BASIC SCIENCES: Original Investigations: Commentary to Accompany
Gellish and associates (3) are to be congratulated for their paper, "Longitudinal Modeling of the Relationship between Age and Maximal Heart Rate," published in this issue of Medicine & Science in Sports & Exercise ®. The authors provide impressive statistical evidence that the commonly accepted maximal heart rate (HRmax)-prediction equation of 220 − age is biased. They demonstrate that 220 − age overestimated measured HRmax for men and women under the age of 40 yr and underestimated HRmax for those older than 40 yr. Their linear equation, derived from a mean follow-up of 9 yr (range: 5-17 yr) in 132 subjects, 206.9 − (0.67 × age), provides a more accurate HRmax estimate. They convincingly support the equation's accuracy with the cross-sectional meta-analysis published by Tanaka et al. (8) and the work of Londeree and Moeschberger (6), who have published nearly identical equations: HRmax = 208 − (0.7 × age) (Tanaka et al.), and HRmax = 206 − (0.7 × age) (Londeree and Moeschberger).
Although the publication of a more accurate equation is noteworthy, the most important aspect of their study, in my judgment, is their statistical methods. They used linear mixed models, which are newer multivariate statistical methods for studying change (7). To my knowledge, they are the first researchers to publish a paper in Medicine & Science in Sports & Exercise ® using this methodology. This statistical method allows researchers to study longitudinal data without the restriction that each subject needs the same number of tests. Their data consist of 132 people who had 908 maximal tests, an average of 6.9 tests per subject. Additionally, the method allows the researcher to include both fixed and random effects in the model. Gellish et al. document that their equation was independent of sex, BMI, and resting heart rate.
Their statistical analyses reveal that the relationship between age and HRmax was nonlinear, but they argue that their linear model was the preferred equation because it was more desirable from a usability point of view. With the current access to computer technology, one might consider using the nonlinear model in practical settings. Linear equations used to model nonlinear data produce systematic prediction errors at the ends of the bivariate distribution. Their data show that the linear and nonlinear HRmax estimates were ±0-2 bpm between age 35 and 65 yr, but the differences at the ends of the bivariate distribution, ages 30 and 75 yr, were 6 and 10 bpm, respectively.
One of their most important findings is that the relation between age and HRmax was nonlinear. In another important study, Fleg et al. (2) used linear mixed-effects regression modeling with 810 people and 2302 tests, an average of 2.8 tests per subject, to study the age-related decline in V˙O2max of subjects enrolled in the Baltimore Longitudinal Study of Aging. Cross-sectional data (4,5) have repeatedly documented a linear decline in V˙O2max with age, whereas Buskirk and Hodgson (1) suggested, in the 1980s, that the relation between age and V˙O2max likely was not linear. Fleg et al. (2) have demonstrated that V˙O2max declined at an accelerated rate with age. With the aging of Americans, this family of statistical models (7) takes on new scientific importance.
ANDREW S. JACKSON
Department of Health and Human Performance
University of Houston
1. Buskirk, E. R., and J. L. Hodgson. Age and aerobic power: the rate of change in men and women. Fed. Proc.
2. Fleg, J. L., C. H. Morrell, A. G. Bos, et al. Accelerated longitudinal decline of aerobic capacity in healthy older adults. Circulation
3. Gellish, R. L., B. R. Goslin, R. E. Olson, A. McDonald, G. D. Russi, and V. K. Moudgil. Longitudinal modeling of the relationship between age and maximal heart rate. Med. Sci. Sports Exerc.
4. Jackson, A. S., E. F. Beard, L. T. Wier, R. M. Ross, J. E. Stuteville, and S. N. Blair. Changes in aerobic power of men ages 25-70 years. Med. Sci. Sports Exerc.
5. Jackson, A. S., L. T. Wier, G. W. Ayers, E. F. Beard, J. E. Stuteville, and S. N. Blair. Changes in aerobic power of women, ages 20 to 64 years. Med. Sci. Sports Exerc.
6. Londeree, B. R., and M. L. Moeschberger. Effect of age and other factors on maximal heart rate. Res. Q. Exerc. Sport
7. Singer, J. D., and J. B. Willett. Applied Longitudinal Data Analysis
. New York, NY: Oxford University Press, 2003.
8. Tanaka, H., K. D. Monahan, and D. R. Seals. Age-predicted maximal heart rate revisited. J. Am. Coll. Cardiol.