Predictive equations for skeletal muscle mass

Nuclear Medicine Department, Southern General Hospital, Glasgow G51 4TF, United Kingdom, E-mail: walter.watson{at}sgh.scot.nhs.uk

Dear Sir:

In their recent study, Lee et al (1) developed 2 equations for predicting skeletal muscle mass with use of magnetic resonance imaging in 244 nonobese and 80 obese subjects. In Equation 4 in their paper, the predictive variables were limb circumferences, skinfold thicknesses, height, sex, age, and race. In Equation 6 the predictive variables were body weight, height, sex, age, and race. These relations were first established in a group of nonobese adults (group A), the relations were then cross-validated in a second group of nonobese adults (group B), and, finally, equations developed for groups A and B together were tested in the obese group. Because of the careful cross-validation procedure, the paper is necessarily complicated, but there appear to be some discrepancies in the paper or possibly misinterpretations on my part.

In the Results, Equation 4 is shown to be successfully validated in obese subjects; however, it is stated in the Discussion that there was a significant difference between measured and predicted skeletal muscle in the obese group. In the development of Equation 6, a preliminary equation for group A was found to cross-validate successfully when applied to group B; however, it is stated in the Discussion that "a small bias was observed when the model developed in group A was cross-validated in the nonobese group B subjects."

Perhaps some of the confusion stems from the misapplication of the Bland-Altman (B-A) statistic, which is widely used in method comparisons (2). In this statistic, if Y and X are different estimates of the same entity (normally assessed by using different analytic techniques), then

where m is the gradient of the regression line and c is the intercept on the y axis. For methods that compare well, we expect m to be close to unity and c to be close to zero. In the B-A statistic, correlation is sought between the methods difference, X - Y, and the average of the 2 methods, (X + Y)/2. Any significant correlation indicates that the difference between the methods is not independent of the magnitude of the measurements, eg, in the present case, the methods might diverge with increasing muscle mass.

Unfortunately, Lee et al appear to have correlated the difference between measured and predicted skeletal muscle with the measured skeletal muscle values only (ie, not the average of the measured and predicted skeletal muscle values). Although this seems relatively trivial, it does significantly distort the B-A statistic (3). For instance, if we take Equation 1 above and subtract each side of the equation from X then

In their method comparisons, Lee et al essentially regressed (X - Y) against X. Therefore, the gradient of the B-A plot becomes (1 - m) and the intercept becomes the value obtained for the regression of Y on X, but with the opposite sign. Unless m = 1, there is a possibility that X - Y will correlate with X because the gradient will be nonzero. It can be seen in Figures 1 and 2 in Lee et al's article that the misapplied B-A plots correlate in 3 of 4 cases and the regression equations obtained for these plots are exactly as predicted above. The one plot that does not correlate (Figure 1B) has the value of m closest to unity, ie, m = 0.976. Given that the data in this study were painstakingly obtained, it is hoped that when the B-A statistic is correctly applied, these potentially spurious correlations will disappear.

REFERENCES

1. Lee RC, Wang Z, Heo M, Ross R, Janssen I, Heymsfield SB. Total-body skeletal muscle mass: development and cross-validation of anthropometric prediction models. Am J Clin Nutr 2000;72:796–803.
2. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;1: 307–10.
3. Gill JS, Zezulka AV, Beevers DG, Davies P. Relation between initial blood pressure and its fall with treatment. Lancet 1985;1:567–9.