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A New Nonexercise-Based VO2max Equation for Aerobically Trained Females

MOH H. MALEK1, TERRY J. HOUSH1, DALE E. BERGER2, JARED W. COBURN1, and TRAVIS W. BECK1

1

University of Nebraska-Lincoln, Human Performance Laboratory, Department of Nutrition and Health Sciences, Lincoln, NE; and 2Claremont Graduate University, Department of Psychology, Claremont, CA

ABSTRACT MALEK, M. H., T. J. HOUSH, D. E. BERGER, J. W. COBURN, and T. W. BECK. A New Nonexercise-Based VO2max Equation for Aerobically Trained Females. Med. Sci. Sports Exerc., Vol. 36, No. 10, pp. 1804 ­1810, 2004. Purpose: The purposes of the present study were to (a) modify previously published VO2max equations using the constant error (CE) values for aerobically trained females, (b) cross-validate the modified equations to determine their accuracy for estimating VO2max in aerobically trained females, (c) derive O2max in aerobically trained females if the modified equations are found to be a new nonexercise-based equation for estimating V inaccurate, and (d) cross-validate the new VO2max equation using the PRESS statistic and an independent sample of aerobically trained females. Methods: A total of 115 aerobically trained females (mean SD: age 38.5 9.4 yr) performed a maximal incremental test on a cycle ergometer to determine actual VO2max. The predicted VO2max values from nine published equations were compared with O2max by examining the CE, standard error of estimate (SEE), validity coefficient (r), and total error (TE). Results: actual V Cross-validation of the modified nonexercise-based equations on a random subsample of 50 subjects resulted in a %TE 13% of the mean of actual VO2max. Therefore, the following nonexercise-based VO2max equation was derived on a random subsample of 80 subjects: VO2max (mL·min 1) 18.528 (weight in kg) 11.993 (height in cm) 17.197(age in yr) 23.522 (h·wk 1 of training) 62.118 (intensity of training using the Borg 6 ­20) 278.262 (natural log of years of training) 1375.878 (R 0.83, R2 adjusted 0.67, and SEE 259 mL·min 1). Cross-validation of this equation on the remaining sample of 35 subjects resulted in a %TE of 10%. Conclusions: The nonexercise equation presented here is recommended over previously published equations for estimating VO2max in aerobically trained females. Key Words: AEROBIC POWER REFERENCE VALUES, CARDIORESPIRATORY FITNESS, HIERARCHICAL LINEAR REGRESSION, MAXIMAL OXYGEN UPTAKE, MAXIMUM CYCLE ERGOMETRY, PREDICTION MODEL

he measure of maximal oxygen uptake (VO2max) is used for many purposes including diagnostic tests, quantifying training intensity for aerobic exercise prescription, monitoring the effects of aerobic training programs, and classifying individuals for health risk (2,3). Typically, direct determination of VO2max involves measurement of expired gas samples during an incremental exercise test to exhaustion using a treadmill or cycle ergometer (1,3). Although this method may be optimal for determining VO2max, often it is not practical because it requires specialized equipment and trained personnel. Therefore, a number of nonexercise- and exercise-based regression equations to estimate VO2max have been developed using variables such as gender, age, height, weight, walking time, frequency of sweating, and Wmax (power

T

Address for correspondence: Moh H. Malek, M.S., CSCS, Human Performance Laboratory, Department of Nutrition and Health Sciences, University of Nebraska-Lincoln, 110 Ruth Leverton Hall, Lincoln, NE 685830806; E-mail: [email protected] Submitted for publication March 2004. Accepted for publication June 2004. 0195-9131/04/3610-1804 MEDICINE & SCIENCE IN SPORTS & EXERCISE® Copyright © 2004 by the American College of Sports Medicine DOI: 10.1249/01.MSS.0000142299.42797.83

