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Sex-Specific Maximum Predicted Heart Rate and Its Prognosis for Mortality and Myocardial Infarction


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Medicine & Science in Sports & Exercise: August 2017 - Volume 49 - Issue 8 - p 1704-1710
doi: 10.1249/MSS.0000000000001285


Maximum predicted heart rate (MPHR), used for calculating “target” heart rate during exercise treadmill testing (ETT), has traditionally been estimated by 220 − age. This formula was originally developed more than four decades ago in a small cohort of only 220 subjects that were mostly men <55 yr old (6). Today, it is still routinely applied in clinical practice, although contemporary populations are older and include higher proportions of women than the original derivation sample. Although several studies have questioned the formula's validity (3,8,13,15,16), it remains widely used partly because data on the outcomes and clinical implications associated with more accurate MPHR formulas are lacking. Because ETT is a common clinical test, more accurate estimation of MPHR could have profound implications in terms of diagnostic workup and clinical decision making.

The Henry Ford Exercise Testing (FIT) project is one of the largest ETT registries to date. Because MPHR was not originally derived in older adults and because its validity has been frequently questioned in women (8,13,15,16), the purpose of this study was to derive sex-specific formulas for MPHR in patients referred clinically for ETT and to determine their prognostic significance relative to the traditional formula of 220 − age.


Study cohort

The FIT project is a retrospective cohort study aimed at investigating the implications of cardiorespiratory fitness on cardiovascular outcomes. The FIT registry included 69,885 consecutive men and women ages 18–96 yr who underwent clinician-referred ETT for any indication at the Henry Ford Health System in metropolitan Detroit, Michigan, between 1991 and 2009. Methodological details of the FIT project have been reported previously (1).

For this study, we excluded patients <40 yr (n = 8611) to avoid referral bias in younger patients referred for sports participation, syncope, tachyarrhythmia, or congenital heart disease (15). To reduce the chance that comorbid diseases or medications may prevent participants from achieving their maximum heart rate, we also excluded patients with known coronary artery disease (CAD) (n = 9823), congestive heart failure (n = 771), atrial fibrillation (n = 1057), and atrial flutter (n = 11); patients taking AV nodal blocking medications (beta blockers, calcium channel blockers, or digoxin) (n = 10,448); patients taking diabetes medications (n = 3549), or patients undergoing revascularization within 90 d of the test (n = 224).

Finally, we excluded patients with missing exercise parameter data (n = 475) and with peak heart rates >200 or <100 bpm (n = 225) as these outliers were likely due to arrhythmia, vasovagal syncope, beta blockade, chronotropic incompetence, or data entry error (excluding these outliers did not affect the study findings). The final study sample was 31,090 patients (see Figure, Supplemental Digital Content 1, Flowchart of study exclusions across the FIT population,

The FIT project was approved by the Institutional Review Board of Henry Ford Health System. Because data were de-identified and collected retrospectively, the Institutional Review Board deemed this study exempt from individual consents.

Treadmill testing

All patients were tested using the standard Bruce protocol (2). For participants with multiple exercise tests, only the results from the first test were considered. In accordance with the American Heart Association and the American College of Cardiology guidelines, ETT was terminated at the discretion of the supervising clinician for reasons that included significant arrhythmias, abnormal hemodynamic responses, ST-segment changes diagnostic for ischemia, or exercise-limiting symptoms such as chest discomfort or dyspnea (7). Otherwise, patients were encouraged to exercise to their maximum ability and were not terminated based on a heart rate criterion.

Resting heart rate and blood pressure (BP) were taken before the ETT with the patient supine. In addition to continuous electrocardiographic monitoring, BP was measured every 3 min during the test. The highest recorded heart rate and BP were considered to be the peak heart rate and BP. Exercise capacity, expressed in estimated METs of task, was calculated by the Quinton treadmill controller (Quinton Instrument Co., Bothell, WA) based on achieved speed and elevation.

Follow-up and event adjudication

Patients were followed for the occurrence of death, myocardial infarction (MI), and need for coronary revascularization. Mortality ascertainment was conducted in April 2013 using an algorithm for searching the Social Security Death Index. A complete algorithmic search was applied to >99.5% of patients. MI was ascertained through linkage with administrative claims files using appropriate International Classification of Diseases, Ninth Revision and Current Procedural Terminology codes (1).

