Application of Bayesian Analysis to the Doubly Labelled Water Method for Total Energy Expenditure in Humans

Rationale: 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 ²H and ¹⁸O 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. Methods: 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 ²H and ¹⁸O enrichments were measured using isotope ratio mass spectrometry (IRMS). Results: The 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). Conclusions: 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 total energy expenditure, and improved handling of outliers and missing data scenarios, particularly if a hierarchical model is used.