Estimating V˙O2peak from a Nonexercise Prediction Model: The HUNT Study, Norway : Medicine & Science in Sports & Exercise

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Estimating V˙O2peak from a Nonexercise Prediction Model

The HUNT Study, Norway


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Medicine & Science in Sports & Exercise 43(11):p 2024-2030, November 2011. | DOI: 10.1249/MSS.0b013e31821d3f6f



Cardiorespiratory fitness is suggested to be an important marker of cardiovascular risk but is rarely evaluated in health care settings. In the present study, directly measured peak oxygen uptake (V˙O2peak) from a diverse population of 4637 healthy participants were used to develop and cross-validate a new nonexercise regression model of cardiorespiratory fitness for men and women.

Methods and Results: 

Multivariable regression analysis was used to develop a nonexercise model of cardiorespiratory fitness for men and women separately with V˙O2peak as the outcome. In the final models, 2067 men (mean age = 48.8 yr) and 2193 women (mean age = 47.9 yr) were included, respectively. Cross-validation of the models was done by standard data splitting procedures with evaluation of constant error and total error of a model developed on one sample and cross-validated on another sample. Age, waist circumference, leisure time physical activity, and resting HR, successively, were the most potent predictors of V˙O2peak for both men and women. Together, 61% and 56% of variance in V˙O2peak, for men and women, respectively, were explained by the full models. SEE was 5.70 and 5.14 for the models including men and women, respectively.


The nonexercise regression model developed in the present study was fairly accurate in predicting V˙O2peak in this healthy population of men and women. The model might be generalized to other healthy populations and might be a valid tool for a rough assessment of cardiorespiratory fitness in an outpatient setting.

Aerobic fitness is a well-established and robust indicator of cardiovascular health and a predictor of premature all-cause mortality. Large-scale epidemiological and experimental studies have identified aerobic fitness as one of the most important determinants of cardiovascular disease and its associated risk factors (3,8,18,34). Direct measurement of peak oxygen uptake (V˙O2peak) by ventilatory gas analysis is generally accepted as the most valid index of aerobic fitness in both health and disease (31). V˙O2peak describes the highest value of oxygen consumption obtained by an individual during dynamical work using large muscle groups (2). Indirect measurement of aerobic fitness estimates V˙O2peak from surrogate measures like treadmill time to exhaustion, submaximal workload, or HR response to exercise. Despite the indubitable importance of aerobic fitness for health, measurements of V˙O2peak in health care settings and population surveillance are rare, maybe for different reasons, including the cost and time consumption of the methods, as well as the potential risks related to maximal physical efforts. V˙O2peak is, however, closely associated with many factors associated with health status, including age, body weight, physical activity (PA) habits, nutritional status, smoking habits, occupation, and some biochemical markers (15,21). As a whole, these variables may explain a substantial proportion of the variance of V˙O2peak in population samples.

Therefore, several "nonexercise models" of aerobic fitness have been developed with the aim of predicting V˙O2peak using easily accessible measures such as age, gender, self-reported level of PA, and body composition (12,14,16). Some of these prediction models have shown promising accuracy and may be better than widely accepted submaximal exercise procedures (11,16). However, most studies on this issue have been limited by small samples, selected populations, or indirect measures of V˙O2peak, factors that may have threatened the validity and generalizability of the estimated models.

In a population-based sample of 4637 healthy participants derived from the Nord-Trøndelag Health Study (HUNT) in Norway, we aimed to develop and cross-validate a new nonexercise regression model of cardiorespiratory fitness (V˙O2peak) for men and women.


Study population.