output at VO2max) (8,9,11,12,15,16,21,24,26 ­28). No studies, however, have utilized habitual physical activity indices such as the intensity, frequency, and duration of exercise training to estimate VO2max. These indices have been shown to affect the oxidative adaptations to endurance training and, therefore, may be particularly useful for estimating VO2max in aerobically trained individuals (14). Recently, Malek et al. (18) evaluated the validity of 18 published regression equations for estimating VO2max in samples of aerobically trained males and females. These equations utilized various combinations of demographic information (e.g., age, height, and weight), ratings of leisure time physical activity, and/or Wmax to predict VO2max (18). The equations were selected for cross-validation because of their widespread popularity for estimating VO2max and/or proposed accuracy for the general populations of adult males and females. The results of the cross-validation analyses indicated that there were significant (P 0.006) mean differences between actual and predicted VO2max for all 18 equations (18). Furthermore, the total prediction error val ues for estimating VO2max were greater than 10% of the mean for actual VO2max for all of the equations. Based on the cross-validation analyses, Malek and colleagues (18) concluded that 16 of the 18 equations were not recom mended for estimating VO2max or prescribing exercise intensity for an aerobic training program in aerobically trained males or females. Only the equations of Storer et al. (26) 1804

that included age, body weight, and Wmax as predictor variables were recommended for estimating VO2max in aerobically trained subjects. The practicality of these equations is limited, however, because they require the subject to perform an exhaustive cycle ergometer test to estimate VO2max. Malek et al. (18) suggested that in an attempt to improve the prediction accuracy of the equations future studies should use the CE (constant error mean difference between actual and predicted VO2max) values from their investigation to adjust the y-intercepts of the equations. This can be accomplished by adding the estimated CE for each prediction equation to the y-intercept of that equation (17). Theoretically, this procedure results in a CE value of zero for the modified equation. The purposes of the present study were to (a) modify previously published VO2max equations using the CE values for aerobically trained females from Malek et al. (18), (b) cross-validate the modified equations to determine their accuracy for estimating VO2max in aerobically trained females, (c) derive a new nonexercise-based equation for estimating VO2max in aerobically trained females if the modified equations are found to be inaccurate, and (d) cross-validate the new VO2max equation using the predicted residual sum of squares (PRESS) statistic and determining total error in an independent sample of aerobically trained females.

METHODS

Experimental approach and design. The current study included three parts: (a) cross-validation procedures were used to determine the accuracy of nine VO2max prediction equations. The y-intercepts of the nine equations had been modified according to the recommendation of Malek et al. (18); (b) because the errors associated with the modified equations were too high for practical use, a new nonexercise-based equation was developed which included demographic information and habitual physical activity indices as predictor variables; and (c) the accuracy of the new nonexercise-based equation was assessed using two separate cross-validation procedures. Subjects. A total of 115 aerobically trained females participated in the present study. We operationally defined an aerobically trained female as someone who had participated in continuous aerobic exercise three or more sessions per week for a minimum of 1 h per session, for at least the past 18 months. In addition, the subjects were asked questions related to their habitual physical activity. Specifically, information was obtained regarding the mode (e.g., "What type of exercise do you perform?"); frequency (e.g., "How many sessions per week do you exercise?"); duration (e.g., "How many hours per week do you exercise?"); length of time performing habitual physical activity (e.g., "How long have you consistently, no more than 1 month without exercise, been exercising?"); and intensity of the exercise performed (e.g., "Indicate, in general, the intensity at which you perform your exercise regimen."). With regard to intensity, subjects rated their perceived exertion using the

