Nonlinear random effects mixture models: Maximum likelihood estimation via the EM algorithm

Abstract

Nonlinear random effects models with finite mixture structures are used to identify polymorphism in pharmacokinetic/pharmacodynamic phenotypes. An EM algorithm for maximum likelihood estimation approach is developed and uses sampling-based methods to implement the expectation step, that results in an analytically tractable maximization step. A benefit of the approach is that no model linearization is performed and the estimation precision can be arbitrarily controlled by the sampling process. A detailed simulation study illustrates the feasibility of the estimation approach and evaluates its performance. Applications of the proposed nonlinear random effects mixture model approach to other population pharmacokinetic/pharmacodynamic problems will be of interest for future investigation.

Performance and Robustness of the Monte Carlo Importance Sampling Algorithm Using Parallelized S-ADAPT for Basic and Complex Mechanistic Models

“…Gradient search algorithms such as the FOCE method can also be parallelized; however, to our knowledge the fraction of the computations of the FOCE method that can be parallelized (and therefore accelerated) is notably less than 99%. Among the parametric EM algorithms (1)(2)(3)(4)(5)(6)13,15,19,52,53), the MC-PEM method requires the fewest number of iterations (often 80-300, depending on the model complexity and data), since the MC-PEM algorithm spends most of its computation time on exploring potential parameter values for each subject per iteration. The MC-PEM algorithm typically uses 1,000-3,000 random samples per subject and iteration for the multidimensional integration to compute the conditional means and conditional var-cov matrices.…”

“…Expectation maximization (EM) algorithms are robust, as they use integration instead of gradient search methods to optimize (update) parameter estimates. State-of-the-art EM algorithms (1)(2)(3)(4)(5)(6) provide the additional advantage that they can approximate the true log-likelihood as precisely as needed by increasing the number of Monte Carlo samples used to approximate the integrals for calculation of the true loglikelihood. Importantly, algorithms, such as the FOCE method, which calculate the exact solution of a formula that approximates the log-likelihood can only improve the quality of the approximation by changing the algorithm (i.e., by using a more complex formula that approximates the loglikelihood more closely).…”

Comparison of nonparametric methods in nonlinear mixed effects models

“…Finite mixtures of (log-) normal distributions could also be an alternative to the parametric assumption (Lemenuel-Diot, Mallet & al. (2005), Wang, Schumitzky & al. (2007)).…”

Population pharmacokinetic/pharmacodynamic mixture models via maximum a posteriori estimation

“…For the maximum likelihood mixture model problem we have successfully used importance sampling to calculate the corresponding integrals in the EM algorithm (see Wang et al 2007). The same method can be applied here and was used in the examples presented below.…”

“…We have previously reported on a maximum likelihood approach using finite mixture models to identify subpopulations with distinct pharmacokinetic/pharmacodynamic properties (Wang et al , 2007). Wakefield and Walker (1997) and Rosner and Mueller (1997) have introduced Bayesian approaches to address this problem within a nonparametric mixture model framework.…”