Application of Bayesian analysis to the doubly labelled water method for total energy expenditure in humans

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 ² H and ¹⁸ 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 ² H and ¹⁸ 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^-1 for women and at 13961 (12851-15347), 13353 (12651-15088) and 13211 (12653-14238) kJ·day^-1 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^-1 for women, and -750 kJ·day^-1 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^-1 vs 10786-18221 kJ·day^-1 ). An analogous, yet smaller, compression is seen in women (7081-12287 kJ·day^-1 vs 6989-13775 kJ·day^-1 ).

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.