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 dataset

Background: Predicting maximal heart rate (MHR) in heart failure and 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 β-blockers treatment. Therefore, using the Metabolic Exercise combined with Cardiac and Kidney Indexes (MECKI) dataset, 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 3,487 HFrEF outpatients on optimized β-blockers treatment from the MECKI dataset were analyzed. Besides excluding all possible confounders, the new equation was derived by using HR data coming from maximal cardiopulmonary exercise test (CPET).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 SEE were 0.24 and 17.5 beats·min-1 with a MAPE = 11.9%. The Keteyian equation had a slightly higher mean absolute percentage error (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% to 11.6%). Conclusions: The derived equation to estimate the MHR in HFrEF patients, by accounting also for the systolic dysfunction degree and anemia, 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 program.