Parameter Estimation of Population Pharmacokinetic Models with Stochastic Differential Equations: Implementation of an Estimation Algorithm

Abstract

Population pharmacokinetic (PPK) models play a pivotal role in quantitative pharmacology study, which are classically analyzed by nonlinear mixed-effects models based on ordinary differential equations. This paper describes the implementation of SDEs in population pharmacokinetic models, where parameters are estimated by a novel approximation of likelihood function. This approximation is constructed by combining the MCMC method used in nonlinear mixed-effects modeling with the extended Kalman filter used in SDE models. The analysis and simulation results show that the performance of the approximation of likelihood function for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for the analysis of population pharmacokinetic data.

On Bayesian asymptotics in stochastic differential equations with random effects

“…The multidimensional situation makes appropriate choices of priors even more difficult. In the context of SDE-based pharmacokinetic models Yan et al (2014), following de la Cruz-Mesía and Marshall (2006), proposed independent normal priors for the components of µ, given by µ i ∼ N A i , B 2 i , and an inverse Wishart prior for Σ with scale matrix Σ 0 and degrees of freedom d + 1. However, because of the difficulties of eliciting information, they assume non-informative priors for the hyperparameters.…”

“…Informative priors can be elicited if historical data, that is, data associated with previous studies, are available. Then, following Yan et al (2014), using the aforementioned non-informative priors, one can first obtain the posterior distributions of µ and Σ, given only the historical data. These posterior distributions based on historical data can then be used as informative prior distributions for Bayesian analysis of the current data.…”

“…Instead, the Metropolis-Hastings (MH) method can be used to sample from the posterior. In the context of pharmacokinetic models, Yan et al (2014) estimate the parameters using a combination of extended Kalman filter and random walk MH algorithm; see also Donnet and Samson (2013) for a comprehensive review on various techniques of classical and Bayesian estimation of SDE's for pharmacokinetic/pharmacodynamic models.…”

“…For our purpose we assume T i = T for each i. Here we remark that Donnet and Samson (2013) discuss population SDE models with measurement errors; see also Overgaard et al (2005), Donnet and Samson (2008), Yan et al (2014), Leander et al (2015); for the i-th individual such models are of the same form as (1.3) and (1.4), but specifics depending upon i, and with θ replaced with φ i , where {φ 1 , . .…”

Exact Gradients Improve Parameter Estimation in Nonlinear Mixed Effects Models with Stochastic Dynamics

“…However, the sparsity and irregular sampling of PK/PD data has made it difficult to directly apply these parameter estimation methods. Nevertheless, some attempts to develop methods for parameter estimation in NLME models with stochastic dynamics have been successful, using for example (i) Bayesian inference (9,10), (ii) expectation maximization (EM) methods (11)(12)(13), and (iii) by expanding the traditional gradient-based estimation methods using Kalman filters (14,15). These methods have been used for several PK/PD applications (16)(17)(18)(19).…”