Statistical analyses

Scatterplots of peak heart rate versus age were constructed separately for women and men. Linear regression analysis was used to determine lines of best fit for each plot and to obtain sex-specific estimates of MPHR as a function of age. Interaction between age and sex was tested. We used bootstrapping for internal validation and compared the root-mean-square error (RMSE) of the sex-specific and traditional (220 − age) formulas (14).

Prognostic significance of target heart rate achievement (defined as 85% MPHR) was assessed for the new sex-specific and traditional formulas. Crude incidence rates and Cox proportional hazard models were used to compare the risks of MI and death based on attainment of the target heart rate. Survival started at the time of ETT with censoring at the time of the relevant event (death or MI) or end of study (April 30, 2013). We used two proportional hazards models with progressive degrees of adjustment. Model 1 adjusted for age, sex, race, body mass index (BMI), clinical indication for testing, resting systolic BP, resting heart rate, history of smoking, history of diabetes, and use of antihypertensive medications, lipid-lowering medications, or inhalers for chronic pulmonary disease. Model 2 further adjusted for METs achieved to determine whether attainment of the target heart rate was associated with outcomes independent of fitness.

To compare outcome development by target heart rate attainment according to the sex-specific and traditional formulas, we classified study participants into three groups: concordant-adequate, achieved target heart rate by both sex-specific and traditional formulas; discordant, achieved target heart rate by either sex-specific or traditional formula only; and concordant-inadequate, failed to achieve target heart rate by both formulas. Receiver operating characteristics, Akaike's information criterion, and Bayesian Information Criterion were used to compare death and MI discrimination of the sex-specific versus traditional MPHR formulas.

All statistical analyses were performed with STATA version 12.0 (StataCorp, College Station, TX). Alpha level was <0.05 (two-sided).


The age of study participants was 55 ± 10 yr (mean ± SD), 49% were women, 70% were White, and 23% were Black (Table 1). BMI was 29 ± 6 kg·m−2, and METs achieved were 9 ± 3. The peak heart rate was 153 ± 15 bpm in women and 154 ± 16 bpm in men.

Peak heart rate was best estimated by 197 − 0.8 × age for women and 204 − 0.9 × age for men (Fig. 1). P for interaction by sex was <0.001. The traditional formula 220 − age consistently overestimated peak heart rate across all ages in both men and women. The overestimation was by 12 ± 2 bpm in women and 11 ± 1 bpm in men when compared with the sex-specific formulas. In bootstrap analyses, the RMSE was 7.1 bpm for the sex-specific formulas and 8.3 bpm for the traditional formula (see Table 1, Supplemental Digital Content 2, Mean maximum predicted heart rate and RMSE of sex-specific and traditional formulas compared to true peak heart rate in the FIT project,

A, Peak heart rate versus age for 15,312 women referred for exercise treadmill testing in the FIT project. B, Peak heart rate versus age for 15,778 men referred for exercise treadmill testing in the FIT project.

Patients achieving target heart rates were younger and able to achieve higher METs; were more likely to be female and White; had lower BMI, Framingham risk scores, and resting systolic BP; and were less likely to have a history of smoking or diabetes or to be taking antihypertensive or lung disease medications (Table 1).

During the 11 ± 5 yr follow-up, we identified 2824 (9%) deaths (1690 men and 1134 women) as well as 661 (2%) MIs. (416 men and 245 women). The fully adjusted (model 2) hazard ratios (95% confidence interval) for mortality comparing patients who achieved ≥85% MPHR to those who did not were 0.76 (0.60–0.97) for the sex-specific formulas and 0.75 (0.62–0.90) for the traditional formula. The corresponding hazard ratios for MI were 0.71 (0.47–1.06) and 0.79 (0.57–1.10), respectively (Table 2 for overall; Table 2, Supplemental Digital Content 3, Sex-stratified risk of all-cause death and MI based on achievement of 85% of maximum predicted heart rate using the sex-specific and traditional formulas, Area under the receiver operating characteristics curve, Akaike's information criterion, and Bayesian Information Criterion for risk of death and MI based on the sex-specific versus traditional MPHR formulas were similar (see Table 3, Supplemental Digital Content 4, Akaike's information criterion, Bayesian information criterion, and area under the receiver operating characteristics curve for risk of death and MI based on failure to achieve 85% of maximum predicted heart rate using the sex-specific and traditional formulas,

