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BASIC SCIENCES: Epidemiology

Nonexercise Models for Estimating V̇O2max with Waist Girth, Percent Fat, or BMI


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Medicine & Science in Sports & Exercise: March 2006 - Volume 38 - Issue 3 - p 555-561
doi: 10.1249/01.mss.0000193561.64152
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V̇O2max links exercise science with health and medicine. Being the quantification of aerobic power, V̇O2max serves as the basis for exercise prescription (4), and derivatives of V̇O2max explain the value of physical fitness in disease and mortality (7,27). The challenge for practitioners in these fields is to obtain a reasonably accurate measurement of V̇O2max. The most accurate measurement method is by indirect calorimetery, tested to exhaustion on a power-regulated device such as a treadmill. This method is of limited application because of equipment requirements and the potential risks of maximal exertion. V̇O2max can be accurately estimated from total elapsed time on the treadmill, but this method also requires maximal effort (10). Submaximal exercise tests are easier on the test subject, but they are less accurate than maximal tests (3,5), and they also demand significant investments in equipment and time (20-60 min). In 1990, Jackson et al. (17) developed two V̇O2max prediction models that did not require exercise testing, and the accuracy of these models were equal to or better than the accuracy of the submaximal exercise models. Derived from several thousand measurements of V̇O2max furnished by the NASA/Johnson Space Center (JSC), Jackson's nonexercise models estimated V̇O2max from a combination of age, gender, self-assessments of activity habit, and either %fat or body mass index (BMI). In 1993, the NASA/JSC began including measurements of waist girths (WG) with the stress test battery. WG measurements were quick and easy to obtain, required inexpensive equipment (a measuring tape), and being a body composition correlate, they were associated with fitness (29,34) and with the same diseases and disorders found with low fitness and obesity (9,13). The purpose of our study was to use NASA/JSC data to investigate the use of WG as a surrogate for body composition in the nonexercise models and to compare the accuracy of nonexercise models that included WG, %fat, or BMI.



All 2801 subjects were employed at the NASA/JSC in Houston, TX, where they were voluntarily tested at the Kelsey-Seybold Clinic location at the JSC, the same multispecialty medical clinic and cardiopulmonary laboratory used in the 1990 Jackson study (17). All procedures and protocols were approved by the JSC committee for the protection of human subjects, and all subjects gave informed consent. Generally, this was a well-educated cohort (87% college graduates), most commonly employed as a scientific, technical, or managerial professional. The race and ethnicity breakdown was 139 black (5.0% of total sample, 111 men, 28 women, age range 27-71 yr), 136 Hispanic (4.9% of total sample, 111 men, 25 women, age range 26-78 yr), 109 Asian-Pacific Islanders (3.9% of total sample, 90 men, 19 women, age range 19-71 yr), and 2417 white (86.3% of total sample, 2104 men, 313 women, age range 20-82 yr).

Clinical examination.

Each subject received a medical examination and was declared clinically healthy before reporting to the cardiopulmonary laboratory. In the laboratory, a staff nurse explained the NASA physical activity status scale (PASS), which allowed each subject to rate his or her activity habit averaged over the past month on a scale ranging from 0 to 10. A rating of 0-1 indicated very low activity, a 0 being described as "avoid walking, always use the elevator, drive whenever possible instead of walking." A rating of 2-3 represented moderate-intensity activity (e.g., golf, bowling, or yard work) ranging from 10 to 60 min·wk−1. Ratings of 4-10 indicated a more serious activity habit, a 4 being equivalent to a weekly total of playing singles tennis for up to 30 min. The highest rating of 10 represented a weekly total of running more than 25 miles or exercising aerobically (e.g., tennis) for > 12 h. The PASS has been validated as an indicator of aerobic fitness in previous studies (14,16,20) and is published in another source (33).

Body composition.

The subjects were measured for body weight and height on a physician's balance scale with subjects dressed in shorts without shoes. WG were measured with a tape at the apex of the umbilicus. Percent body fat (%fat) was estimated from the sum of three gender-specific skinfolds: chest, abdomen, and thigh for men (18), or triceps, suprailium, and thigh for women (19). BMI was computed from weight in kilograms divided by the squared value of height in meters.

