The dangers of predicting ratio standards using multiple regression: A case study using the ratio standard VO_2peak...

There are numerous examples in the literature where researchers use multiple-regression models to predict ratio standards despite known dangers associated with such methodologies. The solution, to use allometric models, also appears to have been ignored, for example, when predicting cardiorespiratory fitness, using the ratio standard VO_2max (ml·kg^-1·min^-1).

Cross-sectional.

This case-study compares a previously published multiple regression equation to predict VO_2peak (ml·kg^-1·min^-1) that adopted additive predictors of body mass index (kg·m^-2) and a 6-minute run/walk test, with an alternative multiplicative allometric model given by VO_2peak (l·min^-1) = M^k1 · HT^k2 · 6WRT^k3 · exp(a + b · age + c · age²) · ε, thought to provide a more interpretable model, as well as providing a superior quality-of-fit.

The strong association between VO_2peak (l·min^-1) and body mass also identified the presence of heteroscedasticity, a characteristic in data that can be resolved using allometry. The allometric model explained over 90 % of the variance (R² = 0.91) compared to less than 60 % (R² = 0.58) reported by the original study. The allometric model's results also appear more interpretable, with a positive mass exponent similar to that previously reported in the literature M^0.66 based on sound physiological grounds. The positive height exponent can also be explained given that taller children have greater lung function. Finally, the age quadratic identified that children's VO_2peak peaks during puberty.

This case study provides powerful evidence that allometric models are more interpretable and provide a superior fit compared with multiple regression models when predicting ratio standards. Note that a simple algebraic adjustment enables researchers to predict the ratio standard VO_2peak (ml·kg^-1·min^-1) without further analyses.