Combining MCMC with 'sequential' PKPD modelling

We introduce a method for preventing unwanted feedback in Bayesian PKPD link models. We illustrate the approach using a simple example on a single individual, and subsequently demonstrate the ease with which it can be applied to more general settings. In particular, we look at the three 'sequential' population PKPD models examined by Zhang et al. (J Pharmacokinet Pharmacodyn 30:387-404, 2003; J Pharmacokinet Pharmacodyn 30:405-416, 2003), and provide graphical representations of these models to elucidate their structure. An important feature of our approach is that it allows uncertainty regarding the PK parameters to propagate through to inferences on the PD parameters. This is in contrast to standard two-stage approaches whereby 'plug-in' point estimates for either the population or the individual-specific PK parameters are required.