Background

Using directly measured cardiorespiratory fitness (i.e. VO_2max) in epidemiological/population studies is rare due to practicality issues. As such, predicting VO_2max is an attractive alternative. Most equations that predict VO_2max 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^0.75) as in the allometric cascade.

Objective

Hence, the purpose of the current study was to develop multiplicative, allometric models to predict VO_2max incorporating most well-known, but some less well-known confounding variables (FVC, forced vital capacity; FEV₁, forced expiratory volume in 1 s) that might provide a more dimensionally valid model (∝ M^2/3) originally proposed by Astrand and Rodahl.

Methods

We adopted the following three-dimensional multiplicative allometric model for VO_2max (l⋅min⁻¹) = M^k1·HT^k2·WC^k3·exp(a + b·age + c·age² + 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.

Results

Analyses revealed that significant predictors of VO_2max were physical inactivity, M, WC, age², %fat, plus FVC, FEV₁. The body-mass exponent was k₁ = 0.695 (M^0.695), approximately∝M^2/3. However, the calculated effect-sizes identified age² and physical inactivity, not mass, as the strongest predictors of VO_2max. The quality-of-fit of the allometric models were superior to equivalent additive models.

Conclusions

Results provide compelling evidence that multiplicative allometric models incorporating FVC and FEV₁ are dimensionally and theoretically superior at predicting VO_2max(l⋅min⁻¹) compared with additive models. If FVC and FEV₁ are unavailable, a satisfactory model was obtained simply by using HT as a surrogate.

中文翻译：

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使用肺功能和三维 （3D） 异速生长法预测 VO2max 为异速生长级联 （M0.75） 提供了新的见解

背景

由于实用性问题，使用直接测量的心肺健康（即 VO_2max）在流行病学/人群研究中很少见。因此，预测 VO_2max 是一个有吸引力的选择。大多数预测 VO_2max 的方程都采用加法模型而不是乘法模型，尽管有证据表明后者提供了更好的拟合和更可生物学解释的模型。此外，合并一些但不是全部混杂变量可能会导致质量指数膨胀 （∝ M^0.75），就像异速生长级联一样。

目的

因此，本研究的目的是开发乘法、异速生长模型来预测 VO_2max，其中包含最知名但一些鲜为人知的混杂变量（FVC，用力肺活量;FEV_1,1 秒内用力呼气量），这可能会提供最初由 Astrand 和 Rodahl 提出的维度更有效的模型 （∝ M^2/3）。

方法

我们采用以下三维乘法异速生长模型，VO_2max （l⋅min⁻¹） = M^k1·HT^k2·WC^k3·exp（a + b·age + c·age² + d·%fat）·ε， （M，体重;HT，身高;WC，腰围;%脂肪，体脂百分比）。使用 Akaike 信息标准加残差诊断评估异速生长模型和等效加法模型之间的模型比较（拟合优度）。请注意，允许截距项“a”因性别和缺乏身体活动等分类固定因素而变化。

结果

分析显示，VO_2max 的显着预测因素是缺乏体力活动、M、WC、年龄 ²、脂肪百分比，加上 FVC、FEV₁。体重指数为 k₁ = 0.695 （M^0.695），大约 ∝M^2/3。然而，计算出的效应大小确定 ² 岁和缺乏身体活动，而不是体重，是 VO_2max 的最强预测因素。异速生长模型的拟合质量优于等效加性模型。

结论

结果提供了令人信服的证据，表明与加法模型相比，结合 FVC 和 FEV₁ 的乘法异速生长模型在预测 VO_2max（l⋅min⁻¹） 方面在维度和理论上更胜一筹。如果 FVC 和 FEV₁ 不可用，则只需使用 HT 作为替代即可获得令人满意的模型。