Participants in the present study were recruited from the third wave of the HUNT study (HUNT-3) that is a large population-based health survey of the total adult population in Nord-Trøndelag County in Norway. Information was collected using a self-administered questionnaire and clinical measurements. In a substudy of HUNT-3, objective measurements of V˙O2max were included, yielding unique reference values for aerobic fitness in the population. A total of 4637 subjects were tested for V˙O2peak. Eligible subjects for exercise testing had to be free from known cardiovascular and lung diseases, cancer, sarcoidosis, and antihypertensive medications. Hence, the population undergoing exercise testing must be considered apparently healthy. A detailed description of the HUNT study has been published elsewhere (13). The study was approved by the regional committee for ethics in medical research, the Norwegian Data Inspectorate, and the National Directorate of Health. All participants gave their written informed consent, and the study was conducted in conformity with the Helsinki declaration.

For this study, 57 subjects were excluded because of missing information on self-reported PA. In addition, 320 subjects were excluded because of missing information on waist circumference (WC) or resting HR (RHR). Finally, 4260 subjects were included in developing the regression model. Height, weight, and WC were measured by internally standardized measures. Height and WC were read to the nearest centimeter (cm), and weight was read to the nearest kilogram (kg). Body mass index (BMI) was calculated as body weight (kg) divided by the squared value of height (m). RHR was calculated by ECG as beats per minute after 5 min of rest.

V˙O2max testing procedures.

Subjects underwent a 10-min warm-up period after a brief introduction to treadmill walking. The warm-up was conducted at moderate intensity where the subjects achieved modest shortness of breath and some sweat, but without exhaustion or lactate accumulation. After the warm-up period, the subjects were equipped with an HR monitor (Polar S610 or RS400; Polar, Kempele, Finland) and a mask (Hans Rudolph; Shawnee, KS) before entering the test treadmill (DK7830; DK City, Taichung, Taiwan).

During the V˙O2max testing, subjects walked or ran on the treadmill at increasing speed and/or incline until exhaustion. Cardiorespiratory variables were measured continuously using portable ergospirometry (MetaMax II; CORTEX Biophysik GmbH, Leipzig, Germany) directly transferred to a PC using CORTEX MetaSoft (version 1.11.5) software. V˙O2max was defined using the following criteria: 1) leveling off of V˙O2 (<2 mL·kg−1·min−1) despite increased speed or incline and 2) an RER > 1.05. A subject's V˙O2max was taken as the mean of the three successive highest V˙O2 registrations achieved. If the subjects seemed to have reached exhaustion but not both the V˙O2max criteria, the test was registered as V˙O2peak. Because 17.7% of the subjects did not achieve the V˙O2max criteria, the term V˙O2peak was used throughout the article. HRpeak, RER, RPE, speed, elevation, and lung ventilation (L·min−1) were also registered at the end of the test. The test equipment was routinely calibrated by trained personnel. Volume ventilation was calibrated at every third test, and gas was calibrated at every fifth one. Ambient room air was automatically checked before each test.

Physical activity questionnaire.

Before the exercise testing, participants were completing a basic HUNT questionnaire that included questions related to leisure time PA habits. Thus, frequency of exercise, stated as, "How often do you exercise?" contained five different response options (never, less than once a week, once a week, two to three times a week, and four or more times a week). Intensity of exercise, stated as, "How hard do you exercise?" contained three options ("no sweat or heavy breath," "heavy breath and sweat," and "push myself to exhaustion"), and duration of exercise contained four options ("<15 min," "between 15 and 30 min," "between 30 and 60 min," and ">60 min").

Statistical procedures.

Descriptive statistics of the population are given as means and SD. The data set was examined for erroneous outliers, and each variable was tested for normality and homoscedasticity of the residuals.

The first step of the analysis was to develop an index of PA for the purpose of precise V˙O2peak estimation. Three different indexes of PA were considered. Relative weighting of the different responses were set grossly on the basis of their relation to V˙O2peak in a regression model. Hence, intensity was weighted more than duration and frequency of the index. These indexes were compared with a PA index previously validated in the HUNT population (19). V˙O2peak was set as the dependent variable, and indexes were set as independent variables in a standard linear regression analysis. Correlations with V˙O2peak and SEE were considered for the two indexes separately.

