Estimating digestible methionine requirements for laying hens using multivariate nonlinear mixed effect models

The purpose of this paper was to develop a unified framework for analyzing dose-response data in farm animals and apply it to meta-analysis of digestible Met requirement studies in laying hens. A database containing Met dose-response data from 23 trials originating from 15 peer-reviewed publications was constructed. A multivariate nonlinear mixed effects model was chosen as the statistical framework to model egg mass (g/d) and feed utilization (%) responses simultaneously. The framework accounted for responses being correlated in both the random effects and the errors, which provided a superior fit to data compared with modeling these separately. The framework was implemented in the NLMIXED procedure in SAS and could accommodate different dose-response functions per response. Three different dose-response functions-the linear broken line, quadratic plateau, and monomolecular functions-were used to identify the best-performing function. The statistical model, which used the quadratic plateau as the functional base for both responses, provided the best fit to data; hence, it was used for biological inference. Effects of secondary covariates of nutritional, genetic, and experimental design origin were investigated, and a systematic trend across studies was detected. The BW of the hens accounted for the majority of the between-study variability by allowing the asymptotic responses to be dependent on the BW. The final estimate of the Met requirement for maximizing egg mass was 356 (SE = 6.1) mg/d, whereas the corresponding Met requirement for maximizing feed utilization was significantly higher (P < 0.001), at 390 (SE = 11) mg/d. Thus, it can be concluded that the biological requirement for digestible Met is at least 356 mg/d. When multiple responses are collected in dose-response studies, these should preferably be analyzed simultaneously because the requirements are established within the same statistical model that accounts for correlation among the errors and among the random effects associated with distinct responses in the model.