Direct application of Bayes theorem for the combination of population pharmacokinetic analyses.
Dokoumetzidis, Aris and Leon Aarons
University of Manchester
We are providing a set of simple formulae that allow the combination of separately performed analyses of population pharmacokinetic (PK) studies, without any further computational effort. More specifically, given the point estimates and standard errors of two population PK analyses, the formulae provide the point estimates and standard errors of the combined analysis of the two. To derive the formulae we considered distributional assumptions applicable for the conjugate priors of the Bayesian problem of "unknown mean and variance". Namely, the joint distribution of mean PK parameters and inter-individual variability, was considered to be Normal-Inverse-Wishart (NIW), while the distribution of the variance of the residual error was considered to be Inverse-Gamma (IG). The presented formulae were derived from the ones that give the mean and variance for the NIW and IG distributions. In order to verify the validity of the approach, the formulae were applied in an example involving the results of fittings of two simulated datasets. These results were combined using the presented formulae and, also, in a separate analysis, the same datasets were pooled and re-analysed together. The results from the formulae and from the pooled analysis were compared and agreement was observed. The formulae presented, offer a very easy-to-use way of combining different analyses which requires no special software and can be done even with a calculator. Also, they provide a way of combing literature information for the purpose of building Bayesian priors to assist the analysis of future studies.