The Dangers of Estimating V˙O2max Using Linear, Nonexercise Prediction Models

PURPOSE: To compare the accuracy and goodness-of-fit of two competing models (linear versus allometric) when estimating V˙O2max (ml.kg.min) using non-exercise prediction models.

METHODS: The two competing models were fitted to the V˙O2max (ml.kg.min) data taken from two previously published studies. Study 1 (the Allied Dunbar National Fitness Survey, ADNFS), recruited 1732 randomly selected healthy participants, aged 16 years and over, from thirty English parliamentary constituencies. Estimates of V˙O2max were obtained using a progressive incremental test on a motorized treadmill. In Study 2 (3), maximal oxygen uptake was measured directly during a fatigue limited treadmill test in older men (n = 152) and women (n = 146) aged 55 to 86 years.

RESULTS: In both studies, the quality-of-fit associated with estimating V˙O2max (ml.kg.min) was superior using allometric rather than linear (additive) models based on all criteria (R, maximum log-likelihood and AIC). Results suggest that linear models will systematically over-estimate V˙O2max for participants in their 20's and under-estimate V˙O2max for participants in their 60's and older. The residuals saved from the linear models were neither normally distributed, nor independent of the predicted values nor age. This will probably explain the absence of a key quadratic age term in the linear models, crucially identified using allometric models. Not only does the curvilinear age decline within an exponential function follow a more realistic age decline (the right-hand side of a bell-shaped curve), but the allometric models identified either a stature-to-body-mass ratio (study 1) or a fat-free-mass-to-body-mass ratio (study 2), both associated with leanness when estimating V˙O2max.

CONCLUSIONS: Adopting allometric models will provide more accurate predictions of V˙O2max (ml.kg.min) using plausible, biologically sound and interpretable models.