Measurement of V̇O2max.

Subjects completed a background questionnaire and informed consent before exercise testing. The Bruce treadmill protocol (8) was followed and oxygen uptake was continuously measured with open-circuit spirometry. A GE/Marquette computer assisted system for exercise (CASE) with a 12-lead electrocardiogram (ECG) was used to continuously monitor heart rate. Metabolic measurements were continuously taken during exercise. The graded exercise stress test was administered on a calibrated GE/Marquette Series 2000 treadmill. Bruce protocol procedures were automatically controlled by the CASE. Expired gases were continuously sampled and analyzed for oxygen and carbon dioxide concentrations by a Jaeger-Tonnies Oxycon Alpha (Viasys Healthcare, Conshohocken, PA), which was calibrated daily with known gases. The highest full minute V̇O2 uptake observed during the final minute of the test (V̇O2peak) was accepted as the functional aerobic capacity and defined physical fitness for that individual provided the respiratory exchange ratio ≥ 1.1. Analysis of the electrocardiograph recorded during the test was used to identify heart disease, and only those with a negative test were included in this study.

Statistical analysis.

Regression models (28) assessed the relationship between V̇O2max and the independent variables. The effect of gender was assessed by adding the dummy-coded gender variable and then by applying multiple regression to determine whether gender provided a significant increase in the explained variance of V̇O2max over the independent variable. Multiple regression was used to develop three nonexercise models to estimate V̇O2max. The dependent variable was measured V̇O2max. The independent variables were age, gender, and PASS, with a different body composition measure (i.e., WG, % fat, or BMI) in each model. The predicted residual sum of squares, or PRESS (15,31) was used to cross-validate each of the three models. All of the data for a single subject are contained in a row, and the PRESS technique computes the residual sum of squares where the residual for each row is computed after dropping that row from the computations. The standard error of estimate % (SEE%) was calculated [(SEE% = SEE/mean V̇O2max) × 100] for each model. The SEE sets variation limits around a predicted V̇O2max, and the SEE% describes the percentage of the actual mean V̇O2max within which the predicted values will generally fall. This is a common method used to evaluate the accuracy of V̇O2max prediction models (6). The models were further examined for accuracy by dividing the data into subgroupings of gender, age, PASS, and V̇O2max, and then by comparing the constant errors (CE) (24) and the error estimates achieved from the estimates of V̇O2max for each subgrouping. The CE values were the calculated mean difference between the measured V̇O2max and V̇O2max predicted by each model [CE = Σ (measured V̇O2max − predicted V̇O2max)/n)].


Table 1 shows the descriptive statistics for the 2417 men and 384 women in the study. Gender differences in size, body composition, and V̇O2max were all significant (P < 0.01) and consistent with North American norms for age by gender (3).

Descriptive statistics for the study sample.

The highly varied nature of the cohort is reflected by the respective female and male data ranges.

Table 2 shows the zero-order correlations between measured V̇O2max and the independent variables in our models. All correlations were significantly different from 0 and ranged from a low of −0.392 for BMI and WG to a high of −0.654 for %fat. Multiple regression was used to test for homogeneity of intercepts and slopes of the male and female regression lines (28). The test for homogeneity of intercepts (i.e., change in R2) was significant for all independent variables except %fat, which had been derived from gender-specific skinfold equations. Adding the dummy-coded gender term (M = 1, F = 0) significantly raised the R2 intercept (excepting %fat as noted). The question of differing slopes was tested by adding the interaction of gender and the independent variable to themodel. Each interaction term accounted for no more than 0.1% of V̇O2max variance. For example, the test of homogeneity of intercepts in Table 2 shows that when estimating V̇O2max with WG, the addition of gender (i.e., V̇O2max = WG + gender), raised the R2 from 0.154 to 0.366, a significant (P < 0.001) 21.2% increase in the explained variance of V̇O2max (R2Δ = 0.212). The test for homogeneity of slopes, however, showed that adding the interaction of WG and gender to the equation [i.e., V̇O2max = WG + gender + (WG × gender)] only raised the explained variance in V̇O2max by 0.1% (R2Δ = 0.001). The difference in the male and female intercepts supported the use of gender in a dummy-coded form as an independent variable in the nonexercise models.