There were 1868 patients (6%) who did not achieve the target heart rate per the traditional MPHR formula but did achieve the target heart rate per the sex-specific formulas (MPHR values based on the traditional formula were higher than those based on the sex-specific formulas in all cases). Compared with the discordant target heart rate patients, concordant-adequate patients were younger and more likely to be White (Table 3). The mortality rate for discordant patients was 14.2 per 1000 person-years, which fell in between rates for concordant-adequate and concordant-inadequate patients (Fig. 2). The hazard ratio for death was 1.99 (1.76–2.24, P < 0.001) for discordant compared with concordant-adequate patients and 0.60 (0.51–0.70, P < 0.001) for discordant compared with concordant-inadequate patients.

Survival probability based on MPHR formula concordance (using the traditional and sex-specific formulas) in 31,090 patients referred for exercise treadmill testing in the FIT project.
Clinical characteristics of 31,090 patients in the FIT project who did or did not achieve target exercise heart rate using the derived sex-specific MPHR formulas.
Risk of all-cause death and MI based on achievement of 85% of MPHR using the sex-specific and traditional formulas.
Clinical characteristics of 31,090 patients in the FIT project by target heart rate achievement per sex-specific and traditional MPHR formula concordance.


In this large cohort of men and women referred for clinical ETT, the traditional formula of 220 − age substantially overestimated MPHR in all age and sex groups. The sex-specific formulas of 197 − 0.8 × age for women and 204 − 0.9 × age for men better represented peak heart rate than the traditional formula in a clinical population ≥40 yr old. Although attainment of the target heart rate using the sex-specific formulas was similarly associated with lower risk of death and MI as the traditional formula, approximately 6% of patients referred for ETT in this cohort had “inadequate” heart rate by the traditional formula but were “adequate” by the sex-specific formulas. This is highly relevant as patients who do not achieve the target heart rate by stress testing are often referred for additional testing or cardiac catheterizations. The use of the sex-specific formulas may help to reclassify risk in such patients and prevent further unnecessary testing, procedural risks, and cost.

Peak heart rate is one of the most commonly used exercise parameters in cardiovascular medicine. The heart rate response to exercise is based on the physiological need to increase cardiac output, and inability to adequately do so may reflect an underlying abnormality (5). Lauer et al. (10) showed that ETT patients unable to achieve 85% MPHR had a 4% absolute increase in mortality risk for only 2 yr. Similarly, Elhendy et al. (4) showed that patients unable to achieve 85% MPHR had increased all-cause and cardiac mortality at 3 yr of follow-up. Because millions of patients undergo ETT around the world each year, it is important to calculate MPHR as accurately as possible.

The traditional formula used to predict MPHR was derived by Fox et al. (6) in the 1970s from a small cohort of 220 subjects. Most of these subjects were men younger than 55 yr old and, therefore, not wholly representative of the general ETT referral population. Since then, the accuracy of the traditional MPHR formula has been questioned many times, and sex-specific formulas have been recommended by several authors (see Table 4, Supplemental Digital Content 5, Prior studies reporting alternative regressions for MPHR calculation, (3,8,13,15,16). For instance, a meta-analysis of 18,712 patients showed alternative regressions for MPHR calculation (208 − 0.77 × age for women and 209 − 0.73 × age for men) (16), and Daida et al. (3) published similar regression equations (213 − 0.90 × age for men) and (203 − 0.76 × age for women) based on 7863 men and 2406 women without cardiovascular disease. Consistent with our findings, previous studies found that the traditional MPHR formula overestimated peak heart rate and recommended incorporation of sex-specific parameters into clinical practice.

Like our findings, the aforementioned studies found optimal MPHR regressions with lower heart rate intercepts than the traditional formula (see Table 4, Supplemental Digital Content 5, Prior studies reporting alternative regressions for MPHR calculation, This may be related to differences in patient characteristics between those studies and the original derivation sample for the traditional formula. We specifically excluded patients with known CAD and other common cardiovascular disease confounders to derive ideal MPHR in “normal” clinical subjects. However, our cohort was still composed of patients that were clinically referred for ETT as opposed to asymptomatic volunteers. It has been hypothesized that a poor exercise heart rate response may be an early manifestation of cardiac ischemia or underlying autonomic dysfunction even if symptoms are not yet evident (17,18). This may explain why symptomatic, clinical patients in our cohort had lower peak heart rate than healthy, asymptomatic volunteers in other studies.

