Identification of the glucose minimal model by stochastic nonlinear-mixed effects methods

The nonlinear mixed effects models (NLMEM) are widespread modeling techniques in PKPD analysis and epidemiological studies because they can produce a description of not only the individual but also of the population features. Moreover, they are able to deal with individual data sparseness by borrowing the lack of information from the entire population. In this way, the NLMEM do not fail where instead other techniques, such as the traditional individual weighted least squares (WLS), sometimes do. The NLME approach relies on the maximization of a likelihood function that due to model parametric nonlinearity not always has an explicit solution. Various techniques have been proposed to solve this problem including the first order (FO) and the first order conditional (FOCE) estimation methods that approximate the likelihood function through a linearization; the expectation maximization algorithm (EM) that maximize the exact likelihood; the Bayesian estimation method where a third stage of variability, the distribution of the population parameters, is taken into account [1]. Recently, new estimation methods that rely on the EM algorithm have been implemented in the last release of the population software NONMEM [2]. These methods are: the iterative two stage (ITS), Monte Carlo importance sampling EM (IMP), Monte Carlo importance sampling EM assisted by Mode a Posteriori estimation (IMPMAP) and the Stochastic Approximation EM (SAEM). Moreover, another new method is available, the Markov Chain Monte Carlo Bayesian Analysis (BAYES), next to the more known FO and FOCE. With this article we want to complete the Denti et al [3] simulation study by evaluating the newest population methods applied on the IVGTT glucose minimal model.