Improving reference equations for cardiorespiratory fitness using multiplicative allometric rather than additive linear models: Data from the Fitness Registry and the Importance of Exercise National Database Registry

Abstract

New improved reference equations for cardiorespiratory fitness have recently been published, using Data from the Fitness Registry and the Importance of Exercise National Database (FRIEND Registry). The new linear equation for VO2max (ml.kg−1.min−1) was additive, derived using multiple-linear regression. An alternative multiplicative allometric model has also been published recently, thought to improve further the quality of fit. The purpose of the current study was to compare the accuracy and quality/goodness-of-fit of the linear, additive model with the multiplicative allometric model using the FRIEND database. The results identified that the allometric model out performs the linear model based on all model-comparison criteria. The allometric model demonstrates; 1) greater explained variance (R2 = 0.645; R = 0.803) vs. (R2 = 0.62; R = 0.79), 2) residuals that were more normally distributed, 3) residuals that yielded less evidence of curvature, 4) superior goodness-of-fit statistics i.e., greater maximum log-likelihood (MLL) and smaller Akaike Information Criterion (AIC) statistics, 5) less systematic bias together with smaller unexplained standard error of estimates. The Bland and Altman plots also confirmed little or no evidence of curvature with the allometric model, but systematic curvature (lack-of-fit) in the linear model. The multiplicative allometric model to predict VO2max was; VO2max (ml.kg−1.min−1) = M-0.854 · H1.44 · exp. (0.424–0.346 · (sex) -0.011.age), where M = body mass and H = height (R2 = 0.645; R = 0.803) and sex is entered as a [0,1] indicator variable (male = 0 and female = 1). Another new insight obtained from the allometric model (providing construct validity) is that the height-to-body-mass ratio is similar to inverse body mass index or the lean body mass index, both associated with leanness when predicting VO2max. In conclusion adopting allometric models will provide more accurate predictions of VO2max (ml.kg−1.min−1) using more plausible, biologically sound and interpretable models.