Examination of data normalization procedures for ... · vascular fitness in. subjects differing in body size and composition, peak VO, data ... excellent physical health were examined.

Examination of data normalization procedures for expressing peak VO, data

MICHAEL J. TOTH, MICHAEL I. GORAN, PHILIP A. ADES, DIANTHA B. HOWARD, AND ERIC T. POEHLMAN Division of Gerontology, Department of Medicine, University of Maryland, Baltimore, Maryland 21201; and Department of Medicine, University of Vermont, Burlington, Vermont 05405

TOTH, MICHAEL J., MICHAEL I. GORAN, PHILIP A. ADES, DIANTHA B. HOWARD,AND ERIC T. POEHLMAN.EXWC-U~~O~ of data normalization procedures for expressing peak VO, data. J. Appl. Physiol. 75(5): 2288-2292, 1993.-Peak 0, uptake (vo2) has traditionally been compared among individuals differing in body composition by dividing measured values (Urnin) by fat- free mass (FFM) (i.e., ratio method). However, the ability of the ratio method to mathematically remove the confounding influence of FFM from peak Vo2 has recently been questioned. Therefore, we compared the effectiveness of the ratio method vs. regression modeling to normalize peak VO, in a large cohort of males and females for differences in FFM. Regression model- ing adjusts peak VO, according to the relationship derived from the regression of peak VO, on FFM. Results showed that peak VO, was 60% higher in males (3.53 & 1.0 l/min) than in females (2.22 t 0.6 Urnin; P < 0.01). With the ratio method (i.e., peak vo,lFFM), peak vo, was 15% higher in males (54.6 t 12 ml. kg FFM-’ l min?) than in females (47.4 t 11 ml l kg FFM-1 l min-‘; P < 0.01). In contrast, when a regression-based approach was employed to normalize values, no significant difference in ad- justed peak VO, was observed between males and females (3.04 * 0.9 vs. 3.01 t 1.0 Urnin). In conclusion, dividing peak VO, by FFM can produce spurious results, because this ap- proach does not take into account the nonzero intercept. There- fore, a regression-based approach should be used to normalize peak VO,.

peak oxygen uptake; gender; fat-free mass; normalization

MAXIMAL AEROBIC POWER [peak 0,uptake (vo,)] is an indicator of an individual’s ability to utilize 0, at maxi- mal exercise (7). Its widespread use as a diagnostic tool for cardiovascular health (1) and its predictive capacity as a marker of energy expenditure and daily energy re- quirements (4, 11) underscore its clinical importance. It is well known that peak VO, depends partially on body size and composition (2). Therefore, to compare cardio- vascular fitness in. subjects differing in body size and composition, peak VO, data have traditionally been nor- malized using a ratio with body weight or fat-free mass as the divisor (i.e., ratio method). The use of such a ratio aims to remove the confounding effects of body size and body composition on peak VO,.

Mathematically, however, the expression of peak VO, as a ratio assumes a linear relationship between peak VO, and fat-free mass (or body weight) with a y-intercept equal to zero [peak VO, = b(FFM), where b is the slope and FFM is fat-free mass]. In fact, the assumption of a zero intercept is rarely satisfied in biological research (18). Therefore, the relationship is probably more accu- rately characterized by the following equation: peak . vo = b(FFM) + c, where c is they-intercept. Thus, when the2ratio method is applied to data that exhibit a nonzero y-intercept, spurious conclusions could be drawn in com- paring peak VO, among individuals who differ in body composition. The inaccuracy of the ratio method as an approach to compare biological data that are body size dependent has previously been reported (5, 6, 13, 18). Despite these important findings, peak Vo2 data con- tinue to be expressed on a per kilogram or per kilogram of fat-free mass basis in scientific literature on exercise physiology.

Our objectives in the present study were 1) to examine the bias introduced by using the ratio method to normal- ize peak VO, in subjects who differ in body composition and 2) to examine the effectiveness of regression model- ing to normalize peak VO, data of individuals and groups differing in body composition. This latter method nor- malizes peak VO, data by adjusting peak VO, values ac- cording to the linear relationship between peak VO, and fat-free mass.

