Revisiting Use of the Ebbeling Prediction Equation - The College ...
Revisiting Use of the Ebbeling Prediction Equation
Sonya M. Arzola, MS
The Geneva Foundation working at Brooke Army Medical Center
Department of Nursing Research
Fort Sam Houston, TX 78234-6200
Stacey Young-McCaughan, RN, PhD
University of Texas Health Science Center San Antonio
School of Medicine, Department of Psychiatry
San Antonio, TX 78229-3900
Maximal oxygen consumption (VO2 max) is one commonly used index of
cardiorespiratory fitness. It can either be directly measured or indirectly
calculated using a regression equation to predict VO2 max from a combination of
variables such as age, heart rate, speed and/or time at either maximal or
submaximal work load on an ergometer or other field test. Direct measurement
has evolved over the years from volumetric gas analyzers, to semi-automated
systems, to automated systems (i.e., the metabolic cart). The direct measurement
of VO2 max requires trained staff using costly, specialized equipment. It can be
time consuming for both the patient and the staff. Thus, indirectly measuring
VO2 max can be more practical in a busy clinical or cost-constrained environment.
The Ebbeling formula is an equation that can be used to predict VO2 max from a
4-minute single-stage submaximal treadmill walking protocol . Speed, heart
rate, age, and gender are used to determine VO2 max using the formula:
VO2 max = 15.1 + (21.8) (speed in mph) - (0.327) (heart rate in bpm)
- (0.263) (speed) (age in years) + (0.000504) (heart rate) (age) + (5.98)
(gender where 0 = female and 1 = male)
The Ebbeling formula was selected to determine VO2 max as a measure of
cardiorespiratory fitness in a quasi-experimental, repeated-measures study
designed to assess how persons within six months of completing treatment for
cancer do over the 18-months following participation in a 12-week exercise
program comparing them to patients who did not participate in the program .
While the Ebbeling protocol is not specific to patients with cancer or older
Professionalization of Exercise Physiologyonline
Vol 12 No 6 June 2009
persons, the protocol and formula were chosen over direct measurement of VO2
max during maximal testing for this study because physician supervision was not
required for patients without existing disease and because patients could better
tolerate the 4-minute test administered five times over 18-months. Also, the
formula had been shown to be reliable and valid  and computer software was
available that quickly calculated the predicted VO2 max .
During baseline testing patients were allowed two- to four-minutes to warm-up on
the treadmill and find a comfortable speed between 2.0 and 4.5 mph at a 0% grade
that elicited a heart rate between 50% and 70% of age predicted maximal heart
rate (APMHR). During the four-minute exercise phase patients walked at the
speed determined during the warm-up phase plus a 5% grade . Subsequent
testing was conducted at the same speed and grade. In the process of analyzing
the data the research team was puzzled by the calculated VO2 max values until it
was realized that two key elements of the structure of the prediction formula had
been inadvertently overlooked.
First Key Element Overlooked
We were studying exercise rehabilitation in patients with cancer. The incidence
of cancer increases with age  and as anticipated, our study sample had a mean
age of 60 years with a range of 31 to 86 years. Unexpectedly however, we found
that as individuals aged instead of calculating increases in predicted VO2 max
with decreases in heart rate, predicted VO2 max decreased with decreases in heart
rate. This change from the expected inverse relationship between heart rate and
predicted VO2 max to an unexpected direct relationship between heart rate and
predicted VO2 max occurred at age 65.
In re-evaluating the prediction equation it was obvious that the negative
coefficient 0.327 has an increasingly larger negative effect on the calculation with
increasing age while the positive coefficient 0.000504 has a decreasingly positive
effect with increasing age. Ebbeling clearly states that the protocol was
developed in a population of typically healthy subjects ranging in age from 20 to
59 years . Although it is mathematically possible to apply the formula to an
older population as we did, this was not appropriate.
Second Key Element Overlooked
To avoid the practice effect of exercise testing where the individual being tested
performs better because of familiarity with the equipment, the research team
standardized the speed at all testing times determined at baseline. Although the
formula was not specifically developed to assess change over time, the research
team used it to assess change over time anticipating that trained study participants
would more easily complete the testing protocol at subsequent testing periods and
that this would be reflected as an increase in VO2 max. However, there was very
little variability in the calculated VO2 max.
In re-evaluating the prediction equation, it was obvious that change in speed,
which the research team had kept constant over time, has the greatest effect on the
calculated VO2 max. As compared with speed that has a large positive coefficient
of 21.8 and thus a large impact on the calculated VO2 max, heart rate has a
relatively small impact on the calculated VO2 max with a small negative
coefficient of 0.327 in one term and a very small positive coefficient of 0.000504
in another term. By standardizing the speed for all testing time points, we
inadvertently eliminated the influence of change in speed over time.
The Ebbeling protocol is an easily conducted, generally well-tolerated, and robust
approach to assess cardiorespiratory fitness recommend for both clinical care and
research studies. However, both clinicians and researchers should be cautioned to
only use prediction equations in the populations for which they were developed
and tested. And when testing individuals over time, repeated measurement of the
variable of interest over time should be carefully chosen as not to inadvertently
Recommendations for Future Research
Future research should develop predication equations for older persons as well as
those with chronic conditions like cancer. Cardiorespiratory fitness has been
repeatedly shown to be predictive of both health benefit and disease reduction.
Sensitive and specific measures will help to better define those benefits in
selected populations and test interventions to further improve health and reduce
1. Ebbeling, C.B., et al. (1991). Development of a single-stage submaximal
treadmill walking test. Medicine & Science in Sports Exercise. 23(8):966-73.
2. Arzola, S.M., S. Young-McCaughan, and S.A. Dramiga. (2007). The Ebbeling
protocol: Tolerability in patients completing treatment for cancer. Journal of
Cardiopulmonary Rehabilitation and Prevention. 27:315-339.
3. Ng, N.K. (1995). METCALC software: Metabolic calculations in exercise and
fitness. Champaign, IL: Human Kinetics.
4. American Cancer Society. Cancer Facts & Figures 2008. Atlanta: American
Cancer Society; 2008.
Disclaimer: The views of these authors are their own and do not purport to reflect
the position of the Army Medical Department, Department of the Army, or the
Department of Defense.
Acknowledgement: Funding for this work was made possible through the
Uniformed Services University of the Health Sciences TriService Military
Nursing Research Grants Program (MDA HU0001-05-1-TS03, TSNRP N05-
006). The authors would like to gratefully acknowledge Travis Vaught for his
assistance calculating the age at which the relationship between heart rate and
VO2 max, and Jim Mintz, PhD for his assistance helping us understand the