Evaluation of non-uniform weighting in non-linear regression for pharmacokinetic neuroreceptor modelling

Pharmacokinetic modelling of dynamic PET data has become an important tool to analyse in-vivo studies in humans and animals. Estimation of the model parameters often requires non-linear regression of an objective function such as weighted least squares. Since the noise properties of the data are not known exactly in practice, several weighting schemes have been proposed. The objective of this study was to evaluate the impact of commonly used weights on neuroreceptor quantification with the simplified reference tissue model (SRTM).

We compared the following weights: uniform, Poisson statistics-based ideal and noisy weights, iterative weighting, and a noise-free approximation of Poisson weights. Ten thousand time-activity curves (TACs) were simulated for several noise levels and the three neuroreceptor PET ligands C-(+)McN5652, C-DASB, and C-raclopride. Each TAC was fitted using weighted non-linear regression of the SRTM. We assessed bias and variation of the parameter estimates as well as quality of fit and parameter distributions.

Results differed substantially between ligands and between model parameters. Best parameter estimates were obtained with the noise-free approximation of Poisson weights. The often-used noisy Poisson weights performed worst for all ligands. Uniform weighting gave acceptable parameter estimates for most setups.

'Choice of weights' is important in pharmacokinetic neuroreceptor quantification with the SRTM. Weights estimated directly from noisy data should be avoided as they can severely degrade parameter estimation and the statistical power of a study. If the noise characteristic of the data is unknown, uniform weighting is recommended.