A sample size computation method for non-linear mixed effects models with applications to pharmacokinetics models

We propose a simple method to compute sample size for an arbitrary test hypothesis in population pharmacokinetics (PK) studies analysed with non-linear mixed effects models. Sample size procedures exist for linear mixed effects model, and have been recently extended by Rochon using the generalized estimating equation of Liang and Zeger. Thus, full model based inference in sample size computation has been possible. The method we propose extends the approach using a first-order linearization of the non-linear mixed effects model and use of the Wald chi(2) test statistic. The proposed method is general. It allows an arbitrary non-linear model as well as arbitrary distribution of random effects characterizing both inter- and intra-individual variability of the mixed effects model. To illustrate possible uses of the method we present tables of minimum sample sizes, in particular, with an illustration of the effect of sampling design on sample size. We demonstrate how (D-)optimal or frequent sampling requires fewer subjects in comparison to a sparse sampling design. We also present results from Monte Carlo simulations showing that the computed sample size can produce the desired power. The proposed method greatly reduces computing times compared with simulation-based methods of estimating sample sizes for population PK studies.