NEW FEMALE VO2max EQUATION

Borg scale (5). All procedures were approved by the University Institutional Review Board (IRB) for Human Subjects, and participants signed an IRB approved informed consent. Maximal cycle ergometer test. Maximal exercise performance was assessed using an incremental exercise protocol on a cycle ergometer (Ergoline 800S; SensorMedics Corp., Yorba Linda, CA). Seat height was adjusted so that subject's legs were at near full extension during each pedal revolution. The power output was continuously increased in ramp fashion by computer control. The exercise duration for the ramp phase was 8 ­12 min as suggested by Buchfuhrer et al. (6). After a period of stabilization at rest, the subjects performed unloaded pedaling (i.e., 0 W) for 3 min followed by the ramp increase in power output (i.e., 30 W·min 1). The subjects were asked to maintain a cycling cadence of 70 rev·min 1. The ramp power output increased until the subject reached voluntary fatigue. A cool-down period with no resistance was performed until heart rate was near that during the unloaded pedaling phase. Minute ventilation (VE) was measured using a mass flow meter and expired fractional concentrations of oxygen and carbon dioxide were continuously monitored by paramagnetic oxygen analyzer and nondispersive infrared CO2 analyzer, respectively (2900; SensorMedics Corp.) (23). The subjects wore a nose clip and breathed through a mouthpiece (2700; Hans Rudolph, Kansas City, MO.). The metabolic cart and breathing valve were calibrated before each test. Oxygen uptake (VO2) and carbon dioxide output (VCO2) were calculated breath-by-breath using standard algorithms. Breath-by-breath data were presented as a five-breath rolling average. Heart rate was continuously obtained throughout the exercise (Quinton 5000; Seattle, WA). A subject's data were used if she met two of the following three criteria during the test (3,4,10): a) 90% of age-predicted maximum heart rate, b) respiratory exchange ratio 1.20, and c) a plateauing of oxygen uptake ( 150 mL·min 1 in VO2 over the last 30 s of the test). Maximum oxygen uptake was determined by taking the highest VO2 value in the last 30 s of the exercise test. In the present study, Wmax was defined as the power output at VO2max. The nine VO2max equations for females cross-validated by Malek et al. (18) are included in Table 1 along with the CE values. The modified equations were cross-validated in the present study on a random sample of 50 females according to the recommendations of Lohman (17). For ex ample, the original equation 3F (Table 1) was VO2max (mL·min 1) (9.39*Wmax) (7.70*BW) (5.88*age) 136.7. This equation was modified by adding the crossvalidation CE of 132 mL·min 1 from Malek et al. (18) to the y-intercept of the original equation 3F (136.7 132 268.7). Thus, the modified equation 3F equation cross validated in the present study was: VO2max (mL·min 1) (9.39*Wmax) (7.70*BW) (5.88*age) 268.7 (Table 2). Statistical analysis. The cross-validation analyses of the nine modified equations in this study (Table 2) were based on an evaluation of the actual VO2max versus the predicted VO2max via calculation of the constant error (CE mean

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TABLE 1. VO2max prediction equations for cycle ergometry that were cross-validated against maximum incremental test. Equation 1 2 3 4 5 6 7 8 9 Reference Jones et al. (15) 1F female Jones et al. (15) 2F female Storer et al. (26) 3F female Wasserman et al. (27) 4F female Fairbarn et al. (11) 5F female Neder et al. (21) 6F female Cooper and Storer (8) 7F female Davis et al. (9) 8F female Metabolic cart (23) 9F female VO2max L min VO2max L min

1

Equation 0.046(ht_cm) 0.025(ht_cm)

1

r 4.93 0.019(wt_kg) (5.88*age) (0.17*age)) (0.027*age) 0.207 535 0.15(lei) 136.7 2.862 0.87 0.89 0.93 NR 0.83 0.92 NR 0.75 2.26 NR

SEE 0.458 0.415 147 NR NR 126 NR 0.269 0.483

CE values from Malek et al. (18) 0.821 0.556 132 997 0.384 936 1.037 1.029 0.902

0.021(age) 0.023(age) (7.70*BW)

1

VO2max mL min VO2max mL min VO2max L min

1

(9.39*Wmax) [(nwt awt

1

86)/2]*(22.78 (0.00899*BW) (8.3*BW)

(0.0158*ht_cm)

1

VO2peak mL min VO2max L min VO2max L min VO2max L min

1

( 14.5*age) ((0.0626*ht_m) [1.6267

(5.4*ht_cm)

(103.2*lei)

0.0455)*(37.03

(0.371*age))

(0.0058*ABW)

1

(0.0135(wt_kg))

(0.0199(age))] (0.01*wt_kg)

1

( 0.18*age)

(0.025*ht_cm)

Note: For equations 1 and 2, the original equation used gender as a predictor variable (0 males; 1 awt, actual weight (kg); BW, body weight (kg); ABW, actual body weight (kg); NR, not reported.

females); age, years; lei, leisure time score; nwt, normal predicted weight (kg);

difference for actual VO2max predicted VO2max), Pearson product-moment correlation (r), standard error of estimate

(SEE SDy (1 r2 ), and total error (TE

(actualVO2max

predictedVO2max)2 /N)