Zero-order correlations between measured V̇O2max and the independent variables and the test of homogeneity for the male and female regression lines.

Shown in Table 3 are the regression coefficients for estimating V̇O2max from three models, which are sorted according to differing expressions of body composition. The models were similar in multiple correlation (~0.81), standard error of estimate (~4.8 mL·kg−1·min−1), and SEE% (~13.3%). Because the gender variable is included, these models can be generalized to men and women. Gender-specific equations can be developed by eliminating the gender variable when estimating V̇O2max for a woman and including it in the estimate for a man. All independent variables contributed significantly (P < 0.001) to the estimation. Correlations among independent variables within the models tended to be low (r < 0.30), with these exceptions: WG and gender (r = 0.52), WG and age (r = 0.39), and %fat and PASS (r = −0.37). The PRESS cross-validation statistics were similar to these regression statistics, supporting the validity of these models.

Multiple regression nonexercise models estimating V̇O2max (mL·kg−1·min−1).

The accuracy of the models was analyzed and compared by obtaining the CE and the standard deviations of the CE for various subsamples of the data. The CE is sometimes described as the mean of the residual. The residual is the difference between the measured V̇O2max and the V̇O2max estimated by the models. A negative CE indicates that, on average, the model tends to overestimate V̇O2max; a positive CE indicates a tendency for the model to underestimate V̇O2max. The standard deviation for the CE values is actually the standard error of estimate for each model for that particular subgroup. Table 4 shows the CE and its standard deviation for each model sorted according to gender and grouping of age, PASS, and V̇O2max. Gender groupings showed essentially no difference in predicting V̇O2max from the total sample or separately by gender. CE values for gender groupings were small, no more than 0.04mL·kg−1·min−1, and the standard errors were very similar to what was obtained from the total sample. For theremaining variables, Table 4 suggests the models are most accurate in predicting V̇O2max for individuals who areolder (age > 50 yr), less active (PASS < 6.5), and withaverage fitness (between 30 and 50 mL·kg−1·min−1). Although theCE for all age groupings were small (<0.20mL·kg−1·min−1), the standard errors were higher for younger groupings, indicating lower accuracy for subjects aged ≤ 50 yr. The lowest CE and standard errors were for the oldest grouping, indicating highest prediction accuracy for subjects over age 50. PASS subgrouping datashowed the models became less accurate whenever theactivity ratings exceeded 6.5, but the average underestimate was still low (<1 mL·kg−1·min−1). Subgroups ofV̇O2max showed high absolute (>3 mL·kg−1·min−1) CE values at the extremes of fitness (<30 and >50 mL·kg−1· min−1). At low fitness, the models systematically overestimated V̇O2max by about 3 mL·kg−1·min−1, and at high fitness, the models systematically underestimated by over twice that amount (~7 mL·kg−1·min−1).

Constant error (CE) and standard deviations (SD) for subgroups of the sample.

Figures 1, 2, and 3 illustrate the tendency for the three models to consistently underestimate V̇O2max for individuals with high fitness butoverestimate V̇O2max for individuals with low fitness.For the 152 subjects whose V̇O2max was measured > 50 mL·kg−1·min−1, but estimated by the models to be < 50mL·kg−1·min−1 their average measured value was 54.1 (±3.2) mL·kg−1·min−1. The average V̇O2max estimated bythe models for these subjects, however, was WG model,47.0 (±3.2) mL·kg−1·min−1; %fat model, 47.4 (±3.4) mL·kg−1·min−1; and BMI model, 46.3 (±2.9) mL·kg−1·min−1. For the 664 subjects with V̇O2max measured as < 30 mL·kg−1·min−1, but estimated >30 mL·kg−1·min−1 their average measured value was 25.9 (±2.9) mL·kg−1·min−1, but the average estimated V̇O2max for these subjects was WG model, 28.9 (±4.8) mL·kg−1·min−1; %fat model, 29.1 (±4.7) mL·kg−1·min−1; BMI model, 29.0 (±4.9) mL·kg−1·min−1.

