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Special Communications: Methods

Derivation of prediction equations for RV in overweight men and women


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Medicine & Science in Sports & Exercise: February 1998 - Volume 30 - Issue 2 - p 322-327
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The assessment of body composition is important to the diagnosis of several chronic diseases as well as to the monitoring of progress during therapeutic intervention. A commonly used method for body composition analysis is through body density determination by hydrostatic weighing. This technique, which was first explored by Behnke et al. (2), is based upon the“Archimedes” principle which states that the volume of an object is equal to the object's loss of weight in water with appropriate correction for the density of the water. The hydrostatic weighing technique for body composition analysis typically requires weighing the subject on land and then performing repeated underwater weighings when the subject is completely submerged while maximally exhaling to residual volume (RV). A main methodological concern in hydrostatic weighing is to account for gas trapped in body compartments that are not truly a part of the tissue composition. Two sources of trapped air that must be taken into account are the RV and the air in the gastrointestinal tract. The gastrointestinal air is represented by a constant value of 100 mL which is assumed for all individuals(5). The RV, however, can either be measured indirectly or estimated through prediction equations (22).

Although the most accurate method of hydrostatic weighing would include the indirect measurement of RV, body composition analysis is routinely performed using a predicted value for RV. Many people use a predicted RV value instead of a measured value because 1) they do not know how to measure RV, 2) they do not have the equipment necessary for measuring RV, 3) the cost of RV measurement is prohibitive, 4) measuring RV is time consuming, and/or 5) it is quicker and easier to use a predicted RV value rather than to measure RV. Thus, predicted RV values are often used in weight loss clinics, fitness clubs, health spas, YMCAs and the like where an accurate measurement of RV is not necessary for the calculation of body density, percent body fat, and lean body weight simply for classification or diagnostic purposes(22). Furthermore, many students of exercise science receive laboratory training in hydrostatic weighing techniques in which predicted or assumed values for RV are used rather than measured values(1,7,10,17). Since hydrostatic weighing is the most common densitometric method for assessing body composition during intervention for the overweight individual, the purpose of this research was to derive and compare regression equations for predicting residual volume in overweight compared with that in normal weight men and women.


Subjects. Experimental procedures for the use of human subjects in this research were performed in accordance with the policy statement regarding the use of human subjects of The American College of Sports Medicine. All subjects signed an informed consent form approved by the University Committee for the Protection of Human Subjects, which described all evaluation procedures and possible risks. A total of 388 healthy men and women participated in this research, 311 in the main study and 77 in the cross validation study. Participants had no metabolic diseases, were not taking medications that may have affected lung volume measurements, and were free from all pulmonary diseases or complications including asthma.

Test procedures. Each subject reported to the laboratory after an overnight fast for body composition determination through hydrostatic weighing at RV. Before hydrostatic weighing, RV was measured on land using the nitrogen dilution technique described by Wilmore (21). Volume measurements from two trials for RV were averaged and recorded as the true RV only if both measurements were within 100 mL of each other. If the discrepancy between the two RV measurements was greater than 100 mL, a third measurement was taken. It was never necessary to make more than three RV measurements to obtain two measurements that were within 100 mL of each other. Body weight was determined using a digital scale and recorded to the nearest 100 g. Height was measured to the nearest centimeter. Subjects were then weighed while being submerged at RV, and 5 to 10 underwater weights were recorded. The heaviest three measurements were averaged to obtain the underwater weight. Percent body fat was calculated by the Siri equation (20). Four comparison groups were formed by dividing the sample population by gender and adiposity. Overweight was defined as body fat > 25% for men and body fat> 30% for women, whereas normal weight was defined as body fat ≤ 25% for men and body fat ≤ 30% for women. Next, 20% of the subjects in each of the four groups were randomly selected and reserved for a cross-validation analysis. Group analyses for the main study were subsequently performed on 80% of the original sample population, whereas cross validation was performed on a random subset (20%) of the original sample (Table 1).

Statistical analyses. Group comparisons within gender were made using ANOVA. A stepwise backward regression was performed for each group using the Systat Statistical Package (version 5.04; Evanston, IL) where RV was regressed on sex, age, weight, and height. The alpha-to-enter and alpha-to-remove values were set at 0.05, while the tolerance was set at 0.01. The independent correlation coefficients for the regression equations generated for each group were tested for equality by the large sample Z test(14). Significance for all analyses was declared at theP < 0.05 level. All group values were reported as mean ± SEM.