Potential predictors of aerobic fitness were checked for zero-order and partial correlation with V˙O2peak, adjusted for age. In our multivariable models, age, PA index, and WC or BMI, in separate models, were forced in an a priori blockwise manner based on the established relationship of these variables to V˙O2peak. The remaining variables, RHR, smoking status, HDL cholesterol, total cholesterol, and mean arterial pressure were then entered in the subsequent block. Only variables that made a considerable influence on the squared multiple correlation coefficient (R2) and are easily measurable in a clinical setting were retained. R2, corresponding R2 change, SEE, and %SEE were presented. %SEE refers to the percentage of the actual mean V˙O2peak within which the estimates generally fall and was calculated as %SEE = (SEE/mean V˙O2peak)100. Tolerance and variance inflation factor were used to assess colinearity between variables.

Cross-validation of the model was done by standard data splitting procedures. Cross-validation was performed by creating the regression analysis on the validation sample, and this equation was used to create predicted scores for subjects in the cross-validation sample. The predicted scores were then correlated with observed scores for V˙O2peak to create the cross-validity coefficient. The difference between the original R2 in the validation sample and the squared cross-validity coefficient constitute the degree of shrinkage one can expect when using the model on an independent but similar sample. Constant errors (CE) were calculated as the sum of the measured minus the predicted values divided by sample size for the total validation and cross-validation sample, respectively (CE = ∑(measured − predicted)/n). Total error (TE) was calculated as the square of the difference divided by sample size (√∑(measured − predicted)2/n). TE represents the TE of a model developed on one sample and validated on another sample. The validation, cross-validation, and total sample were further divided into subgroups according to age, V˙O2peak, and PA level. We report measured and predicted V˙O2peak within groups, CE, and TE. The validation and cross-validation sample were then combined, and the multiple regression analysis was repeated on the total sample as recommended by others (10,27).

The statistical analyses were performed with SPSS version 14.0 (SPSS, Inc., Chicago, IL).


Descriptive characteristics of the total, male, and female populations are presented in Table 1. Mean characteristics of the validation and cross-validation samples were distributed equally (see Table 1, Supplemental Digital Content 1,, which describes the mean characteristics of the samples). Further descriptive data of the HUNT-3 population is extensively described in a previous study (1).

Descriptive data for the total, male, and female participants.

Prediction of V˙O2peak.

Age, PA, and WC accounted for most of the variance in predicting V˙O2peak (R2 = 0.59 for men and R2 = 0.54 for women, Tables 2 and 3), whereas RHR made a small contribution (R2 = 0.61 for men and R2 = 0.56 for women, Tables 2 and 3). HDL cholesterol, total cholesterol, smoking status, and mean arterial pressure made no considerable contribution as predictors of V˙O2peak. Including BMI as the predictor variable instead of WC yielded only negligible alterations in R2 and SEE. The final regression equation was 100.27 − (0.296 × age) − (0.369 × WC) − (0.155 × RHR) + (0.226 × PA-index) for men and 74.74 − (0.247 × age) − (0.259 × WC) − (0.114 × RHR) + (0.198 × PA-index) for women (Table 4). Neither the inclusion of interaction terms nor the inclusion of polynomials could influence the R2 of the model appreciably.

Results of regression analysis for the total population sample.
Multiple regression coefficients for predicting V˙O2peak (mL·kg−1 ·min−1) in the total sample.
Composition of two different indexes of PA and their relation to V˙O2peak.

PA index.

V˙O2peak in subgroups of different intensity, frequency, and duration of PA was similar if subjects reported to exercise at low intensity, independent of frequency and duration of the PA (data not shown). Hence, we developed an index of PA where responding "no sweat…" on the intensity questions was weighted equally as not being active at all, independent of the response on frequency and duration, giving a summary index of 0. The new index was compared with a formerly validated index of PA in the HUNT population (19) (Table 4), and it showed a slightly better correlation with measured V˙O2peak than the former index (r = 0.44 vs 0.38 and 0.39 vs 0.34 for men and women, respectively).

