80% of MHR according to the new and the Keteyian equations was the most accurate in identifying the HR at the AT (MAPEs = 11.3-11.6%). CONCLUSION: The derived equation to estimate the MHR in HFrEF patients, by accounting also for the systolic dysfunction degree and anaemia, improved slightly the Keteyian formula. Both formulas might be helpful in identifying the true maximal effort during an exercise test and the intensity domain during a rehabilitation programme.研究目的：射血分数降低型心力衰竭（heart failure with reduced ejection fraction, HFrEF）患者的最大心率（maximal heart rate, MHR）预测仍是临床亟待解决的重点难题。在此背景下，凯捷扬公式（Keteyian equation）是目前唯一在接受优化β受体阻滞剂（beta-blockers）治疗的射血分数降低型心力衰竭队列中推导得到的心率预测公式。因此，本研究借助代谢运动与心肾指数（Metabolic Exercise combined with Cardiac and Kidney Indexes, MECKI）数据集，旨在推导适用于该人群的最大心率预测公式，以对凯捷扬公式进行外部验证；同时评估既往经典最大心率预测公式的准确性，并分析其与无氧阈（anaerobic threshold, AT）测得心率的相关性。 方法与结果：本研究分析了MECKI数据集中3487名接受优化β受体阻滞剂治疗的射血分数降低型心力衰竭门诊患者的数据。在排除所有潜在混杂因素后，本研究利用最大心肺运动试验的心率数据推导得到全新的最大心率预测公式。简化后的推导公式为：109 - 0.5×年龄 + 0.5×静息心率 + 0.2×左心室射血分数（left ventricular ejection fraction, LVEF） - 5（若血红蛋白＜11 g/dL）。该公式的决定系数（R²）为0.24，估计标准误为17.5次/分钟，平均绝对百分比误差（mean absolute percentage error, MAPE）为11.9%。凯捷扬公式的平均绝对百分比误差略高，为12.3%。与之相反，福克斯公式与田中公式的平均绝对百分比误差显著更高。基于新公式与凯捷扬公式计算得到的75%~80%最大心率区间，在识别无氧阈对应的心率时准确性最高，平均绝对百分比误差为11.3%~11.6%。 结论：本研究推导的射血分数降低型心力衰竭患者最大心率预测公式，纳入了左心室收缩功能障碍程度与贫血状态，相较凯捷扬公式有小幅优化。两款公式均有助于准确识别运动试验中的真实最大运动强度，以及康复训练中的运动强度区间。