Shuhua Hu

This study evaluates an automatic differentiation (AD)-assisted first-order conditional estimation (FOCE) algorithm integrated into the FOCE Extended Least Squares (FOCE ELS) framework within Phoenix NLME 8.6. AD is a method commonly used in machine learning to provide exact (to machine precision) values for the partial derivatives of a function. There are two modes of AD, forward mode and reverse mode [1]. In the case of nonlinear regression, the objective function of interest is the negative twice the log-likelihood (−2LL), expressed as a function of the model parameter values. Previously released versions of NLME use finite difference (FD), a numerical approximation for the partial derivative. To examine the impact of AD compared to FD on execution speed, we constructed 72 models ranging from one to three compartments. All models included Michaelis-Menten elimination, first-order absorption, and combined additive and proportional residual error models. The models were selected to provide a range of complexity and numerical identifiability, from simple, well-identified models to complex, poorly identifiable ones. We demonstrate that AD improves performance in both the estimation and covariance steps. The AD method had no significant impact on estimation robustness or the success of the covariance step.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis–Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi‐Random Parametric Expectation Maximization (QRPEM) for a realistic two‐compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log‐normal cases.

A distributed delay approach was proposed in this paper to model delayed outcomes in pharmacokinetics and pharmacodynamics studies. This approach was shown to be general enough to incorporate a wide array of pharmacokinetic and pharmacodynamic models as special cases including transit compartment models, effect compartment models, typical absorption models (either zero-order or first-order absorption), and a number of atypical (or irregular) absorption models (e.g., parallel first-order, mixed first-order and zero-order, inverse Gaussian, and Weibull absorption models). Real-life examples were given to demonstrate how to implement distributed delays in Phoenix^® NLME™ 8.0, and to numerically show the advantages of the distributed delay approach over the traditional methods.