Cross-validation of the prediction model.

The coefficient of determination (R2) was stable between the validation sample (0.62 and 0.55) and the cross-validation sample (0.61 and 0.56) in both men and women, respectively, indicating a robust model (see Table 2, Supplemental Digital Content 2,, for results of the regression analysis for the validation sample). In addition, the CE for the validation and the cross-validation samples were close to zero in both men (0.12 and 0.10, respectively) and for women (0.02 in both), indicating a valid estimation of the mean V˙O2peak (see Tables 3 and 4, Supplemental Digital Content 3 and 4, and, for a description of the errors of prediction in the validation and cross-validation sample of men and women). The total sample yielded similar CE values as the validation sample with insignificant CE values for women (0.00) or men (0.00) (Table 5).

Measured versus predicted V˙O2peak and error statistics across subgroups in the total sample for men and women.

In subgroups of age, V˙O2peak, and PA, our model remained stable with the exception of V˙O2peak subgroups. In the latter subgroups, the model tended to overestimate V˙O2peak among the least fit participants (<35 mL·kg−1·min−1 for men and <30 mL·kg−1·min−1 for women) with a subsequent underestimation of the most fit subjects (>50 mL·kg·min−1 for men and >40 mL·kg·min−1 for women). CE values in the total population were −5.35 and −3.85 for the least fit men and women and 4.39 and 4.37 for the most fit. Corresponding TE values were 6.91 and 5.51 for the least fit and 6.73 and 6.43 for the most fit. For the medium-fit subjects (V˙O2peak between 35 and 50 mL·kg−1·min−1 for men and between 30 and 40 mL·kg−1·min−1 for women), the model seemed to predict V˙O2peak well (CE, 0.49 and −0.23 for men and women, respectively).

Cross-classification of subjects.

Cross-classification into quartiles of measured and predicted V˙O2peak showed that the model managed to classify subjects into the correct fitness categories reasonably well (Table 6). There were 64.2% of women in the lowest predicted quartile who were correctly classified into the lowest measured quartile, whereas there were 90.2% who were correctly classified into one of the two lowest measured quartiles. Similarly, 67.9% of men were correctly classified into the lowest predicted and measured quartile, and 92.5% were correctly classified into one of the two lowest measured quartiles. In the upper quartiles, 65.2% of women and 68.4% of men were correctly classified into the correct one, whereas 91.2% of women and 93.6% of men were classified within the closest measured quartile. Upper bound cutoff values for predicted quartile 1 and 2 were 31.9 and 35.9 mL·kg−1·min−1 for women and 39.2 and 44.0 mL·kg−1·min−1 for men, respectively.

Cross-tabulation between measured and predicted V˙O2peak quartilesa for men and women.


The nonexercise regression model developed in the present study was fairly accurate in predicting V˙O2peak in this healthy population of men and women (R2 = 0.61 and SEE = 5.70 for men and R2 = 0.56 and SEE = 5.14 for women). Approximately 90% of the subjects obtained the predicted V˙O2peak within the nearest quartile of measured V˙O2peak, applied to both genders. The cross-validation, assessed by data splitting procedures, showed good model stability, suggesting that it may be generalized to other similar populations without major shrinkage of accuracy. Our model bears a close resemblance to other nonexercise equations by including similar variables such as age, PA, body composition, and RHR (12,14,24). Comparison of β weights suggests that age may be the most potent determinant of V˙O2peak, followed by WC, PA, and RHR. In general, BMI and WC contributed equally to the explained variance, but WC was chosen in the final model because of a slightly better fit among men. A similar contribution of BMI and WC to prediction of aerobic fitness is also described in previous studies (7,33).

