Nonlinear Mixed-Effects Models for PET Data

Objective: The current state-of-the-art for compartment modeling of dynamic PET data can be described as a two-stage approach. In Stage 1, individual estimates of kinetic parameters are obtained by fitting models using standard techniques, such as nonlinear least squares, to each individual's data one subject at a time. Population-level effects, such as the difference between diagnostic groups, are analyzed in Stage 2 using standard statistical methods by treating the individual estimates as if they were observed data. While this approach is generally valid, it is possible to increase efficiency and precision of the analysis, allow more complex models to be fitted, and also to permit parameter-specific investigation by fitting data across subjects simultaneously. We explore the application of nonlinear mixed-effects (NLME) models for estimation and inference in this setting. Methods: In the NLME framework, subjects are modeled simultaneously through the inclusion of random effects of subjects for each kinetic parameter; meanwhile, population parameters are estimated directly in a joint model. Results: Simulation results indicate that NLME outperforms the two-stage approach in estimating group-level effects and also has improved power to detect differences across groups. We applied our NLME approach to clinical PET data and found effects not detected by the two-stage approach. Conclusion: The proposed NLME approach is more accurate and correspondingly more powerful than the two-stage approach in compartment modeling of PET data. Significance: The NLME method can broaden the methodological scope of PET modeling because of its efficiency and stability.