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Population kinetic modeling approaches, implemented as nonlinear mixed effects models, are attracting growing interest in many fields of biomedicine thanks to their value in estimating population features from sparsely sampled data. However, their application often entails approximations of the original model function, whose effect is difficult to gauge in general. We apply negative log-likelihood profiling to assess the effect of model approximation on the glucose-insulin Minimal Model, and compare nonlinear mixed-effects approximate methods to two-stage methods. Our preliminary findings suggest that nonlinear mixed effects models provide accurate parameter estimates, but also point out that the reliability of such estimates may be affected by large population variability and small sample size.