A Branch and Bound method for the exact parameter identification of the PK/PD model for anesthetic drugs

TL;DR

This paper introduces a branch-and-bound global optimization method for exact parameter identification in PK/PD models of anesthetic drugs, ensuring minimal prediction error and handling non-convex problems.

Contribution

It develops a novel branch-and-bound algorithm that guarantees finding the exact parameters for nonlinear PK/PD models, improving over existing methods.

Findings

Successfully identified exact parameters in all simulation cases.

Demonstrated robustness despite non-convexity of the problem.

Applicable to a broader class of nonlinear regression problems.

Abstract

We address the problem of parameter identification for the standard pharmacokinetic/pharmacodynamic (PK/PD) model for anesthetic drugs. Our main contribution is the development of a global optimization method that guarantees finding the parameters that minimize the one-step ahead prediction error. The method is based on a branch-and-bound algorithm, that can be applied to solve a more general class of nonlinear regression problems. We present some simulation results, based on a dataset of twelve patients. In these simulations, we are always able to identify the exact parameters, despite the non-convexity of the overall identification problem.