The accuracy of our model is similar to that of other studies with large population samples. A widely cited model by Jackson et al. (14) reported an SEE of 5.70 mL·kg−1·min−1 including age, PA, BMI, and gender as predictor variables, whereas Whaley et al. (32) and Malek et al. (24) reported SEE values of 5.60 and 4.90 mL·kg−1·min−1. Considering the mean V˙O2peak in those studies, %SEE corresponded to 11%-13% but was not reported in all studies. The error of prediction in our model was comparable to commonly used submaximal exercise models that typically show a 10%-20% margin to the actual V˙O2peak. For example, a multistage shuttle run test (23), Rockport 1-mile walk test (17), and 6-min walk test (29) report SEE of 3.8-5.4 mL·kg−1·min−1. Compared with the well-known Åstrand-Rhyming maximal treadmill test (r = 0.83, SEE = 5.7 mL·kg−1·min−1), our nonexercise equations show a slightly better accuracy (9).

A thorough cross-validation analysis was done to avoid the potential problem of overfitting that could weaken external validity of the regression equation (28). Across subgroups of age and PA, the error estimates of the model seemed quite stable. Across subgroups of V˙O2peak, however, there was a tendency to systematically over- and underestimate predicted values for the low- and high-fit subjects, respectively. This finding is in accordance with previous findings by Jackson et al. (14), Heil et al. (12), and Jurca et al. (16) who also found larger errors of the estimate at the extremes of fitness. Consequently, specific models that more properly estimate fitness of younger and aerobically trained subjects have arisen (24), whereas accurate prediction models for the least fit groups are sparse. As pointed out by Wier et al. (33), loss of predictive accuracy in a high-fit population may not sustain a pressing problem in public health settings because high fitness is not associated with any potential harm or disease. The systematic overestimation in the low fitness group could be more precarious because aerobic fitness is suggested to be a continuum from health to disease with particularly increasing risk of chronic disease among the least fit subjects. However, cross-classification of subjects into corresponding quartiles of predicted and measured V˙O2peak showed that approximately 90% of subjects of both sexes were classified correctly within the nearest quartile of measured V˙O2peak. For women, this indicates that a woman with a predicted value <32 mL·kg−1·min−1 most probably has an actual V˙O2peak <35 mL·kg−1·min−1. A man with a predicted value <40 mL·kg−1·min−1 equally is very likely to have an actual V˙O2peak <44 mL·kg−1·min−1. According to a recent cross-sectional study of the present population, V˙O2peak below 35 mL·kg−1·min−1 for women and 44 mL·kg−1·min−1 for men were associated with increased odds of the metabolic syndrome (1). Hence, the present model may identify subjects with aerobic fitness levels associated with increased cardiovascular risk.

A potential reason for the increasing error in prediction among low- and high-fit subjects in the present study may be due to a limitation of the self-reported PA variables to discriminate exercise behaviors with a different effect on aerobic fitness. By putting together an index that takes into account the limited ability of low-intensity exercise to influence V˙O2peak, we gained improvement in accuracy of prediction. It seems reasonable, however, that especially, the range of intensity response options was too narrow to properly discriminate subjects of high and low fitness. Intensity is reported to be the strongest characteristic of both self-reported and objectively measured PA's association to a fitness response in a population and should therefore be measured properly (7,26). However, Kurtze et al. (19) reported that the HUNT questionnaire was a better measure of intense PA than overall objective energy expenditure, supporting its utility in research with interest in moderate- to high-intensity PA. The correlation between PA index and V˙O2peak in the present study was 0.39 for women and 0.44 for men, which is close to the estimates in an assessment of 12 studies that had validated self-reported PA indices to V˙O2peak that showed a median correlation of 0.41 (30).