METHODS AND MATERIALS

Subjects. A total of 523 individuals, 322 males (17-78 yr; 42 t 19 yr) and 201 females (18-81 yr; 45 t 17 yr), in excellent physical health were examined. Criteria for subject selection were as follows: no clinical symptoms or signs of heart disease, resting blood pressure <140/90, normal resting electrocardiogram (ECG), a normal 12- lead ECG response to an exercise stress test, absence of any prescription or over-the-counter medication that could affect cardiovascular function, no family medical history of diabetes or obesity, and weight stability (k2 kg) by medical history within the past year. The nature,

2288 0161-7567/93 $2.00 Copyright 0 1993 the American Physiological Society

NORMALIZATION OF PEAK i’o, 2289

TABLE 1. Physical characteristics of healthy males lines of each group must be parallel (i.e., have equal and females slopes) 17 2) the proper form of the relationship between

the dependent variable and the covariate has been fitted (i.e., linear or curvilinear), 3) the variance of the resid- uals is similar in each group, and 4) the covariate must be fixed (that is, there should be a minimal amount of in- traindividual variation in the measurement of the covar-

Males Females

Height, cm Weight, kg Fat-free mass, kg Fat mass, kg %Fat

322 201 42219 (17-78) 45~117 (18-81)

177k7 (162-200) 164+7* (146-182) 78+11 (60-132) 62+9-f (45-106) 6528 (48-98) 46+5-j- (35-66) 13+7 (1.7-47) 16+7t (5-51) 16k7 (2-39) 25k8.k (10-48)

Values are t P < 0.01.

means it_ SD; nos. in parentheses are ranges. * P < 0.05;

purpose, and possible risks of the study were carefully explained to each subject be fore th .ey gave thei r consent to participate. The experimental protocol was approved by the Committee on Human Research for the Medical Sciences of the University of Vermont.

Measurement of peak VO, Peak VO, was assessed by a progressive and continuous test to exhaustion on a treadmill as previously described (12). Briefly, a comfort- able initial walking or jogging speed was found for each subject. After the first 3 min, the incline was increased by 2.5% every 2 min while a constant treadmill speed was maintained. Peak VO, was recorded as the highest 0, uptake for 1 min during the test. Attainment of peak vo2 for each subject was defined as the subject having reached their age-predicted maximal heart rate and hav- ing a maximal respiratory exchange ratio >l.O. Test-re- test conditions (within 1 wk) for peak VO, in a previous group of volunteers yielded an intraclass correlation of 0.94 and a coefficient of variation of 3.8% in 25 males (12) and 0.98 and 3.4%, respectively, in 18 females (3).

Body composition. Body composition was estimated with the use of the Siri equation (15) from body density by using underwater weighing with simultaneous mea- surement of lung volume by helium dilution. Fat-free mass was estimated as total body weight minus fat weight. The reproducibility of percent body fat was exam- ined using test-retest conditions (within 1 wk). The in- traclass correlation in a previous group of volunteers for the estimation of percent body fat reached 0.98 and the coefficient of variation was 4.9% in 25 males (12) and 0.97 and 4.2%, respectively, in 18 females (3).

Statistics. The difference between male and female physical characteristics and peak VO, normalized using the ratio method (ml l kg FFM-1 . min-‘) were assessed by unpaired t tests. The relationships between peak VO, and body composition variables were determined using linear regression analysis. Mean differences in peak VO, between men and women were compared by using the ratio method with fat-free mass as the divisor and with analysis of covariance. Analysis of covariance allows for the removal of a linear effect of the covariate (fat-free mass or body weight) on peak VO, without making the assumption of a zero intercept. Before applying analysis of covariance, however, it is important to appreciate sev- eral underlying assumptions. These assumptions include I) the relationship between the dependent variable and

0 20 40 60 80 100

Fat-free moss (kg)

the covariate is the same in all groups (e.g., male and female) [that is, in a linear relationship, the regression

FIG. 1. Relationship of peak 0, uptake (VO,) with fat-free mass in males (n = 322) and females (n = 201).

iate relative to the range of observations). All of these assu mptions were met by our data set. To illustrate the potential differences in the ratio method and analysis of covariance when comparing individuals with different levels of body composition, we compared differences in adjusted peak VO, between men and women using the two methods. All values are expressed as means t SD, unless otherwise specified.

RESULTS

Physical characteristics. The physical characteristics of both males and females are described in Table 1. This population represents a broad age range of healthy volun- teers varying in body composition. Males were signifi- cantly taller (P < 0.05), weighed more (P < O.Ol), and possessed a greater quantity of fat-free mass (P < 0.01) compared with females. Females showed a higher level of percent body fat (P < 0.01) and fat mass (P < 0.01) com- pared with males.

