(701f) Estimating Reaction Model Uncertainty with Bayesian Markov Chain Monte Carlo

The use of kinetic models to predict reaction performance is becoming an integral element of pharmaceutical process development.  These models, built on fundamental mechanistic understanding and laboratory data, must be characterized by how well they can describe experimental observations.  This task of quantifying uncertainty for reaction models is complicated by model non-linearity and experimental error.  Because experimental error may not follow a conventional distribution, the validity of common statistical assumptions behind least-squares regression and normal error distributions should be reexamined when fitting models to data.

This paper reports a comparison of different techniques to compare parameter regression and confidence intervals for pharmaceutically relevant chemical reaction models.  Simulated experiments were created by adding two types of noise (normally distributed and experimentally measured) collected using two analytical techniques (HPLC versus inline FTIR) to four types of kinetic models (linearized, exponential, coupled ODE and DAE).  The best fit parameter values and confidence intervals were then calculated according to a multivariate t-distribution or two different Bayesian Markov-Chain Monte Carlo algorithms: one estimating error assuming a normal error distribution and a new, more adaptable non-parametric likelihood function.  The uncertainty estimates were evaluated based on their ability to correctly regress the model parameter’s probability distribution in scenarios common to pharmaceutical reaction engineering.  The findings indicate that while multivariate t-distributions are sufficient for simpler non-linear models with normal error distributions, only BMCMC accurately estimates parameter ranges when errors are non-normal or when the model system is complex.