Department of Epidemiology and Biostatistics, Drexel University, Philadelphia, Pennsylvania, USA.
J Appl Physiol (1985). 2013 Jul 15;115(2):251-9. doi: 10.1152/japplphysiol.00295.2013. Epub 2013 May 2.
Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in energy expenditure (EE). Study objective is to apply quantile regression (QR) to predict EE and determine quantile-dependent variation in covariate effects in nonobese and obese children. First, QR models will be developed to predict minute-by-minute awake EE at different quantile levels based on heart rate (HR) and physical activity (PA) accelerometry counts, and child characteristics of age, sex, weight, and height. Second, the QR models will be used to evaluate the covariate effects of weight, PA, and HR across the conditional EE distribution. QR and ordinary least squares (OLS) regressions are estimated in 109 children, aged 5-18 yr. QR modeling of EE outperformed OLS regression for both nonobese and obese populations. Average prediction errors for QR compared with OLS were not only smaller at the median τ = 0.5 (18.6 vs. 21.4%), but also substantially smaller at the tails of the distribution (10.2 vs. 39.2% at τ = 0.1 and 8.7 vs. 19.8% at τ = 0.9). Covariate effects of weight, PA, and HR on EE for the nonobese and obese children differed across quantiles (P < 0.05). The associations (linear and quadratic) between PA and HR with EE were stronger for the obese than nonobese population (P < 0.05). In conclusion, QR provided more accurate predictions of EE compared with conventional OLS regression, especially at the tails of the distribution, and revealed substantially different covariate effects of weight, PA, and HR on EE in nonobese and obese children.
高级数学模型有可能捕捉到导致能量消耗（EE）的复杂代谢和生理过程。研究目的是应用分位数回归（QR）预测 EE，并确定非肥胖和肥胖儿童中协变量效应的分位数依赖性变化。首先，将基于心率（HR）和体力活动（PA）加速度计计数以及儿童年龄、性别、体重和身高特征，开发 QR 模型以预测不同分位数水平下的每分钟清醒 EE。其次，QR 模型将用于评估 EE 条件分布中体重、PA 和 HR 的协变量效应。QR 和普通最小二乘法（OLS）回归在 109 名年龄为 5-18 岁的儿童中进行了估计。对于非肥胖和肥胖人群，EE 的 QR 建模均优于 OLS 回归。与 OLS 相比，QR 的平均预测误差不仅在中位数τ=0.5（18.6%对 21.4%）处较小，而且在分布的尾部也明显较小（τ=0.1 时为 10.2%对 39.2%，τ=0.9 时为 8.7%对 19.8%）。体重、PA 和 HR 对非肥胖和肥胖儿童 EE 的协变量效应在分位数上有所不同（P<0.05）。PA 和 HR 与 EE 之间的关联（线性和二次）在肥胖人群中比非肥胖人群更强（P<0.05）。总之，QR 提供了比传统 OLS 回归更准确的 EE 预测，尤其是在分布的尾部，并且揭示了非肥胖和肥胖儿童中体重、PA 和 HR 对 EE 的协变量效应有很大的不同。
