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.

中文翻译：

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使用乘法异速生长而非加性线性模型改进心肺适能参考方程：来自健身登记处的数据和运动国家数据库登记的重要性。

最近发布了新的改进的心肺适能参考方程，使用来自健身登记处和运动重要性国家数据库 (FRIEND 登记处) 的数据。VO2max (ml.kg-1.min-1) 的新线性方程是可加的，使用多元线性回归得出。最近还发布了另一种乘法异速生长模型，认为可以进一步提高拟合质量。当前研究的目的是使用 FRIEND 数据库比较线性加性模型与乘法异速生长模型的准确性和质量/拟合优度。结果表明异速生长模型优于基于所有模型比较标准的线性模型。异速生长模型表明；1) 更大的解释方差（R2 = 0.645；R = 0.803）与（R2 = 0.62；R = 0.79），2) 更正态分布的残差，3) 产生较少曲率证据的残差，4) 优越的拟合优度统计，即更大的最大对数似然 (MLL) 和更小的赤池信息准则 (AIC) 统计，5)较少的系统偏差以及较小的无法解释的估计标准误差。Bland 和 Altman 图也证实了异速生长模型很少或没有曲率的证据，但线性模型中的系统曲率（缺乏拟合）。预测 VO2max 的乘法异速生长模型是；VO2max (ml.kg-1.min-1) = M-0.854 · H1.44 · exp。(0.424-0.346 · (sex) -0.011.age)，其中 M = 体重，H = 身高（R2 = 0.645；R = 0.803），性别作为 [0,1] 指示变量输入（男性 = 0 和女性 = 1）。从异速生长模型中获得的另一个新见解（提供结构有效性）是身高体重比类似于反向体重指数或瘦体重指数，两者在预测最大摄氧量时都与瘦身相关。总之，采用异速生长模型将使用更合理、生物学上合理和可解释的模型提供更准确的 VO2max (ml.kg-1.min-1) 预测。