Demographic data is contained in Table 1. The four groups of men in both the main study and validation study were similar in age, height, and RV, but as expected, the overweight were dissimilar from the normal weight in body weight and adiposity. The overweight women in both the main study group and the validation group were significantly older than the normal weight women, in addition to weighing more and having a greater percent body fat. However, the four groups of women were similar in height and RV.

When RV was regressed on age, weight, and height, a RV prediction equation was derived for each of the four groups in the main study (normal weight men, overweight men, normal weight women, overweight women). The equations for overweight men and women were remarkably similar, as were those for the normal weight men and women (data not shown). However, the equations for the overweight were different from those generated for the normal weight men and women. Specifically, weight was a significant predictor variable in the regression equations for the overweight groups, whereas weight was not a significant predictor for the normal weight groups. Furthermore, the large sample Z test revealed that the independent correlation coefficients for the RV prediction equations for men and women, within either the overweight or the normal weight group, were not significantly different. All of these data implied that sex was not a contributing variable for the prediction of RV in either the overweight or normal weight populations. Hence, to confirm this implication, the stepwise regression analysis was performed again on data from both sexes within either the normal weight or overweight group, this time including sex as a possible contributor for predicting RV. In this case, sex was not found to be a contributing factor for the prediction of RV in either the overweight or normal weight men and women (level of significance ranged from P < 0.25 to P < 0.71). The resulting prediction equations for RV in normal weight and overweight men and women are presented in Table 2.

To ensure the stability of the new regression equations, a cross validation was run on the data obtained from the normal weight and overweight cross-validation groups (Table 1). Similar to the main study groups, sex was not a significant predictor variable for RV in any of the validation groups. Therefore, data from the sexes were combined and the regressions run again for the normal weight and overweight groups, as was done in the main study. In each instance, no difference was found between the main study and validation study for the generated RV regression equations or their respective r values (Table 2). The large sample Z test revealed that the independent correlation coefficients for the cross-validation RV prediction equations were not significantly different from those derived from the main study. Furthermore, the SEE for predicting RV was similar for all of the equations (Table 2).


Although the measurement of lung volumes dates back to 1800 when Sir Humphrey Davy described a hydrogen dilution method with which he measured his own lung volume (9), the measurement of lung volumes in the general population for descriptive analyses is still performed today(18). The most difficult of the lung volumes to measure is the RV, which cannot be directly assessed through conventional spirometric analysis but must be measured indirectly through some other approach such as plethysmography, closed-circuit dilution of an inert gas, or open-circuit nitrogen washout during oxygen breathing. Since all the methods for measuring RV indirectly are time consuming, relatively expensive, and require specialized equipment and training, the use of prediction equations for RV has become popular. For example, many weight loss clinics, fitness clubs, health spas, YMCAs, and the like do hydrostatic weighing in portable tanks, swimming pools, etc., but do not measure lung volumes. Under these circumstances, it is unnecessary to obtain an accurate measurement of RV before body composition analysis through hydrostatic weighing simply for diagnostic and classification purposes (22). Furthermore, there are many undergraduate as well as graduate programs in exercise science in which hydrostatic weighing is being taught in laboratories where facilities dictate that RV be predicted rather than measured. In an effort to accommodate students in these less equipped laboratories, several laboratory manuals contain laboratory experiences in pulmonary function and body composition analysis in which RV is either an assumed value (17), predicted from height and age (1,7) or predicted from vital capacity measurements done on a simple spirometer (10). If the determination of RV, in and of itself, is not of paramount interest, as in body composition analysis by hydrostatic weighing, the use of a predicted value for RV may suffice (22). However, since the accuracy of the predicted RV value may affect the validity of the subsequent calculations for body density through hydrostatic weighing, the use of appropriate prediction equations for the specific population or individual being studied is important.

The purpose of this research was to derive and compare regression equations for predicting RV in overweight men and women compared with those in normal weight men and women. Accordingly, distinct population-specific equations were derived for predicting RV when sex, age, weight, and height were independent linear variables. Age, height, and weight were significant predictor variables for RV in the overweight men and women, whereas only age and height contributed significantly to the prediction of RV in the normal weight men and women. Although it may seem logical that as body size increases with added adiposity RV may be affected, several investigators have found that weight did not contribute significantly to the predictability of RV(Table 3). On the other hand, Chinn and Allen(6) found that weight and adiposity, as measured by skinfold thickness, contributed significantly to the prediction of RV in men, while Grimby and Söderholm (12) also found that weight was a contributing factor for men. In women, weight(18) and adiposity (13) have been found to be necessary components in RV prediction equations.