For the derivation of the new nonexercise-based equation, VO2max, weight, height, age, duration, number of years performing habitual physical activity, and intensity at which the subject's performed their daily exercise were examined using the Statistical Package for the Social Sciences software (v. 12.0, SPSS Inc., Chicago, IL) for screening of missing values, outliers, and distributional properties and transformed, if necessary, for parametric analyses. The positively skewed length of time that subject's had been performing habitual physical activity was transformed with a natural logarithm to reduce skewness, and improve the normality, linearity, and homoscedasticity of residuals. No cases had missing data. To generate a new equation for estimating VO2max for aerobically trained females, we computed hierarchical linear

regression of the nonexercise variables onto VO2max 1 (mL·min ) for 80 subjects selected randomly from the pool of 115 subjects. Specifically, we entered the anthropometric variables (e.g., body weight and height) into the first block then entered age into the second block, and then entered the habitual physical activity indices (e.g., duration, intensity of the exercise, and the length of time subjects performed habitual physical activity) into the third, fourth, and fifth blocks, respectively. This approach was taken to compare the relative contribution, based on R2 change, of the three groups of variables (anthropometric, age, and habitual phys ical activity indices) to the prediction of VO2max in aerobically trained females. The new nonexercise-based equation was cross-validated using the predicted residual sum of squares (PRESS) method (13). The PRESS approach to cross-validation is based on the error in prediction for each case when only that case is deleted from the model-generating process (20). This term is called the "predicted residual" in SAS (22) and the "deleted residual" in SPSS (25). PRESS is defined as the

TABLE 2. Modified VO2max prediction equations for cycle ergometry that were cross-validated against maximum incremental test. Equation 1 2 3 4 5 6 7 8 9 Reference Jones et al. (15) 1F female Jones et al. (15) 2F female Storer et al. (26) 3F female Wasserman et al. (27) 4F female Fairbarn et al. (11) 5F female Neder et al. (21) 6F female Cooper and Storer (8) 7F female Davis et al. (9) 8F female Metabolic cart (23) 9F female VO2max L min VO2max L min

1

Equation 0.046(ht_cm) 0.025(ht_cm)

1

0.021(age) 0.023(age) (7.70*BW)

4.109 0.019(wt_kg) (5.88*age) (0.17*age)) (0.027*age) 0.15(lei) 268.7 997 0.591 1471 1.037 2.306

1

VO2max mL min VO2max mL min VO2max L min

1

(9.39*Wmax) [(nwt awt

1

86)/2]*(22.78 (0.00899*BW) (8.3*BW)

(0.0158*ht_cm)

1

VO2peak mL min VO2max L min VO2max L min VO2max L min

1

( 14.5*age) ((0.0626*ht_m) [1.6267

(5.4*ht_cm)

(103.2*lei)

0.0455)*(37.03

(0.371*age)) 1.029

(0.0058*ABW)

1

(0.0135(wt_kg))

(0.0199(age))] (0.01*wt_kg)

1

( 0.18*age) males; 1

(0.025*ht_cm)

1.358

Note: For equations 1 and 2, the original equation used gender as a predictor variable (0 awt, actual weight (kg); BW, body weight (kg); ABW, actual body weight (kg).

females); age, years; lei, leisure time score; nwt, normal predicted weight (kg);

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TABLE 3. Cross-validation of the modified equations for maximal oxygen uptake (VO2max) in aerobically trained females (N 50). Predicted VO2max CE t r SEE (mL min 1) Equation Reference (mL min 1) (X SD) 1 2 3 4 5 6 7 8 9 Jones et al. (15) 1F female Jones et al. (15) 2F female Storer et al. (26) 3F female Wasserman et al. (27) 4F female Fairbarn et al. (11) 5F female Neder et al. (21) 6F female Cooper and Storer (8) 7F female Davis et al. (9) 8F female Metabolic cart (23) 9F female 2712 2690 2664 2724 2725 2711 2725 2718 2700 411 393 451 211 337 180 268 238 323 114 93 67 127 128 115 128 121 102 2.25 1.93 2.26 2.70 2.65 2.53 2.78 2.50 2.22 0.61 0.63 0.89 0.55 0.58 0.62 0.58 0.52 0.61 321 312 186 336 328 317 328 344 319 0.05/9

SEE%* 12% 12% 7% 13% 13% 12% 13% 13% 12%

TE (mL min 1) 374 348 217 353 362 337 348 359 339

% TE** 14% 13% 8% 14% 14% 13% 13% 14% 13%

Note: All values from prediction equations were converted to milliliters per minute. Alpha adjusted by Bonferroni procedure (P of actual VO2max 100]. ** %TE calculated as [TE/mean of actual VO2max 100].

0.006). * %SEE calculated as [SEE/mean

sum of squares of the predicted or deleted residuals, and the PRESS adjusted R2 (Rp2) can be calculated as 1 (PRESS/ SStotal). Also, we calculated a PRESS standard error of estimate (SEEp) using the following equation:

SEEp

PRESS/N .

