Comparing two software programs for fitting nonlinear, one- and two-compartment age-dependent digestion models: a Monte Carlo analysis

Abstract Using compartmental modeling of digesta kinetics is a valuable tool to ruminant nutritionists assessing and quantifying the site and extent of digestion. To increase the value of one- (G2) and two-compartment (G2G1), age-dependent models, we characterized the repeatability and agreement of 2 software systems for fitting these models. We constructed replicated datasets of fecal marker concentrations over time by sampling 81 synthetic concentration profiles representing 81 animal and diet combinations. Datasets contained fecal marker concentrations for 15 nominal times after dosing (0, 9, 12, 15, 18, 24, 32, 40, 48, 60, 72, 84, 96, 108, and 120 h). Dataset were constructed by adding random errors to samples from hypothetical true marker concentration profiles. Errors included sampling time and marker concentration measurement. The resulting fecal marker concentration datasets were fit to G2 and G2G1 models with programs written for 2 software systems (R and SAS). The resulting model parameters, K0, λ or λ1, K2, and τ, were used to calculate particle passage rate, gastrointestinal DM fill, fecal DM output, gastrointestinal mean retention time, and rumen retention time. We evaluated the repeatability of each software and the agreement between software packages. When fitting the 8,100 datasets to the G2 model, all converged for both software. When fitting the same datasets to a G2G1 model, however, 369 did not converge for SAS and 1 did not converge for R. Non-convergence can be a significant problem when an experiment has minimal experimental units. The R software produced more repeatable model parameter estimates than SAS, but the ratios of repeatability to mean values were generally less than 10%. Bias and SD of differences between software packages were small, however G2G1 models produced smaller bias and SD of differences than the G2 models. Bias and SD for derived digestion parameters between models and software packages were also small. Again the G2G1 model had smaller biases and SD of differences than the G2 model. Repeatability for derived digestion parameters were better with R than with SAS, but the mean differences were small. The G2G1 model produced more repeatable results than the G2 model, but differences between software were small for the G2G1 model.