Modeling the influence of body size onV˙o2 peak: effects of model choice and body composition

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Abstract
This study examined the bivariate relationship between peak oxygen uptake (V˙o2 peak; l/min) and body size in adult men (n = 1,314, age 17–66 yr), using both “simple” and “full” iterative nonlinear allometric models. The simple model was described byV˙o2 peak =Mb (or FFMb) exp(c SR-PA) exp(a +d age) ε (whereM is body mass in kg; FFM is fat-free mass in kg; SR-PA is self-reported physical activity; ε is a multiplicative error term; and exp indicates natural antilogarithms). The full model was described byV˙o2 peak =Mb (or FFMb) exp(c SR-PA) exp(a +d age) +e (ε), wheree is a permittedY-intercept term. TheM exponent obtained from simple allometry was 0.65 [95% confidence interval (CI), 0.59–0.71], suggestive of a curvilinear relationship constrained to pass through the origin. This “zeroY-intercept” assumption was examined via the full allometric model, which revealed anM exponent of 1.00 (95% CI, 0.7–1.31), together with a positiveY-intercept term (e) of 1.13 (95% CI, 0.54–1.73). The FFM exponents were not significantly different from unity in either the simple or full allometric models. It appears that the curvilinearity of the simple allometric model (using totalM) is fictitious and is due to the inappropriate forcing of the regression line through the origin. Utilizing FFM as the body-size variable revealed a linear relationship between body size andV˙o2 peak, irrespective of model choice. We conclude that the population mass exponent forV˙o2 peak is close to unity.