A comparison of performance between parametric and nonparametric estimation for nonlinear mixed-effects models
Shijun Wang, Andrew C. Hooker, Mats O. Karlsson
Dept. of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objective: Nonparametric (NP) methods estimating discrete parameter distributions offer an alternative to parametric methods in pharmacometric analyses. This study aims to evaluate the performance of the NP estimation method in NONMEM 7 in comparison with the first-order conditional estimation or Laplacian method with or without interaction (FOCEI)1.
Method: The FOCEI and NP methods were compared for 23 PK and PD models previously developed based on real data. For the NP method both the default number of support point, which is equal to the number of individuals of the data set, and an increased number using the extended grid method2 were tested. Model fits based on NP and FOCEI were compared based on objective function values (OFVs) and prospective OFVs using 5-fold cross-validation. Additionally, reference distributions of the difference between the NP and FOCEI OFVs were created using stochastic simulation and estimation (SSE), where the original parametric models were used to generate 100 simulated data sets and then the difference between the OFV of the FOCEI and NP methods was calculated for each simulated data set.
Results: The estimated model fit to data was better for the NP compared to the FOCEI method as judged by lower OFVs. The range of difference in OFV was 7-1441. However, when the (178- -4606) SSE reference distributions of OFV differences indicated that a decrease in OFV for NP methods during fitting was larger than expected by chance at p<0.05 in 2 of 23 models. When the OFV was evaluated prospectively through cross-validation, lower prospective OFVs for the FOCEI method (range of difference 5-5850). Use of the extended grid method did not change the relative performance of the two methods.
Conclusion: The better fit to data of the NP method can be expected given that more parameters are estimated. The better predictive performance for new data of the FOCEI method in all examples can be understood from the local nature of discrete NP distributions.
 Savic et al. Eur J Pharm Sci 37:27-35 (2009)  Savic and Karlsson AAPS J 11:615-27 (2009)