RPEM: Randomized Monte Carlo parametric expectation maximization algorithm

Area of Science:

• Pharmacometrics
• Computational Statistics
• Numerical Analysis

Background:

• Accurate population parameter estimation is crucial in pharmacometrics for understanding drug behavior.
• Existing methods like Importance Sampling (IMP), Stochastic Approximation Expectation Maximization (SAEM), and Quasi-Random Parametric Expectation Maximization (QRPEM) have limitations.
• The Metropolis-Hastings algorithm provides a robust framework for sampling complex probability distributions.

Purpose of the Study:

• To introduce a novel Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm, termed Randomized Parametric Expectation Maximization (RPEM).
• To evaluate the performance of RPEM against established methods (IMP, SAEM, QRPEM) in terms of speed and accuracy.
• To demonstrate the utility of RPEM for parameter estimation in pharmacokinetic models.

Main Methods:

• Developed RPEM by integrating discrete and continuous variable sampling using the Metropolis-Hastings algorithm, inspired by quantum Monte Carlo methods.
• Compared RPEM with NONMEM's IMP, Monolix's SAEM, and Certara's QRPEM.
• Utilized a realistic two-compartment voriconazole model with ordinary differential equations and simulated data for evaluation.

Main Results:

• RPEM demonstrated comparable speed and accuracy to IMP, SAEM, and QRPEM in reconstructing population parameters.
• The algorithm proved effective for both normal and log-normal parameter distributions.
• RPEM successfully estimated parameters for the complex voriconazole pharmacokinetic model.

Conclusions:

• RPEM is a fast, accurate, and high-performance algorithm for Monte Carlo Parametric Expectation Maximization.
• The novel RPEM algorithm offers a viable alternative to existing methods for population pharmacokinetic analysis.
• RPEM's foundation in quantum Monte Carlo principles suggests potential for broader applications in complex modeling scenarios.