Inter-study variability in population pharmacokinetic meta-analysis: when and how to estimate it?

Population pharmacokinetic analysis is being increasingly applied to individual data collected in different studies and pooled in a single database. However, individual pharmacokinetic parameters may change randomly from one study to another. In this article, we show by simulation that neglecting inter-study variability (ISV) does not introduce any bias for the fixed parameters or for the residual variability but may result in an overestimation of inter-individual (IIV) variability, depending on the magnitude of the ISV. Two random study-effect (RSE) estimation methods were investigated: (i) estimation, in a single step, of the three-nested random effects (inter-study, inter-individual and residual variability); (ii) estimation of residual variability and a mixture of ISV and IIV in the first step, then separation of ISV from IIV in the second. The one-stage RSE model performed well for population parameter assessment, whereas, the two-stage model yielded good estimates of IIV only with a rich sampling design. Finally, irrespective of the method used, ISV estimates were valid only when a large number of studies was pooled. The analysis of one real data set illustrated the use of an ISV model. It showed that the fixed parameter estimates were not modified, whether an RSE model was used or not, probably because of the homogeneity of the experimental designs of the studies, and suggest no study-effect in this example.