A second series of cross-validation analyses of the new equation based on 80 subjects was conducted on the remaining 35 aerobically trained females using the same statistical methods (e.g., CE, r, SEE, and TE) that were used to cross-validate the modified equations in the present study. A power analysis showed that with N 80, the power exceeded 80% for a test to detect an R2 added of 0.05 for a single predictor added to a regression model that had attained R2 0.55 using k 5 predictors (alpha 0.05) (7). Because of the large range between the highest and lowest CE values reported for females by Malek et al. (18) we selected the median CE value (902 mL·min 1) to conduct a power analysis for the second cross-validation analyses. With a total of 35 subjects the power to detect a large effect size (Cohen's d 2.24, alpha 0.05) between group means for a two-tailed paired t-test exceeded 80%.

Derivation of the new nonexercise equation (N 80). Eighty aerobically trained females were randomly selected for the derivation group from the pool of 115 subjects (Table 4). All six predictors were significantly related to actual VO2max (Table 5), and each predictor contributed independently (P 0.01, Table 6) to the model. As shown in Table 6, the proportion of variance in VO2max predicted 2 by the model (R adjusted) was 0.67 (SEE 247 mL·min 1). First cross-validation of the new nonexercise equation using PRESS. The cross-validation results of the PRESS method for the new nonexercise-based equation are shown in Table 6. For this model, Rp2 was nearly as large as the R2 adjusted (0.63 vs 0.67), and the SEEp value was nearly equal to the corresponding SEE value (247 vs 259 mL·min 1).

TABLE 4. Characteristics of subjects (mean

SD). Derivation (N 80) Cross-Validation (N 35) 39 (9.6) 166 (6.7) 62.4 (7.6) 15 7 13 -- -- 5.8 (3.7) 7.5 (2.4) 11.7 (4.7) 14 (1.9) 98 (4.9) 237 (43) 18 (1.7) 2729 (402) 44.1 (7.3)

RESULTS

Cross-validation of the modified equations (N 50). Table 3 includes the results of the cross-validation analyses for the nine modified equations. The mean ( SD) actual VO2max for the random sample of 50 females used to crossvalidate the modified equations was 2597 399 mL·min 1. None of the modified equations had a significant CE value at a Bonferroni corrected alpha of P 0.006 (0.05/9). The validity coefficients (r) ranged from 0.52 (equation 8F) to 0.89 (equation 3F). The SEE values ranged from 186 (equation 3F) to 344 mL·min 1 (equation 8F). The TE values ranged from 217 (equation 3F) to 374 mL·min 1 (equation 1F). These values corresponded to %TE (e.g., [TE/mean of actual VO2max] 100) that were 8% of the mean actual VO2max.

NEW FEMALE VO2max EQUATION

Demographic information Age (yr) Height (cm) Weight (kg) Activity patterns Mode of exercise (number) Triathletes Cyclists Marathoners Adventure racers Rowers Years of training Frequency (sessions wk 1) Duration (h wk 1) Intensity of training (Borg 6­20) Maximal cycle ergometer test % predicted maximum heart rate (220 age) Wmax (W) RPE (6­20) at VO2max VO2max (mL min 1) VO2max (mL kg 1 min 1)

38 (9.5) 166 (6.6) 60.0 (7.9) 34 20 20 5 1 5.1 (3.2) 7.0 (2.4) 11.0 (4.3) 14 (1.7) 97 (5.0) 229 (47) 18 (1.5) 2594 (431) 43.2 (6.6)

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TABLE 5. Correlation matrix of VO2max and independent variables. VO2max Weight (kg) (mL min 1) -- VO2max (mL min 1) Weight (kg) 0.43** -- Height (cm) 0.58** 0.61** Age (yr) 0.42** 0.31 Duration (h wk 1) 0.42** 0.13 Intensity (Borg 6­20) 0.40** 0.11 Years of training 0.26* 0.10 Note: N 80; * P 0.05; ** P 0.01; natural log of years.

