Non linear mixed effects analysis in PET PK-receptor occupancy studies

The characterisation of a pharmacokinetic-receptor occupancy (PK-RO) relationship derived from a PET study is typically modelled in a conventional non-linear least squares (NLLS) framework. In the present work, we explore the application of a non-linear mixed effects approach (NLME) and compare this with NLLS estimation (using both naive pooled data and two-stage approaches) in the context of a direct PK-RO relationship described by an Emax model, using simulated data sets. Target and reference tissue time-activity curves were simulated using a two-tissue compartmental model and an arterial plasma input function for a typical PET study (12 subjects in 3 dose groups with 3 scans each). A range of different PET scenarios was considered to evaluate the impact of between-subject variability and reference region availability. The PET outcome measures derived from the simulations were then used to estimate the parameters of the PK-RO model. The performance of the two approaches was compared in terms of parameters estimates (square mean error SME, root mean square error RMSE) and prediction of the exposure-occupancy relationship. In general, both NLME and NLLS estimation methods provided unbiassed and precise population estimates for the Emax model parameters, although a slight bias was observed for the individual-NLLS method due to a few outliers. The increased value of NLME over NLLS was most notable in the estimation of the between-subject variability (BSV), especially in the case of a more complex PK-RO model when no reference region was available (maximum SME and RMSE values related to BSV of EC₅₀ of 27.6% and 86.5% from NLME versus 264.6% and 689.5% from NLLS). Overall, the NLME approach provided a more robust estimation and produced less-biassed estimates of the population means and variances than either the NLLS approach for the simulations considered.