Tekwe Carmen D, Zoh Roger S, Bazer Fuller W, Wu Guoyao, Carroll Raymond J
Department of Epidemiology and Biostatistics, Texas A&M University, College Station, Texas, U.S.A.
Department of Animal Science, Texas A&M University, College Station, Texas, U.S.A.
Biometrics. 2018 Mar;74(1):127-134. doi: 10.1111/biom.12706. Epub 2017 May 8.
Objective measures of oxygen consumption and carbon dioxide production by mammals are used to predict their energy expenditure. Since energy expenditure is not directly observable, it can be viewed as a latent construct with multiple physical indirect measures such as respiratory quotient, volumetric oxygen consumption, and volumetric carbon dioxide production. Metabolic rate is defined as the rate at which metabolism occurs in the body. Metabolic rate is also not directly observable. However, heat is produced as a result of metabolic processes within the body. Therefore, metabolic rate can be approximated by heat production plus some errors. While energy expenditure and metabolic rates are correlated, they are not equivalent. Energy expenditure results from physical function, while metabolism can occur within the body without the occurrence of physical activities. In this manuscript, we present a novel approach for studying the relationship between metabolic rate and indicators of energy expenditure. We do so by extending our previous work on MIMIC ME models to allow responses that are sparsely observed functional data, defining the sparse functional multiple indicators, multiple cause measurement error (FMIMIC ME) models. The mean curves in our proposed methodology are modeled using basis splines. A novel approach for estimating the variance of the classical measurement error based on functional principal components is presented. The model parameters are estimated using the EM algorithm and a discussion of the model's identifiability is provided. We show that the defined model is not a trivial extension of longitudinal or functional data methods, due to the presence of the latent construct. Results from its application to data collected on Zucker diabetic fatty rats are provided. Simulation results investigating the properties of our approach are also presented.
哺乳动物氧气消耗量和二氧化碳产生量的客观测量用于预测其能量消耗。由于能量消耗无法直接观察到,它可被视为一个潜在结构,具有多个物理间接测量指标,如呼吸商、体积氧消耗量和体积二氧化碳产生量。代谢率定义为体内新陈代谢发生的速率。代谢率也无法直接观察到。然而,热量是体内代谢过程产生的结果。因此,代谢率可以通过热量产生加上一些误差来近似估算。虽然能量消耗和代谢率相关,但它们并不等同。能量消耗源于身体功能,而新陈代谢可以在身体内发生而无需进行体力活动。在本手稿中,我们提出了一种研究代谢率与能量消耗指标之间关系的新方法。我们通过扩展我们之前关于MIMIC ME模型的工作来实现这一点,以允许对稀疏观察到的功能数据进行响应,定义稀疏功能多指标、多原因测量误差(FMIMIC ME)模型。我们提出的方法中的均值曲线使用基样条进行建模。提出了一种基于功能主成分估计经典测量误差方差的新方法。使用期望最大化(EM)算法估计模型参数,并对模型的可识别性进行了讨论。我们表明,由于存在潜在结构,所定义的模型不是纵向或功能数据方法的简单扩展。提供了将其应用于在Zucker糖尿病脂肪大鼠上收集的数据的结果。还给出了研究我们方法特性的模拟结果。