Identification of a normalization variable for peak Vo2. We focused our initial efforts on identifying a variable that would serve as the most appropriate index to nor- malize peak VO, data. Fat-free mass was the best predic- tor of peak VO, in the whole group (r = 0.77, P < 0.01; Fig. 1). Fat-free mass also showed the highest simple correla- tion with peak TO, in both the males (r = 0.60; P < 0.01) and the females (r = 0.61; P < 0.01) when compared with other body composition variables such as body weight (males, r = 0.47, P < 0.01; females, r = 0.03, not signifi- cant) and fat mass (males, r = -0.34, P < 0.01; females, r = . -$45, P < 0.01). The regression equations in which L .n- . ̂peak V 0, is predicted from fat-free mass are

0= male A = female r = 0.77 P < 0.01

2290 NORMALIZATION OF PEAK i’o,

peak VO, (Urnin) (1) ’ ’ = -1.018 + [O.O70(fat-free mass; kg)]

for males and

peak Tjo2 (Urnin) (2)

= -1.078 + [O.O7l(fat-free mass; kg)] ‘- ’

for females. The intercepts for both the male (-1.018 t 0.33) and female (-1.078 t 0.31) regressions of peak VO, with fat-free mass were significantly different from zero (P < 0.01). The slopes of these regressions (males, b = 0.070-t0.005; f emales, b = 0.071 t 0.007) were not signifi- cantly different.

Statistical examination of the ratio method. The regres- sion model for peak VO, as defined from our data set is

peak VO, = [b(FFM)] + c (3)

where b is the slope and- c is the y-intercept (i.e., the predicted value for peak VO, when fat-free mass equals zero). The traditional approach to normalize peak VO, has been to divide peak VO, by fat-free mass. This ap- proach assumes a model of

peak VO, = I>(FFM) (4)

(i.e., y-intercept = 0). However, when the ratio method is used to normalize data that are represented by the rela- tionship described in Eq. 3, the result is shown in Eq. 5. From Eq. 5, it is clear that the ratio method does not mathematically eliminate the effect of fat-free mass from the regression equation given the continued pres- ence of the term, -l.O18/fat-free mass (i.e., c/FFM).

Regression equation (Eq. I)

peak VO, = -1.018 + O.O70(FFM)

Ratio method

peak vos -1.018

FFM ~ + 0.070

= FFM (5)

It should be noted that if the y-intercept (c) in the rela- tionship of peak Tjoz to fat-free mass were zero, then the two models would be equivalent, and dividing by fat-free mass would remove its effect from the regression equa- tion.

Hypothetical example of the bias introduced by the ratio method. We next focused our attention on evaluating the potential bias of the ratio method on peak VO,, as shown in Fig. 2..The regression line represents the relationship of peak VO, with fat-free mass in the male group, as de- rived from Eq. 1. For example, subject A, possessing a fat-free mass of 40 kg and a peak VO, of 1.78 l/min, has a ratio of 0.045 (or a peak Vo2 of 45 ml l kg-’ l min-‘). How- ever, subject B, possessing a fat-free mass of 80 kg and falling on the same regression line, would have a pre- dicted peak VO, of 4.58 l/min and a ratio of 0.057 (or a peak VO, of 57 ml. kg-’ l min-l). Because subjects A and B fall directly on the regression line, they should theoreti- cally possess identical normalized peak Tjoa values. How- ever, because the ratio method incorrectly assumes a zero intercept for the relationship of peak VO, with fat-free mass, the values of subjects A and B normalized using the ratio method are not identical. From the examination of

6

r 5 c .-

Y

: h 2

60 80

Fat-free moss (kg)

FIG. 2. Bias introduced by ratio method. Regression line represents relationship of peak VO, to fat-free mass in male group. Theoretically, because both subjects A and B fall on regression line, each should pos- sess identical normalized peak VO, values (i.e., ratios). However, these ratios are not similar [0.045 < 0.057 1. kg fat-free mass (FFM)-’ . min-‘1 because ratio method fails to account for nonzero y- intercept. These ratios can be converted to ml l kg FFM-’ l min-’ by multiplying each by 1,000.

the normalized peak Tjop of each subject, it can be noted that subject B is overestimated relative to the peak Vop of subject A. The practical implications are that, when the ratio method is used in a population displaying a large range of fat-free mass, subjects possessing a smaller quantity of fat-free mass will have their normalized peak VO, systematically underestimated relative to subjects with larger amounts of fat-free mass.

