Additional features and graphs in the new npde library for R
Emmanuelle Comets (1), Thi Huyen Tram Nguyen (1), France Mentré (1)
(1) INSERM, UMR 738, Paris, France; Univ Paris Diderot, Sorbonne Paris Cité, Paris, France
Objectives: (1) to present new features of the npde library 2.1 for the computation and diagnostic of normalised prediction discrepancies [1-3]; (2) to propose a new method to re-scale the npd/npde maintaining the shape of the profile of the observations.
Methods: The normalised prediction discrepancy (npd) for observation yij is obtained by computing the prediction discrepancy (pd) as the quantile of yij within its predictive distribution, and transforming the pd using the inverse normal function. Normalised prediction distribution errors (npde) are obtained using a similar approach but after decorrelation of both the observed and simulated values, and are needed for statistical tests. npde were recently extended to handle BQL data using imputation methods .
Under the null hypothesis of model adequacy, both npd and npde should follow a normal distribution. Visual assessment of the fit is usually performed via scatterplots of npd/npde versus time or model predictions, which are akin to residual plots and should exhibit no trend. Prediction intervals using model simulations can be added to highlight model misspecification . Version 2.1 of the npde library includes these new features.
Here, we propose additional graphs obtained by transforming the npd/npde using the mean and standard deviation of the simulated observations at each time point (or within each bin). This preserves the shape and variability of the profile.
Results: We illustrate the new features and graphs on two simulated examples, a PD study of viral load data (COPHAR3-ANRS 134 trial)  and a PK example based on the theophylline data . We show examples of handling various levels of BQL data. In unbalanced designs, transformed npd/npde (tnpd/tnpde) using a reference profile provide a similar pattern to VPC, without the need to stratify the data according to design or covariate, and can therefore be used in conjunction with npd/npde plots.
Conclusion: npd/npde are widely used to assess nonlinear mixed effect models, and show good statistical properties . They handle design and covariate heterogeneity naturally. This is particularly valuable in unbalanced designs, and distinguish these metrics from VPC and their many flavors (pcVPC ,...). Transformed npd/npde, which help visualise the shape and variability of the process being modelled, provide an alternative to npd/npde in the scatterplots versus time or predictions, and will be included in the next version of the library.
Acknowledgments: The research leading to these results has received support from the Innovative Medicines Initiative Joint Undertaking under grant agreement n° 115156. This work was part of the DDMoRe project but does not necessarily represent the view of all DDMoRe partners.
 Mentré F and S Escolano S. Prediction discrepancies for the evaluation of nonlinear mixed-effects models. J Pharmacokinet Biopharm, 2006, 33:345-67.
 Brendel K, Comets E, Laffont C, Laveille C, Mentré F. Metrics for external model evaluation with an application to the population pharmacokinetics of gliclazide. Pharm Res, 2006; 23:2036-49.
 Comets E, Brendel K, Mentré F. Computing normalised prediction distribution errors to evaluate nonlinear mixed-effect models: The npde add-on package for R. Comput Meth Prog Biomed, 2008; 90:154-66.
 Nguyen THT, Comets E, Mentré F. Extension of NPDE for evaluation of nonlinear mixed effect models in presence of data below the quantification limit with applications to HIV dynamic model. J Pharmacokinet Pharmacodyn, 2012; 39: 499-518.
 Comets E, Brendel K, Mentré F. Model evaluation in nonlinear mixed effect models, with applications to pharmacokinetics. J-SFdS, 2010; 1:106-28.
 Brendel K, Comets E, Laffont C, Mentré F. Evaluation of different tests based on observations for external model evaluation of population analyses. J Pharmacokinet Pharmacodyn, 2010; 37:49-65.
 Bergstrand M, Hooker AC, Wallin JE, Karlsson MO. Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS J, 2011; 13:143-51.