Nevill Alan M, Wyon Matthew, Myers Jonathan, Harber Matthew P, Arena Ross, Myers Tony D, Kaminsky Leonard A
Faculty of Education, Health and Wellbeing, University of Wolverhampton, Walsall Campus, Gorway Road, Walsall, WS1 3BD, UK.
Division of Cardiology, VA Palo Alto Health Care System, Palo Alto, CA, USA.
Sports Med. 2025 Apr 13. doi: 10.1007/s40279-025-02208-3.
Using directly measured cardiorespiratory fitness (i.e. VO) in epidemiological/population studies is rare due to practicality issues. As such, predicting VO is an attractive alternative. Most equations that predict VO adopt additive rather than multiplicative models despite evidence that the latter provides superior fits and more biologically interpretable models. Furthermore, incorporating some but not all confounding variables may lead to inflated mass exponents (∝ M) as in the allometric cascade.
Hence, the purpose of the current study was to develop multiplicative, allometric models to predict VO incorporating most well-known, but some less well-known confounding variables (FVC, forced vital capacity; FEV, forced expiratory volume in 1 s) that might provide a more dimensionally valid model (∝ M) originally proposed by Astrand and Rodahl.
We adopted the following three-dimensional multiplicative allometric model for VO (l⋅min) = M·HT·WC·exp(a + b·age + c·age + d·%fat)·ε, (M, body mass; HT, height; WC, waist circumference; %fat, percentage body fat). Model comparisons (goodness-of-fit) between the allometric and equivalent additive models was assessed using the Akaike information criterion plus residual diagnostics. Note that the intercept term 'a' was allowed to vary for categorical fixed factors such as sex and physical inactivity.
Analyses revealed that significant predictors of VO were physical inactivity, M, WC, age, %fat, plus FVC, FEV. The body-mass exponent was k = 0.695 (M), approximately∝M. However, the calculated effect-sizes identified age and physical inactivity, not mass, as the strongest predictors of VO. The quality-of-fit of the allometric models were superior to equivalent additive models.
Results provide compelling evidence that multiplicative allometric models incorporating FVC and FEV are dimensionally and theoretically superior at predicting VO(l⋅min) compared with additive models. If FVC and FEV are unavailable, a satisfactory model was obtained simply by using HT as a surrogate.
由于实际操作问题，在流行病学/人群研究中直接测量心肺适能（即最大摄氧量）的情况很少见。因此，预测最大摄氧量是一种有吸引力的替代方法。尽管有证据表明乘法模型能提供更好的拟合效果和更具生物学解释性的模型，但大多数预测最大摄氧量的方程采用的是加法模型而非乘法模型。此外，像在异速生长级联中那样，纳入部分而非全部混杂变量可能会导致质量指数（∝M）膨胀。
因此，本研究的目的是开发乘法异速生长模型来预测最大摄氧量，纳入最知名但也有一些不太知名的混杂变量（用力肺活量（FVC）、第1秒用力呼气量（FEV）），这可能会提供一个比最初由阿strand和罗达尔提出的更具维度有效性的模型（∝M）。
我们采用以下三维乘法异速生长模型来预测最大摄氧量（升·分钟）=体重·身高·腰围·exp（a + b·年龄 + c·年龄 + d·体脂百分比）·ε，（体重，身高，腰围，体脂百分比）。使用赤池信息准则和残差诊断评估异速生长模型与等效加法模型之间的模型比较（拟合优度）。请注意，对于性别和身体活动不足等分类固定因素，截距项“a”允许变化。
分析表明，最大摄氧量的显著预测因素是身体活动不足、体重、腰围、年龄、体脂百分比，以及用力肺活量、第1秒用力呼气量。体重指数为k = 0.695（体重），近似于∝M。然而，计算出的效应量表明年龄和身体活动不足而非体重是最大摄氧量的最强预测因素。异速生长模型的拟合质量优于等效加法模型。
结果提供了令人信服的证据，即与加法模型相比，纳入用力肺活量和第1秒用力呼气量的乘法异速生长模型在预测最大摄氧量（升·分钟）方面在维度和理论上更具优势。如果无法获得用力肺活量和第1秒用力呼气量，仅使用身高作为替代就能得到一个令人满意的模型。