The reason that weight or some other indicator of obesity does not consistently appear as a predicting variable for RV may not be completely elucidated at this time, but one possible explanation is the makeup of the sample populations studied. No researchers have investigated RV in the overweight population by itself. The mean body weights for the groups of men and women where RV prediction equations were previously derived may or may not be representative of the average for the entire population. Thus, the relative proportions of lean, normal weight, and overweight individuals in a given sample studied may affect the significance level weight plays as a contributing factor for RV prediction in that given mixed population. Hall et al. (13) came the closest to studying an overweight population when they studied British women. Although the women in their study were not grouped according to weight or degree of adiposity, the mean percent body fat for the entire sample studied was 35.4 ± 0.6%, which is considered overweight. This value is not far from the 39.4 ± 0.5% body fat of our overweight group of women, although our women were much heavier than those of Hall et al. (84.3 ± 1.5 kg and 63.0 kg respectively). Regardless, Hall's team did find that percent body fat as well as body mass index (BMI, wt(kg)/ht(m2)) were important for predicting RV.

Further support for the notion that the relative proportion of lean, normal weight, and overweight individuals in a sample population affects regression equations derived for predicting RV, or more specifically, affects the magnitude of significance body weight plays in predicting RV, comes from our own data. As shown previously, when our sample population was divided into normal weight and overweight groups, body weight was a significant predictor for RV in the overweight but not in the normal weight men and women(Table 2). Nonetheless, when we combined the data from the overweight groups with the normal weight groups in our study, as have all previous investigators, body weight just barely became a significant predictor for RV (P = 0.046). However, any generalized prediction equation coming from this mixed sample would be skewed toward the overweight population, in that 185 out of the 311 subjects (59%) were classified as overweight. Furthermore, the average body fat content for this mixed sample became 30.3 ± 0.6%, which is considered overweight. Moreover, the correlation coefficient for the prediction equation for this combined sample population was 0.63 with a SEE of 0.421, both of which would contribute to a less accurate prediction of RV than any of the equations we derived for the separate normal weight and overweight populations (Table 2).

With this assumption, we made comparisons among the measured RV values, the predicted RV values that were derived from the body-type specific equations, and the RV values generated from the mixed sample of normal weight and overweight men and women (generalized equation). In the normal weight subjects, the measured value for RV was not significantly different from the predicted values derived from either the body-type specific equations or the generalized equation. However, in the overweight population, the necessity of using a body-type specific equation including body weight as a factor became more evident. The measured RV value in the overweight subjects was 1.579± 0.035, which was not different from the value of 1.553 ± 0.022 derived from the body-type specific equation. On the other hand, when the generalized equation was applied to the overweight subjects, a value of 1.705± 0.021 was derived for RV, which was significantly (P < 0.000) higher than that obtained through either direct measurement or from the body-type specific equation.

To reveal the effect this error in RV prediction accuracy would have in subsequent percent body fat calculations, the measured and predicted RV values for the overweight sample were placed into the percent body fat formulas where every other variable in the formulas was held constant. The difference in percent body fat where RV was measured versus predicted by the generalized equation was about 0.7%, which was much higher than the difference of only 0.1% for the body-type specific predictions. This difference in calculated percent body fat may not seem physiologically significant, but depending upon the degree of overweight, it could mean a few to several pounds of body fat to the individual.

To investigate further the confounding effects of body weight on predicting RV in a mixed population of normal weight and overweight individuals, we combined the data from our normal weight subjects with a random sample of overweight subjects to make a proportion that would reflect the U.S. adult population (33% overweight). The prediction equation subsequently derived did not contain body weight as a predictor variable (P = 0.103). Hence, the data clearly show that the magnitude of significance that body weight plays as a predictor variable for RV depends upon the relative proportion of overweight individuals included in the sample population being studied. All these data show that although a single generalized prediction equation can be derived for the entire population, such an equation is less accurate than one derived specifically for either the normal weight or overweight population.

It should also be noted that the SEEs for the regression equations derived in this paper are similar to those reported earlier for normal weight adults and that the multiple correlation coefficients reported here for predicting RV are generally higher than those reported earlier for normal weight men and women (Table 3). This infers that using these new RV prediction equations for normal weight adults would not be any less accurate than using the previously derived equations and that the prediction equations for the overweight provide the same degree of accuracy as those for normal weight men and women. In fact, when we used the large sample Z test to compare the independent correlation coefficient for our regression equation with those of other investigators, we found that our equation for normal weight men and women was significantly better than that of Boren et al.(3) as well as being better than that of Paoletti et al.(18).

