Efficient Precision Dosing Under Estimated Uncertainties via Koopman Expectations of Bayesian Posteriors with Pumas

Abstract

Personalized precision dosing is about mathematically determining effective dosing strategies that optimize the probability of containing a patients outcome within a therapeutic window. However, the common Monte Carlo approach for generating patient statistics is computationally expensive because thousands of simulations need to be computed. In this manuscript we describe a new method which utilizes the Koopman operator to perform a direct computation of expected patient outcomes with respect to quantified uncertainties of Bayesian posteriors in a nonlinear mixed effect model framework. We detail how quantities such as the probability of being within the therapeutic window can be calculated with a choice of loss function on the Koopman expectation. We demonstrate a high performance parallelized implementation of this methodology in Pumas(R) and showcase the ability to accelerate the computation of these expectations by 50x-200x over Monte Carlo. We showcase how dosing can be optimized with respect to probabilistic statements respecting variable uncertainties using the Koopman operator. We end by demonstrating an end-to-end workflow, from estimating variable uncertainties via Bayesian estimation to optimizing a dose with respect to parametric uncertainty.