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

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.