Relationship between V̇O2max estimated with the WG model and measured by indirect calorimetry. Provided are the line of identity and the 95% confidence interval. The areas within the dashed lines show where the model tends to either underestimate or overestimate V̇O2max. Data from the entire sample (N = 2801) were used for this analysis.
Relationship between V̇O2max estimated with the %fat model and measured by indirect calorimetry. Provided are the line of identity and the 95% confidence interval. The areas within the dashed lines show where the model tends to either underestimate or overestimate V̇O2max. Data from the entire sample (N = 2794) were used for this analysis.
Relationship between V̇O2max estimated with the body mass index (BMI) model and measured by indirect calorimetry. Provided are the line of identity and the 95% confidence interval. The areas within the dashed lines show where the model tends to either underestimate or overestimate V̇O2max. Data from the entire sample (N = 2799) were used for this analysis.


Results of this study showed that the model with WG estimated V̇O2max with no appreciable difference in accuracy compared with the models using either %fat or BMI, thus supporting the use of WG as a surrogate for body composition in the nonexercise models. The three nonexercise models are very similar in their capacity to provide valid and accurate estimates of V̇O2max. The accuracy of these models is comparable to the accuracy of models that estimate V̇O2max with various forms of physical exercise performed at submaximal effort. For example, the SEE for the nonexercise models in this study were within the range of submaximal exercise test SEE, and the SEE% for each of these models (13.2-13.7%) were also within the normal 10-20% for models that predict V̇O2max with submaximal exercise (26).

Compared with the Jackson et al. 1990 study (17), our study drew on a larger sample (2801 compared with 2009 in 1990), especially a larger number of women (348 in our sample compared with 195 in 1990), and achieved an improvement in prediction accuracy, evidenced by larger R2 and smaller SEE values. The large number of highly varied adults receiving maximal measurements of V̇O2max in our study helps support the generalizablity of the three prediction models. Most studies that produced regression models from measurements of V̇O2max tended to be limited to smaller (N < 200) homogeneous groups of either middle-aged, low fit (21) or young, high fit (11,12,22,25) subjects. These studies were designed to develop prediction equations for a targeted homogeneous group. Heil et al. (14) drew on V̇O2max measurements of a larger (N = 439) group of adult men and women with heterogeneous V̇O2max and validated the Jackson et al. nonexercise models (17) for predicting V̇O2max of samples who are heterogeneous in terms of fitness.

The relationship between V̇O2max and gender, age, exercise habit, and body composition has been well established (5,26). Although V̇O2max is defined by the amount of oxygen processed per unit of body weight, comparison of zero-order correlations with measured V̇O2max showed the correlation with body weight (r = −0.25) was lower than the correlations with the quality of weight variables represented by the body composition terms in our study (i.e., waist girth, %fat, BMI) (Table 2).

Figures 1, 2, and 3 show that the models are less accurate when predicting V̇O2max at the extremes of fitness. The underestimation bias by the nonexercise models for highly fit individuals (V̇O2max > 55 mL·kg−1·min−1) was previously reported in the Jackson et al. study (17) and verified with highly fit, college-aged students tested to maximal capacity on a treadmill (22). Malek et al. (24) reported this problem was pervasive for nonexercise models that were validated with measurements of V̇O2max on a cycle ergometer. In a follow-up study, these same authors developed a more accurate nonexercise model for aerobically trained females because they found that correcting with the CE values for the nonexercise models they had previously studied did not adequately reduce the inaccuracies in predicting V̇O2max in highly fit women (25). Estimating V̇O2max for high fit individuals is not a pressing problem for the typical work force because no negative consequences are seen from high fitness (i.e., no disease or mortality risks) and because high fitness is comparatively rare. For example, 6% of the subjects in the NASA/JSC sample were measured with a V̇O2max > 50 mL·kg−1·min−1. If the need for accuracy in determining the V̇O2max of a high fit person is acute, then more accurate measurements (e.g.,maximal exercise tests) are available. The systematicover estimation of V̇O2max for people with low fitness (<30 mL·kg−1·min−1) is more troublesome, because of the higher percentage of people in the adult population with this condition (24% at NASA/JSC) and the associated risks oflow fitness (32). Therefore, a stress test designed to detect heart disease may be warranted whenever the models predictV̇O2max to be < 30 mL·kg−1·min−1. Furthermore, the tendency to overestimate by about 3 mL·kg−1·min−1 for this population subgroup can be corrected by applying Lohman's technique (23) of adding to the intercept the appropriate CE value indicated in Table 4.

