A method for robust model order reduction in pharmacokinetics

We present a Bayesian automated method to reduce by lumping, a large system described by differential equations which takes into account parameter variability. Model reduction is a potentially useful tool to simplify large systems but suffers from lack of robustness over the model parameter values. With the present method we address this problem by incorporating a prior parameter distribution in the determination of the optimal lumping scheme in a Bayesian manner. Applications of this method may include PBPK models for the drug distribution and/or Systems Biology models for the drug action. The method builds on our previously published algorithm for lumping that works stepwise, reducing the system's dimension by one at each step and where each successive step is conditional to the previous ones. We applied the methodology to a PBPK model for barbiturates taken from the literature. An arbitrary variability of 20% CV was added to the nominal reported parameter values. The Bayesian method performed better than the method which ignored the parameter variability, producing a lumping scheme which, while not optimal for any parameter value, was optimal on average. On the other hand the simple, non-Bayesian method produced a lumping scheme which while optimal for the nominal parameter values, was very poor for most other values within the prior distribution. Further, we discuss the generality of a lumping strategy to reduce a model and we argue that this is more powerful than elimination of states, with the latter being almost a special case of lumping.