The application of a Bayesian approach to the analysis of a complex, mechanistically based model

The Bayesian approach has been suggested as a suitable method in the context of mechanistic pharmacokinetic-pharmacodynamic (PK-PD) modeling, as it allows for efficient use of both data and prior knowledge regarding the drug or disease state. However, to this day, published examples of its application to real PK-PD problems have been scarce. We present an example of a fully Bayesian re-analysis of a previously published mechanistic model describing the time course of circulating neutrophils in stroke patients and healthy individuals. While priors could be established for all population parameters in the model, not all variability terms were known with any degree of precision. A sensitivity analysis around the assigned priors used was performed by testing three different sets of prior values for the population variance terms for which no data were available in the literature: "informative", "semi-informative", and "noninformative", respectively. For all variability terms, inverse gamma distributions were used. It was possible to fit the model to the data using the "informative" priors. However, when the "semi-informative" and "noninformative" priors were used, it was impossible to accomplish convergence due to severe correlations between parameters. In addition, due to the complexity of the model, the process of defining priors and running the Markov chains was very time-consuming. We conclude that the present analysis represents a first example of the fully transparent application of Bayesian methods to a complex, mechanistic PK-PD problem with real data. The approach is time-consuming, but enables us to make use of all available information from data and scientific evidence. Thereby, it shows potential both for detection of data gaps and for more reliable predictions of various outcomes and "what if" scenarios.