Fast and Flexible Differential Equation Model Fitting with Application to Pharmacometrics

Differential equations are widely used to analyze and simulate the dynamics of complex systems in the physical, biological and social sciences. Inferences with such models are challenging due to both statistical and computational complexity. Stan is a widely used, open-source, probabilistic programming language and Bayesian inference engine. We propose to extend Stan by incorporating solvers for ordinary differential equations and differential algebraic equations. We expect to achieve a substantial speedup over the existing state-of-the-art, due to Stans automatic differentiation library and efficient estimation algorithms. We will also extend Stan to deal with events arising from external inputs such as multiple dosing in pharmacology. We will evaluate the tools produced using pharmacometric data with a range of sophisticated statistical and mathematical models in common use. The result will be an even more flexible Bayesian statistics platform that supports analysis of heterogeneous collections of data conditioned on models of great stochastic and deterministic complexity and quantitative prior knowledge. This work will be commercialized by incorporation of the enhanced Stan platform within Metrums Metworx cloud computing platform. The result will be a more efficient and flexible computational environment for data analysis and simulation relevant to a range of scientific and engineering applications.