Access to actual measurements of V̇O2max is uncommon. Therefore, investigators select models that estimate V̇O2max on the basis of a number of factors, including accuracy, safety, expense, and convenience. The accuracy of submaximal exercise methods is similar to our nonexercise models, but each of the submaximal methods tend to perform more poorly than the nonexercise models on safety, expense, and convenience. Models that estimate V̇O2max from treadmill tests that are performed to voluntary exhaustion, but which do not use indirect calorimetry, are high in accuracy (based on total treadmill time from our data, R = 0.91, SEE = 3.4 mL·kg−1·min−1). As with submaximal exercise tests, however, they compare less favorably on the remaining criterion. Although less accurate than total treadmill tests, the nonexercise models developed in this study provide estimates of V̇O2max that are valid for a wide range of adults, and they are safer, quicker, less expensive, and more convenient.

Ethnic effects

Ethnicity has not been reported as a significant variable in a V̇O2max prediction equation. However, when we calculated CE values for ethnic subgroups of our data, we found the models provided an accurate fit for white subjects (86.3% of the sample), but they were less accurate for black, Hispanic, and Asian-Pacific Islander subjects. To examine this more closely, we reanalyzed the data, adding race as a nominal variable. The dummy coding described in Pedhauzur (28) was used to define ethnicity for this analysis. The addition of ethnicity to the models significantly (P < 0.001) raised the R2 but only by 0.008, 0.006, and 0.004 for the WG, %fat, and the BMI models. Reasons for these significant, but low (<0.9%), increases in the explained variance in V̇O2max are not clear. Body composition is a powerful variable in V̇O2max (16,17,20), and the ethnic differences in body composition that have been described in the literature (1,2,30) may have accounted for these effects. It should be emphasized that the nonwhite groups in our study were small (<140 subjects); the white group was not only large (2417 subjects), it was between 17 and 22 times larger than each of the nonwhite groups. The small sample sizes of the nonwhite ethnic groups and the disparate differences in the sample size of the white group relative to the other groups may have influenced whatever ethnic effects we found in our models. Whether ethnic effects really exist on V̇O2max can only be determined by more study that includes cross-validation research with large samples of similar-sized groups of whites, blacks, Hispanics, and Asian-Pacific Islanders. After considering these warnings, investigators may adjust for ethnicity by adding the CE values provided here to the intercept of the models in Table 3. We are providing only those adjustments that significantly (P < 0.05) altered the V̇O2max estimated by our models. The WG model CE adjustment for black subjects is −2.86mL·kg−1·min−1 (±4.91 mL·kg−1·min−1), and for Asian-Pacific Islanders the CE adjustment is −1.06 mL·kg−1·min−1 (±5.42 mL·kg−1·min−1). The %fatmodel adjustment for black individuals is −2.89 mL·kg−1·min−1 (±5.28 mL·kg−1·min−1). The BMI model adjustment is −2.07 mL·kg−1·min−1 (±5.22 mL·kg−1·min−1) for blacks and 1.30 mL·kg−1·min−1 (±5.29 mL·kg−1·min−1) for Hispanics. If a CE adjustment for an individual's ethnicity is not included here, then the models in Table 3 need no adjustment to estimate the V̇O2max for that individual.

This work was supported by the Kelsey Research Foundation, Houston, Texas. Since 1966, Kelsey-Seybold Clinic has provided medical services to the astronauts and employees at the NASA/Johnson Space Center, Houston, Texas.


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