To test the hypothesis that the body-type specific RV prediction equations from this study can more accurately predict RV than the equations from other researchers, data from our cross-validation groups were entered into the prediction equations produced from our main study sample as well as into all of the equations listed in Table 3. The measured RV values were then compared with the predicted RV values derived from all the equations. The measured RV for overweight women was significantly different from the predicted RV value derived from all of the other equations except for our body-type specific equation. The measured RV value for normal weight women was significantly different from all the predicted values except that of Grimby and Söderholm (12) and the body-type specific predicted value. For overweight men, the measured RV was significantly different from all the predicted RV values except that of Goldman and Becklake (11) and our body-type specific prediction. With the normal weight men, the body-type specific equations, as well as those of Boren (3) and Grimby and Söderholm(12), predicted the measured RV accurately, whereas the other equations did not. Thus, in every single case, the body-type specific equations predicted a RV value that was similar to the measured RV, whereas no other set of equations from earlier researchers could consistently predict a RV value similar to that which was measured. Needless to say, the regression equations for RV in the overweight population presented in this paper should be used in place of any previously used equation derived from the general population.

A paradox seems to arise when a predicted value for RV needs to be included in the calculations for determination of body composition through hydrostatic weighing. In other words, how does the technician know which RV prediction equation to use for hydrostatic weighing calculations when body composition of the individual is not yet known? Visual inspection of the client will usually reveal whether the individual is normal weight or overweight. However, in situations where this determination cannot easily be made, we suggest using body mass index (BMI). When we regressed percent body fat on BMI for our sample population, we obtained a correlation coefficient of 0.80 (P< 0.000) for both men and women. Using their respective regression equations, the criteria for RV prediction in the overweight (men, 25% fat; women, 30% fat) corresponded to BMI values of 29.0 for men and 24.1 for women. Thus, the RV prediction equations for the overweight should be used for men with a BMI over 29 and for women with a BMI over 24. This guidance would apply for all individuals except those with a high BMI because of increased muscularity rather than increased body fat. Under these conditions, visual inspection of the individual along with questioning about exercise routines would assist the technician in making the proper choice of RV prediction equations.

Using this advice for selecting the proper RV prediction equation, one might question whether a cutoff point of a 24 BMI for women would really classify a woman as overweight. It must be remembered that the 24 BMI cutoff for women in this data set corresponds to a body fat content of >30%, which is generally accepted as obese. Furthermore, one must realize that the use of BMI for classification of obesity or overweight is confusing itself and subject to debate. For example, in reports from the National Institutes of Health (NIH) over a dozen different terms are used to classify the same degree of overweight (4,15). However, according to all the major sources categorizing overweight, the classification of a BMI 24 falls into the overweight range. The 1983 BMI tables and nomograms used in NIH consensus and reports set the desirable BMI for men at 22.7 and for women at 22.4. The Health Professionals Guide to the understanding and treatment of obesity sets the cutoff between the acceptable range and overweight range for women at a BMI of 23.5 and for men at a BMI of 24.5 (8). The health care professional's desk reference, Guidance for Treatment of Adult Obesity(19), states that a BMI of 23 or above is associated with a higher risk of hypertension; a BMI of 22 or above is associated with a higher risk for cardiovascular disease; and a BMI of 20 or above is associated with a higher risk for type II diabetes. Moreover, the Nurses Health Study data have shown that the relative risk of death for women from all causes increased by 20% as BMI rose from 19 to 21.9(16). Hence, according to the data on health risk and weight, a BMI above 19 would be indicative of too much weight relevant to morbidity and mortality in women.

In spite of this minor concern over selection of the proper equation, the RV prediction equations presented in this paper can be used for almost all healthy adults since these equations were derived from a sample with ages ranging from 18 to 71 yr and a body fat content ranging from 5.1 to 52.0%.

Application. It must be remembered that prediction equations are not absolute, but only estimates of the true RV which may vary considerably under certain circumstances. Thus, care should be taken in the selection of an assumed predicted value. While this will not influence the relative values for body density or percent body fat, it may greatly affect the absolute values. Under research conditions where absolute accuracy is necessary, it is imperative to measure the RV. Under conditions where a predicted RV value is acceptable, separate prediction equations should be used for overweight versus normal weight individuals to assure the best predicted value.


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