Statistical identifiability and convergence evaluation for nonlinear pharmacokinetic models with particle swarm optimization

Abstract

The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiablity of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model.

Integrating Dynamic Positron Emission Tomography and Conventional Pharmacokinetic Studies to Delineate Plasma and Tumor Pharmacokinetics of FAU, a Prodrug Bioactivated by Thymidylate Synthase

“…Mathematical identifiability, also referred to as structural or deterministic identifiability, is the identifiability of model parameters from noise‐free data. Statistical identifiability, also termed numerical identifiability, is the identifiability of parameters estimated from noise data . The mathematical identifiability mostly is not a challenge in PK modeling because a PK model is developed by the use of the ordinary differential equations that have solid theoretical and mathematical foundations.…”

“…The major challenge in identifiability of PK modeling predominantly results from the statistical identifiability because of the paucity of samples and high residual variability. Several methods have been published to diagnose the statistical identifiability of PK modeling . In these methods, numerous runs with different initial values are performed, and then convergence to different solutions can indicate a lack of identifiability .…”

“…Statistical identifiability, also termed numerical identifiability, is the identifiability of parameters estimated from noise data. [14][15][16] The mathematical identifiability mostly is not a challenge in PK modeling because a PK model is developed by the use of the ordinary differential equations that have solid theoretical and mathematical foundations. The major challenge in identifiability of PK modeling predominantly results from the statistical identifiability because of the paucity of samples and high residual variability.…”

Extended two-stage adaptive designs with three target responses for phase II clinical trials

“…PSO has also successfully used for estimation in statistical problems. For example, Kim and Li (2011, 2014) applied PSO to estimate parameters in nonlinear mixed-effects pharmacokinetics models, and Kim et al (2012) employed PSO to estimate efficacy of different lung cancer screening methods. In each of the above problems, we observed, as many others had, the flexibility of PSO and how it can be readily modified to solve an optimization problem at hand.…”

A Swarm Optimization approach for clinical knowledge mining

“…Several mathematical, evolutionary and swarm intelligence optimization approaches have been proposed in the literature. Some of these approaches used in medical informatics and clinical diagnosis are the following: Numerical analysis [9], Linear programming [10], NonLinear analysis [11], genetic algorithm (GA) [12], Immune-GA [13], Simulated Annealing [14], Tabu Search [15], Ant Colony Optimization [16], Artificial Bee Colony (ABC) [17] Algorithm, Particle Swarm Optimization (PSO) [18,19] .…”