Investigations of the weighted residuals in NONMEM 7
Joakim Nyberg(1), Robert J. Bauer(2), Andrew C. Hooker(1)
(1): Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden, (2): Icon Development Solutions, Ellicott City, Maryland, USA
Objectives: Improving the calculations of the weighted residuals has proven to be of high importance; especially if the model is highly nonlinear in the random effects [1,2]. Various new and published methods for calculating the weighted residuals have been implemented in NONMEM 7 [3]. The aim of this project is to investigate these new methods.
Methods: A sigmoidal Emax-model (gamma=4.5) that showed the importance of using CWRES versus WRES was used to investigate the different residuals [1]. Emax and EC50 both had between subject variability (BSV) corresponding to ~71% CV. The study design was rich; 200 individuals with 25 observations each.
Five different scenarios were investigated with the true and a misspecified model (gamma=1): 1) Additive residual unexplained variability (RUV), 2) proportional RUV, 3) exponential RUV, 4) exponential BSV on the proportional RUV, 5) Between occasion variability on Emax with an additive RUV.
The residuals investigated were: NWRES (First order (FO) residuals without interaction), WRESI (FO residuals with interaction), CWRES (FO conditional residuals without interaction), CWRESI (FO conditional residuals with interaction), ECWRES (Monte Carlo calculated weighted residuals without interaction), EWRES (Monte Carlo calculated weighted residuals with interaction) and the NPDE (Normalised Prediction Distribution Errors). The simulation based residuals were calculated with the default number of samples (300) but in some cases a more intense sampling was also investigated (3000 samples). Interaction was always used in the estimation line, however MAXEVAL=0 or EONLY=1 was used to disable any population parameter estimation. All the residuals were calculated for 100 simulated data sets with the true and misspecified model and hypothesis tests for mean 0, variance 1 and normality were calculated.
Results: The CWRES and NPDE seem to outperform the other residual diagnostics. Furthermore the CWRES was, in general, better than the NPDE when the default number of samples was used. When more samples were used, either NPDE or CWRES could be better in different situations. When simulation from the model is not possible NPDE cannot be used. The other simulation based residuals (ECWRES, EWRES) didn't perform as well as the CWRES and NPDE. CWRESI didn't seem to be better than CWRES or NPDE even when the there was interaction in the model. As expected the NWRES and WRESI were not performing well in any of the investigated cases.
References:
[1] Hooker AC, Staatz CE, Karlsson MO. Conditional weighted residuals (CWRES): a model diagnostic for the FOCE method. Pharmaceutical research 2007; 24: 2187-97.
[2] Comets E, Brendel K, Mentré F. Computing normalized prediction distribution errors to evaluate nonlinear mixed effects models: the npde add-on package for R. Computer Methods and Programs in Biometrics 2008; 90:154-166.
[3] NONMEM users guide. Introduction to NONMEM 7. Icon Development Solutions (2009)