Adjustment of individual peak Vo2 values using regres- sion analysis. We suggest that regression analysis (to which analysis of covariance reduces when we have only one group) represents a more suitable statistical ap- proach to normalize peak VO, data. The regression line in Eq. 3 can be rewritten in a form centered around the mean (X) of the normalizing variable (fat-free mass) as follows

Y= Y+b(X-X) (6)

where Y is the mean peak Vo2, X is a value of fat-free mass, and Y is the corresponding predicted (average) value of peak VO,. For an individual whose peak Tjoz is Y0 and whose fat-free mass is X0, the regression line permits adjustment for the difference between X0 and X. The individual’s adjusted peak VO, is

Y I o = Y. - b(X, - x) (7)

In effect, Yb restates the peak VO, value as if the individ- ual’s fat-free mass were X. This form of the equation now permits the calculation of an individual’s adjusted peak VO, given values for b and X0. With the use of Eq. 7, the normalized peak VO, values for subjects A and B are now - identical, as shown below, using X = 58 kg (the mean of fat-free mass in our data set) and b = 0.07. These values

NORMALIZATION OF PEAK vo, 2291

2.5

2.0

Measured

P<O.Ol

0

4.0

3.5

3.0

2.5

2.0

Covariance

NS

0

Peak $0 Peak \iO, adjusted

(L l min 021

) for fat-free mass

(L l min -1

)

were derived from the relationship of peak VO, and fat- free mass in our data set

1.78 - 0.07(40 - 58) = 3.04 llmin (8)

4.58 - 0.07(80 - 58) = 3.04 l/min (9)

Adjustment of mean values using regression analysis. We examined gender differences in peak VO, using the ratio method and analysis of covariance in our cohort of healthy males and females. During the test of peak VO,, males reached a slightly higher maximal respiratory ex- change ratio (1.11 t 0.07) compared with females (1.09 t 0.07; P < 0.01). There was no difference in the maximal heart rate between males and females (180 t 21 vs. 178 t 17 beats/min; data not shown).

Analysis of covariance can use the relationship be- tween Y and the covariate X to adjust group means of Y for possible differences among the groups’ means on X. For a linear relationship, the model is given by

Y ij = ci + bXi + eti (10)

where i refers to the group and j refers to the individual, b is the common slope for all groups, ci is the intercept for the ith group, and eii is the residual or the difference be- tween observed and predicted values for each individual. Adjusted group means (Yi) are therefore calculated ac- cording to the relationship between peak VO, (Y) and the covariate fat-free mass (X) as shown below

Y : = Yi - b(Xi - X,> (IO

where Yi is the mean peak VO, of the ith group, Xi is the mean fat-free mass for the ith group, and Xg is the grand mean for the covariate. It is important to note that analy- sis of covariance can be applied to a nonlinear relation- ship as well (8). Using analysis of covariance on our data, we found that the slope of the relationship between peak VO, and fat-free mass did not differ significantly between males and females. A value of b of 0.069 was then used to calculate group adjusted means.

Figure 3 shows peak VO, on an absolute basis, peak VO, normalized using analysis of covariance, and peak VO, normalized with fat-free mass in the denominator (i.e., ratio method). Measured peak VO, was 60% higher in males than in females (3.53 t 1.0 vs. 2.22 t 0.6 l/min).

40

Peak VO,

(ml *kgFFM-’ emin-‘)

FIG. 3. Gender differences in peak VO, in measured values and data normal- ized by ratio method and by analysis of covariance, using fat-free mass as nor- malizing variable.

When the data were normalized using the ratio method, men showed a 15% higher peak VO, compared with women (54.6 t 12.1 vs. 47.4 t 11 ml l kg FFM-1 l min-‘; P < 0.01). In contrast, when peak VO, is adjusted for fat-free mass using analysis of covariance, no differences in the adjusted mean values between males and females were found (3.04 t 0.9 vs. 3.01 t 1.0 l/min).

DISCUSSION

In the methods

present study of normalizin

, we examined and g peak Tjo2 data an

compared two d their impact

on data analysis. The traditional ratio divides peak VO,

method, which by fat-free mass, was compared with

regression analysis, a statistical approach that adjusts peak VO, for the linear relationship between peak VO, and fat-free mass.