Approximately 6% of participants in our study achieved adequate heart rate using the derived sex-specific formulas but were inadequate or “near-adequate” using the traditional formula. Survival in this group fell in between that of patients who did and did not achieve the target heart rate using both formulas. It is not known how many of these patients were referred for further diagnostic procedures because of inadequate stress tests, and whether these additional tests or procedures altered long-term outcomes.

Recent estimates show that more than 3.8 million stress tests are performed in the United States alone each year (9). A considerable portion of these patients may be referred for further testing and may receive unnecessary radiation or invasive angiography. Indeed, more than 34% of stress tests have been shown to be ordered inappropriately, with associated annual costs estimated more than $500 million and future cases of cancer estimated at 491 per year (9).

Furthermore, less than 38% of cardiac catheterization patients were found to have obstructive CAD after noninvasive testing (11), and less than 3% of exercising patients without typical angina had positive nuclear stress tests (12). Thus, there is potential for excessive radiation and increased cost with unnecessary additional testing in near-adequate ETT patients. Per our estimates, use of the sex-specific formulas would reclassify 228,000 (6% of 3.8 million) stress tests from “inadequate” to “adequate” per year in the United States alone.

For clinical use, we have provided nomograms for MPHR determination for women and men (see Table 5, Supplemental Digital Content 6, Women's nomogram for MPHR during exercise testing,; Table 6, Supplemental Digital Content 7, Men's nomogram for MPHR during exercise testing, using the sex-specific and traditional formulas. At the time of exercise testing, clinical providers may use these nomograms to determine MPHR using the patient's age and sex. Alternatively, sex-specific MPHR can also be easily estimated by rounding the intercept (i.e., 200 − 0.8 × age for women or 200 − 0.9 × age for men) based on the derivations in this study.

Strengths and limitations

There are many important strengths to this study. 1) This is among the largest studies to date evaluating peak heart rate versus age in both women and men. 2) Unlike prior studies, which have commonly used a cross-sectional design, our study used a cohort design with 11 yr of mean follow-up for clinical events. For this reason, we were able to compare long-term prognostic significance of our formulas to that of the traditional MPHR formula, which has not been done previously. 3) All patients in this study were clinically referred for ETT by a health care provider, which makes results more applicable to routine clinical populations. Prior studies evaluating peak heart rate have commonly included asymptomatic volunteers.

Some limitations, however, need to be considered in the interpretation of our findings. First, our results were derived from a single health care system. Although the FIT cohort is large and diverse, further studies are needed to confirm the generalizability of our findings in other populations. Second, we did not have data on obstructive CAD, which is needed to better evaluate the diagnostic implications of MPHR formulas. Third, MI was ascertained based on an administrative claims database. This is inherently less rigorous than methodologies using blinded event adjudication based on a uniform definition for MI. Finally, it remains unclear how changes to peak heart rate calculation would translate to changes in clinical care. We were unable to determine precisely how many patients would have avoided repeat or further testing with use of these newly proposed formulas. Follow-up studies will be needed to evaluate the clinical changes resulting from use of sex-specific MPHR formulas.


In this cohort of patients referred for clinical ETT, the sex-specific formulas of (197 − 0.8 × age) for women and (204 − 0.9 × age) for men better predicted MPHR than the traditional formula (220 − age). Achievement of ≥85% MPHR was similarly associated with lower risk of death and MI when using the sex-specific compared with the traditional formulas, even after adjustment for confounders, and approximately 6% of ETT patients were reclassified from having inadequate to adequate stress tests. External validation is needed to confirm these findings, and further investigation is needed to determine whether these sex-specific formulas may reduce further testing in patients achieving near-adequate stress tests.

There are no disclosures and no conflicts of interest. There are no sources of funding. The results of the study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation. Results of the present study do not constitute endorsement by the American College of Sports Medicine.


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