Height (cm)

Age (yr)

Duration (h wk 1)

Intensity (Borg 6­20)

Years of Training

-- 0.29** 0.17 0.10 0.04

-- 0.16 0.08 0.24*

-- 0.25* 0.06

-- 0.24*

--

Second cross-validation of the new nonexercise equation using an independent sample (N 35). Table 7 includes the results of the cross-validation analyses for the new nonexercise equation (Table 6) based on the subsample of 35 aerobically trained females who were withheld from the derivation of the equation. The mean pre dicted VO2max was 2658 mL·min 1 (Table 7) compared with the actual VO2max of 2729 mL·min 1 (Table 4). The mean CE value of 71 mL·min 1 (the difference between predicted and actual) was not significantly different from zero, t (34) 1.61, P 0.05. The validity coefficient (r) and SEE values were 0.76 and 264 mL·min 1, respectively. The TE value was 268 mL·min 1, which corresponded to a %TE of 10% of mean actual VO2max.

DISCUSSION

When compared with the results of Malek et al. (18) for the previously published equations, the cross-validation analyses of the modified equations in the present study (Table 3) resulted in lower CE, SEE, and TE values and higher validity coefficients (r) for all equations. Despite these improvements in accuracy, however, the %TE values for the modified nonexercise-based equations (equations 1F, 2F, 4F, 5F, 6F, 7F, 8F, and 9F) were 13%. Equation 3F had a %TE of 8%, which was an improvement from the original cross-validation value (% TE 12%) reported by Malek et al. (18). Equation 3F, however, is limited for practical use because it requires a maximal test to determine Wmax. In cases where Wmax is available, however, the modified version of equation 3F (Table 2) is recommended for estimating VO2max in aerobically trained females. To further increase the accuracy of a nonexercise-based model, a new equation using demographic variables and habitual physical activity indices was developed. The derivation of the new nonexercise-based equation in the present study resulted in a validity coefficient of R 0.83 and a SEE of 247 mL·min 1 (Table 6). This SEE was substantially less than those for the modified equations (Table 3; 312­344 mL·min 1) cross-validated in the present study.

TABLE 6. New VO2max prediction equation for aerobically trained females. Predictor Variables Equation Present study Weight (kg) 18.528 Ht (cm) 11.993 Age (yr) 17.197 Duration 23.522 Intensity 62.118 Years of Training 278.262

Information about the subject's habitual physical activity was used as predictor variables to develop the new nonexercise-based equation. In the current study, the regression equation yielded R2-adjusted 0.33 when using only height and weight. This value increased to R2-adjusted 0.40 when age was added to the equation. Next, the habitual physical activity indices (e.g., duration, intensity of the exercise, and the length of time subjects performed habitual physical activity) were added in the final three steps of the regression model resulting in R2-adjusted values of 0.48, 0.58, and 0.67, respectively (Table 6). The habitual physical activity indices, which have not been used in previously developed equations, substantially improved the accuracy for the estimation of VO2max in aerobically trained females when compared with the use of age, height, and weight alone. To determine the generalizability of the new equation, we conducted two cross-validation analyses. For the PRESS procedure, the R2 adjusted for the new equation (R2 0.67) and Rp2 (Rp2 0.63) were similar. This was also true for the SEE (247 mL·min 1) and SEEp (259 mL·min 1) values. In the second analysis, the actual VO2max values for an independent cross-validation sample of aerobically trained fe males (N 35) was compared with estimated VO2max values from the new nonexercise-based equation. The results indicated close agreement between the actual and pre dicted VO2max values as represented by the small, nonsignificant CE value (71 mL·min 1). In addition, the SEE% of 9.7% was lower than the 10 ­20% values reported for most field methods such as step tests, submaximal cycle ergome ter tests, or walk/run tests used to estimate VO2max (19,28). Furthermore, the TE, which is the best single criterion for determining the accuracy of an equation because it combines the errors associated with the SEE and CE (17), was 268 mL·min 1, which corresponded to a %TE of 10%. This value was 3­ 4% less than the %TE values for the modified nonexercise equations (Table 3). There are a number of benefits to using two separate cross-validation procedures. First, through the use of the PRESS statistic, we were able to determine the relative

Constant (mL min 1) 1375.878

R 0.83

R2 (adjusted) 0.67

Rp2 0.63

SEE (mL min 1) 247

SEEp (mL min 1) 259 0.01)

Note: N 80; natural log of years; Rp2, PRESS squared multiple correlation coefficients; SEEp, PRESS standard error of estimate. Each predictor contributed significantly (P to the model beyond all of the other predictors.

