Propagation of population PK and PD information using a Bayesian approach: dealing with non-exchangeability

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Objectives: To implement a conservative prior that safeguards against population non-exchangeability of prior and data likelihood, in the framework of population pharmacokinetic / pharmacodynamic analysis, incorporating multi-level hierarchical modelling.

Methods: Three different exercises were performed: (i) We investigated the use of parametric priors in the multilevel hierarchical modelling framework. (ii) We assessed the average performance of the a multilevel hierarchical model compared to the standard mixed effect model, considering also some interesting extreme cases. (iii) We implemented an application with a small Proof of Principle (PoP) study, which demonstrates the propagation of information across PD studies using multilevel modeling.

Results: Fitting with the 4-stage model and informative parametric priors performed similarly with meta-analysis of the test datasets combined with datasets that the priors came from, demonstrating that parametric priors can be used alternatively to meta-analysis. Further, the 4-stage model gave posterior distributions which have larger uncertainty but at the same time are unbiased, compared to the 3-stage model, and therefore implements a more conservative prior in a formal way, which is appropriate when the prior and the test populations are not exchangeable. For the application with PoP study, the statistical power of detecting the difference in potency of two drugs, when inter-study variability was present, was much greater when an extra stage in the hierarchical model to account for it, was used.

Conclusions: by applying the prior one hierarchical level above the level of the parameters of interest, we implemented a more conservative prior, compared to applying the prior directly on the parameters of interest. The approach is equivalent to Bayesian individualization, offers a safeguard against bias from the prior and also avoids the danger of the data being overwhelmed by a strong prior.