Nonlinear Mixed Effects to Improve Glucose Minimal Model Parameter Estimation: A Simulation Study in Intensive and Sparse Sampling

Abstract

Intravenous glucose tolerance test (IVGTT) minimal model parameters are commonly estimated by weighted least squares (WLSs) on each subject data. Sometimes, with sparse data, individual parameters cannot be satisfactorily obtained. In such cases, a population approach could be preferable. These methods allow borrowing information across all subjects simultaneously, quantifying population features directly, and subsequently, deriving individual parameter estimates. In this paper, we assessed different estimation methods on simulated datasets. Besides the standard WLS approach, we applied iterative procedures (iterative two-stage (ITS) and global two-stage (GTS) methods) as well as nonlinear mixed-effects models (NLMEMs), where the likelihood is based on model linearization: first-order (FO), FO conditional estimation (FOCE), and Laplace (LAP) approximations. The synthetic dataset, initially very rich, was progressively reduced (by 50% and 75%) in order to assess the robustness of the results in sparsely sampled situations. Our results show that, even with intensive sampling, population approaches provide more reliable parameter estimates. Moreover, these estimates are remarkably more robust when the data become scarce. ITS and GTS encounter critical problems when single subjects have very poor sampling schedules, whereas the NLMEM (excluding FO) methods are more versatile and able to cope with such situations. FOCE appears as the most satisfactory approach.