Historically, studies that have examined peak VO, have used the ratio method to normalize data for subjects of varying However,

body size and this approach

composition (2, 9, 10, 16,- 17). has been criticized in recent

years (5, 6, 13). Frequently, this method has employed body weight as the divisor to characterize the functional capacity of the 0, transport system. Our data suggest that fat-free mass is a more appropriate index to normal- ize peak Vo2 data because fat-free mass accounts for a greater proportion of the variance in peak VO, (r2 = 60%) than body weight (r2 = 22%) among individuals. This finding is not surprising, because fat-free mass is com- posed of the metabolically active tissue (i.e., muscle) that is primarily responsible for the production of energy to perform e xternal work ( 14) . Because of the strong statis- tical and physiological rel ationship between peak VO, and fat-free mass, we propose that it be adopted as the variable of choice for normalization of peak VO,.

Our data show that the relationship between peak VO,

and fat-free mass has a y-intercept that is significantly different from zero (in males, -1.018 t 0.33; P < 0.01). Therefore, the linear relationship between peak I~o, and fat-free mass should be represented by an equation that includes a nonzero intercept. However, using the ratio method to normalize peak Tjo, for fat-free mass makes the erroneous assumption that the relationship between the variables is linear and contains a zero y-intercept.

2292 NORMALIZATION OF PEAK Voz

Moreover, it is clear that when the ratio method is ap- plied to variables, the relationship of which has a nonzero &intercept, it does not adequately rem ove the e ffect of the normalizin g variable (fat-free mass) from the depen- dent variable (peak VO,; see Fig. 3). Interestingly, earlier work (2) employing a smaller sample size (n = 54) showed that the intercept of the regression line of maxi- mal 0, uptake on fat-free mass was close to zero, al- though no statistical examination of this difference was presented. Collectively, our results indicate that when the ratio method is used to normalize variables that ex- hibit a nonzero y-intercept, individuals with a large amount of fat-free mass will have their peak Vo2 overes- timated compared with individuals with a lower quantity of fat-free mass, because this method fails to account for the presence of a negative intercept (see Fig. 2).

Regression modeling represents a more suitable ap- proach to compare peak VO, in individuals and groups who differ in body composition (e.g., male vs. female; old vs. young) This statistical approach adjusts peak-%, ac- cording to the linear relationship between peak VO, and fat-free mass developed from the data being analyzed and thus takes into account the y-intercept, if signifi- cantly different from zero. Therefore, regression analysis produces adjusted peak VO, data for individuals with the effect of the normalizing variable completely removed. Regression modeling can be used to normalize peak VO,

with fat-free mass or body weight as the normalizing vari- able. If body weight accounts for a substantially smaller proportion of the variance in peak VO,, however, use of body weight will yield less-accurate adjusted values.

We subsequently examined gender differences in peak VO, in a large cohort of data to illustrate the statistical problem of using the ratio method vs. regression model- ing. With the ratio method, peak VO, was 15% higher in males than in females, as other studies have found (9,10, 16, 17). However, when peak 00, was compared using fat-free mass as the covariate, no difference between males and females was noted. This example underscores the possibility that different normalization procedures may lead to different results. Furthermore, the ratio method produces a different conclusion than regression modeling because of its failure to take into account the nonzero y-intercept. It will be helpful in future studies to evaluate the validity of the ratio and regression ap- proaches against an independent criterion (such as work capacity or performance in a running event) to distin- guish gender differences in peak VO,.

In conclusion, we suggest that regression modeling be used to normalize peak VP, in all experimental designs where a measure of peak VO, independent of body com- position is desired. As long as its underlying assumptions are satisfied, a regression-based approach can be used to adjust individual and/or group mean values.

The authors thank all the subjects who volunteered for this study. The authors extend special appreciation to Drs. A. W. Gardner and D. L. Ballor for their constructive criticisms on the manuscript and to an anonymous reviewer, who substantially improved the manuscript.

E. T. Poehlman is supported by National Institute of Aging Grant AG-07857, National Institute of Aging Research Career and Develop- ment Award K04-AG-00564, and the American Association of Retired Persons Andrus Foundation. M. I. Goran is supported by a grant from the American Diabetes Association and the US Dept. of Agriculture. P. A. Ades is supported by National Institute of Aging Clinical Investi- gator Award K08-AG-00426. This study was funded in part by the General Clinical Research Center (RR-109) and the Sims Obesity/Nu- trition Research Center.

Address for reprint requests: E. T. Poehlman, Geriatrics (18), Univ. of Maryland, 10 North Greene St., Baltimore, MD 21201.

Received 25 September 1992; accepted in final form 21 June 1993.

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