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

• Published in: NeuroImage (Orlando, Fla.) Vol. 76; pp. 155 - 166
• Main Authors: Berges, Alienor, Cunningham, Vincent J., Gunn, Roger N., Zamuner, Stefano
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.08.2013; Elsevier; Elsevier Limited
• Subjects: Algorithms; Biological and medical sciences; Brain - diagnostic imaging; Drug dosages; Economic models; Fundamental and applied biological sciences. Psychology; Humans; Mean square errors; Models, Neurological; Non-linear least squares approach; Non-linear mixed effects approach; Nonlinear Dynamics; PET study; Pharmacokinetics; Population; Positron-Emission Tomography; Radiopharmaceuticals - pharmacokinetics; Randomized Controlled Trials as Topic; Receptor occupancy; Studies; Vertebrates: nervous system and sense organs; Non-linear least squares approach; Non-linear mixed effects approach; Pharmacokinetics; Receptor occupancy; PET study; Biological receptor
• ISSN: 1053-8119; 1095-9572; 1095-9572
• DOI: 10.1016/j.neuroimage.2013.03.006

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. •We compared NLME and NLLS analyses with simulated PET data and a direct PK-RO model.•Analysis performance was based on bias and precision of the parameter estimates.•NLME produced less biassed estimates of the population means and variance than NLLS.