Another source of prediction error is the genetic contribution to V˙O2peak that obviously weakens the correlation between PA and aerobic fitness. It has been suggested that heredity may be responsible for as much as 25%-50% of the variation in V˙O2peak in a heterogeneous population, whereas factors such as PA, body composition, and lifestyle constitute the remaining proportion (4). Furthermore, a series of studies by Bouchard and Rankinen (5) revealed a considerable heterogeneity in the ability to respond to exercise. A sample from the HERITAGE Family Study was followed during 20 wk with a uniform exercise program. The range of V˙O2peak response was reported from 0 to 1 L·min−1 (0%-50%), and about 75%-80% of the heterogeneity in training response could not be explained by factors such as age, gender, race, or baseline training status. Bearing that in mind, an R2 of approximately 0.60 in the present study, meaning that 60% of the variation is accounted for by the selected variables, could be as close as one may come with nonexercise predictor variables in an unselected population.

The main strength of the present study is its size and its population-based design. A direct maximal exercise test to determine V˙O2peak by ventilatory gas analysis is an advantage compared with the indirect estimates commonly used in population studies. Jurca et al. (16) reported that prediction models obtained in a cohort where V˙O2peak was directly measured showed a better correlation and a lower error of the estimate than cohorts using indirect measures. Also, the independent variables used in this study are valid, easily obtainable, and therefore feasible in a time-limited health care setting.

The HUNT population is suggested to be fairly representative for Norway as a whole and not very different from many communities in the Western world (13). The population is, however, homogenous with respect to ethnicity and socioeconomic circumstances, and a generalization of our findings may be limited to similar populations. It could be a limitation that the study only included apparently healthy people. Compared with the total HUNT population, the HUNT Fitness sample has a slightly lower BMI and WC as well as higher HDL cholesterol and PA levels (1). Nevertheless, a recent study of the HUNT Fitness sample showed that the prevalence of metabolic syndrome only differed by 0.8% between the HUNT Fitness sample and the total HUNT population (1).

It is possible that some variables not included in this study could have yielded a better estimate. It has been suggested that a single question on personal perception of functional ability (i.e., their ability to exercise comfortably for 1 and 3 miles) may be effective in predicting aerobic fitness (11). In fact, that variable outperformed questions related to level of PA as a correlate to V˙O2peak. Questions on PA in the HUNT study are not identical with questions used in other studies, and this limits our ability to compare and cross-validate our findings with other populations. Furthermore, we were not able to measure percent body fat, which may be a slightly better predictor than BMI and WC (33). However, percent body fat is a more complicated measure of body composition and may not be feasible for practical use in public health settings. Similarly, objective measurements of PA with accelerometers or step counts have yielded more accurate estimates of V˙O2max in previous studies but may be practically inconvenient (6,7).

To be a useful tool for risk stratification in health care settings, it is important that prediction models can identify low-fitness subjects. Cross-classification of subjects within quartiles of measured and predicted V˙O2peak revealed a reasonable ability of the model to correctly classify subjects. Furthermore, consensus about a specified threshold of aerobic fitness that may substantially increase cardiovascular risk is essential and not yet established.

It seems clear that an evaluation of cardiorespiratory fitness provides valuable additional information to conventional markers of cardiovascular risk (20,22,25). Currently, lack of simple and accurate devices for direct measurement of V˙O2peak is restricting objective and quick assessment in an outpatient setting. Hence, a nonexercise model as presented in the present study may be a useful and feasible tool for a rough estimate of cardiorespiratory fitness, whereas direct measurement of V˙O2peak should be used for a more precise examination in people identified as being low fit.

The study was supported by grants from the K. G. Jebsen Foundation, Norwegian Council on Cardiovascular Disease (BN), and Norwegian Research Council Funding for Outstanding Young Investigators (UW). IJ was supported by the Liaison Committee between the Central Norway Regional Health Authority and the Norwegian University of Science and Technology and by the Swedish Council of Working Life and Social Research. The HUNT Study is established through a collaboration between the HUNT Research Centre (Faculty of Medicine, Norwegian University of Science and Technology), the Nord-Trøndelag County Council, and the Norwegian Institute of Public Health.

There are no further disclosures and no conflicts of interest to report.

The results of the study do not constitute endorsement by the American College of Sports Medicine.


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©2011The American College of Sports Medicine