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TABLE 7. Cross-validation of new maximal oxygen uptake (VO2max) equation in a random independent sample of aerobically trained females. SEE Predicted VO2max (mL min 1) (mean SD) CE t r (mL min 1) SEE%* Equation Present study Note: N 2658 272 71 1.61 0.76 264 9.7% 100]. 35; * %SEE calculated as [SEE/mean of actual VO2max 100]. ** %TE calculated as [TE/mean of actual VO2max

TE (mL min 1) 268

% TE** 10%

accuracy of our equation based on N 1 cases from the sample used to derive the equation. Holiday et al. (13) stated "The PRESS statistic and associated residuals do not require the data to be split, [and] yield alternative unbiased estimates of R2 and SEE. . ." (p. 612). As a result of using the PRESS statistic, the new nonexercise-based equation was found to have high generalizability for a population of aerobically trained females (Table 6). Studies such as Neder et al. (21) and Davis et al. (9) used only the PRESS statistic to validate their equations. Thus, these studies provided only a single-level validation approach. Herein lies a major difference between the present study and previous studies, which have derived new equations for estimating VO2max. An essential concern in developing a new equation is how well the model will work for new cases from the same population. The present study addressed this concern by using the PRESS statistic to determine the generalizability of the new nonexercise-based equation. To further corroborate the validity of the equation, the actual and predicted VO2max values for an independent sample of aerobically trained females were compared (Table 7). Therefore, the second benefit of using two separate cross-validation procedures is that the investigator provides two levels of validation. Holiday et al. (13) stated, "A central tenet of crossvalidation is that the custodians of the model should not release a prediction equation to the user community without some assurance that it will do a good job" (p. 616). To our knowledge, no other studies in the literature have used the two-level validation approach outlined in the present study for a nonexercise-based VO2max equation. Therefore, based on the results of two separate cross-validation procedures, REFERENCES

1. AMERICAN COLLEGE OF SPORTS MEDICINE., B. A. FRANKLIN, M. H. WHALEY, E. T. HOWLEY, and G. J. BALADY. In: ACSM's Guidelines for Exercise Testing and Prescription. Philadelphia: Lippincott Williams & Wilkins, 2000, pp. 33­130. 2. AMERICAN COLLEGE of SPORTS MEDICINE., M. L. POLLOCK, G. A. GAESSER, et al. American College of Sports Medicine Position Stand: the recommended quantity and quality of exercise for developing and maintaining cardiorespiratory and muscular fitness, and flexibility in healthy adults. Med. Sci. Sports Exerc. 30:975­991, 1998. 3. ATS/ACCP. ATS/ACCP statement on cardiopulmonary exercise testing. Am. J. Respir. Crit. Care Med. 167:211­277, 2003. 4. BAUMGARTNER, T. A., and A. S. JACKSON. Measurement for Evaluation in Physical Education and Exercise Science, 7th Ed. Boston: WCB/McGraw-Hill, 2003, pp. 219 ­251. 5. BORG, G. Borg's Perceived Exertion and Pain Scales. Champaign, IL: Human Kinetics, 1998, pp. viii, 130. 6. BUCHFUHRER, M. J., J. E. HANSEN, T. E. ROBINSON, D. Y. SUE, K. WASSERMAN, and B. J. WHIPP. Optimizing the exercise protocol for cardiopulmonary assessment. J. Appl. Physiol. 55:1558 ­1564, 1983. 7. COHEN, J. A power primer. Psychol. Bull. 112:155­159, 1992.

NEW FEMALE VO2max EQUATION

the new nonexercise-based equation derived in the present study is recommended for estimating VO2max for aerobically trained females.

CONCLUSION

The results of the present study, in conjunction with those of Malek et al. (18), indicated that the original and modified versions (Table 2) of the nonexercise-based equations resulted in TE values (% TE 13­14%) that were too large to be of practical value for estimating VO2max in aerobically trained females. The modified equation of Storer et al. (Tables 2 and 3) is recommended for estimating VO2max in aerobically trained females only when an estimate of Wmax from a maximal cycle ergometer test can be obtained. However, because this requires the subject to perform a maximal cycle ergometer test to determine Wmax for the estimation of VO2max the new nonexercise-based equation derived in the present study (Table 6), overcomes this limitation by using only demographic and habitual physical activity information to estimate VO2max. Given the cross max is not available, the new validation %TE of 10%, if W nonexercise-based equation derived in this study is recom mended for estimating VO2max in aerobically trained females.

We thank the various triathlete, cycling, running, and adventure racing clubs in Southern California for participating in this study. Note: Data were collected while Mr. Malek was a research associate in the David Geffen School of Medicine at UCLA.

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