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The uncertainty associated with parameter estimations is essential for population model building, evaluation, and simulation. Summarized by the standard error (SE), its estimation is sometimes questionable. Herein, we evaluate SEs provided by different non linear mixed-effect estimation methods associated with their estimation performances. Methods based on maximum likelihood (FO and FOCE in NONMEMTM, nlme in SplusTM, and SAEM in MONOLIX) and Bayesian theory (WinBUGS) were evaluated on datasets obtained by simulations of a one-compartment PK model using 9 different designs. Bootstrap techniques were applied to FO, FOCE, and nlme. We compared SE estimations, parameter estimations, convergence, and computation time. Regarding SE estimations, methods provided concordant results for fixed effects. On random effects, SAEM and WinBUGS, tended respectively to under or over-estimate them. With sparse data, FO provided biased estimations of SE and discordant results between bootstrapped and original datasets. Regarding parameter estimations, FO showed a systematic bias on fixed and random effects. WinBUGS provided biased estimations, but only with sparse data. SAEM and WinBUGS converged systematically while FOCE failed in half of the cases. Applying bootstrap with FOCE yielded CPU times too large for routine application and bootstrap with nlme resulted in frequent crashes. In conclusion, FO provided bias on parameter estimations and on SE estimations of random effects. Methods like FOCE provided unbiased results but convergence was the biggest issue. Bootstrap did not improve SEs for FOCE methods, except when confidence interval of random effects is needed. WinBUGS gave consistent results but required long computation times. SAEM was in-between, showing few under-estimated SE but unbiased parameter estimations.

To be able to estimate accurately parameters entering a non-linear mixed effects model taking into account that one or more subpopulations of patients can exist rather than assuming that the entire population is best described by unimodal distributions for the random effects, we proposed a methodology based on the likelihood approximation using the Gauss–Hermite quadrature. The idea is to combine the estimation of the model parameters and the detection of homogeneous subgroups of patients in a given population using a Gaussian mixture for the distribution of the random effects. As the accuracy of the likelihood approximation is likely to govern the quality of the estimation of the different parameters entering the nonlinear mixed effects model, we based this approximation on the use of an adjustable Gauss– Hermite quadrature. Moreover, to complete this methodology, we propose a strategy allowing the detection and explanation of heterogeneity based on the Kullback–Leibler test, which was used to estimate the number of components in the Gaussian mixture. In order to evaluate the capability of the method to take into account heterogeneity, this strategy was performed in a PK/PD analysis using the database and the structural model selected in a previous analysis. In this analysis, non-responders were found out using NONMEM [Beal and Sheiner. NONMEM Users Guides. NONMEM Project Group, University of California, San Francisio, 1992] in a population of diabetic patients treated with a once-a-day new formulation of an antidiabetic drug. The authors looked for a subpopulation of patients for whom the therapeutic effect would vanish. In this paper, we looked for subpopulations of patients exhibiting specificities with respect to different parameters entering the description of the effect. The results obtained with our approach are compared in terms of parameter estimation and heterogeneity detection to those obtained in the previous analysis.