Ruan Yue, Bluck Les C J, Smith James, Mander Adrian, Singh Priya, Venables Michelle
University of Cambridge Metabolic Research Laboratories, Wellcome Trust-MRC Institute of Metabolic Science and Department of Paediatrics, University of Cambridge, Cambridge, CB2 0QQ, UK.
MRC Elsie Widdowson Laboratory (formerly MRC Human Nutrition Research), Fulbourn Road, Cambridge, CB1 9NL, UK.
Rapid Commun Mass Spectrom. 2018 Jan 15;32(1):23-32. doi: 10.1002/rcm.8013.
The doubly labelled water (DLW) method is the reference method for the estimation of free-living total energy expenditure (TEE). In this method, where both H and O are employed, different approaches have been adopted to deal with the non-conformity observed regarding the distribution space for the labels being non-coincident with total body water. However, the method adopted can have a significant effect on the estimated TEE.
We proposed a Bayesian reasoning approach to modify an assumed prior distribution for the space ratio using experimental data to derive the TEE. A Bayesian hierarchical approach was also investigated. The dataset was obtained from 59 adults (37 women) who underwent a DLW experiment during which the H and O enrichments were measured using isotope ratio mass spectrometry (IRMS).
TEE was estimated at 9925 (9106-11236) [median and interquartile range], 9646 (9167-10540), and 9,638 (9220-10340) kJ·day for women and at 13961 (12851-15347), 13353 (12651-15088) and 13211 (12653-14238) kJ·day for men, using normalized non-Bayesian, independent Bayesian and hierarchical Bayesian approaches, respectively. A comparison of hierarchical Bayesian with normalized non-Bayesian methods indicated a marked difference in behaviour between genders. The median difference was -287 kJ·day for women, and -750 kJ·day for men. In men there is an appreciable compression of the TEE distribution obtained from the hierarchical model compared with the normalized non-Bayesian methods (range of TEE 11234-15431 kJ·day vs 10786-18221 kJ·day ). An analogous, yet smaller, compression is seen in women (7081-12287 kJ·day vs 6989-13775 kJ·day ).
The Bayesian analysis is an appealing method to estimate TEE during DLW experiments. The principal advantages over those obtained using the classical least-squares method is the generation of potentially more useful estimates of TEE, and improved handling of outliers and missing data scenarios, particularly if a hierarchical model is used.
双标记水（DLW）法是估算自由生活状态下总能量消耗（TEE）的参考方法。在该方法中，同时使用了氢（H）和氧（O）两种标记物，针对标记物分布空间与总体水不一致的情况，采用了不同方法来处理。然而，所采用的方法可能会对估算的TEE产生显著影响。
我们提出了一种贝叶斯推理方法，利用实验数据修改空间比的假设先验分布以推导TEE。还研究了贝叶斯分层方法。数据集来自59名成年人（37名女性），他们接受了DLW实验，在此期间使用同位素比率质谱法（IRMS）测量了氢和氧的富集情况。
分别使用归一化非贝叶斯方法、独立贝叶斯方法和分层贝叶斯方法时，女性的TEE估算值分别为9925（9106 - 11236）[中位数和四分位间距]、9646（9167 - 10540）和9638（9220 - 10340）kJ·天，男性的TEE估算值分别为 13961（12851 - 15347）、13353（12651 - 15088）和13211（12653 - 14238）kJ·天。分层贝叶斯方法与归一化非贝叶斯方法的比较表明，不同性别在行为上存在显著差异。女性的中位数差异为 - 287 kJ·天，男性为 - 750 kJ·天。与归一化非贝叶斯方法相比，男性从分层模型获得的TEE分布有明显压缩（TEE范围为11234 - 15431 kJ·天 对比10786 - 18221 kJ·天）。女性也有类似但较小的压缩（7081 - 12287 kJ·天 对比6989 - 13775 kJ·天）。
贝叶斯分析是DLW实验中估算TEE的一种有吸引力的方法。与使用经典最小二乘法相比，其主要优点是可能生成更有用的TEE估算值，以及更好地处理异常值和缺失数据情况，特别是使用分层模型时。
