Improved diagnostic plots require improved statistical tools. Implementation in MONOLIX 4.0
Marc Lavielle, Hector Mesa
INRIA Saclay, France
Objectives: Model evaluation is a crucial part of model building. The modeler needs numerical and graphical tools for deciding if the proposed model adequately describes the underlying system. Because of the complexity of pharmacometrics models (mixed effects models, non linearities, covariates, residual errors, BLQ data,...), these tools must be used carefully to avoid misinterpretation due to a poor use. Several diagnostic tools (VPC, npde, weighted residuals,...) have been already developed and implemented in different softwares (Xpose, Monolix, ...). Our objective is to improve some of these existing tools and implement them in MONOLIX 4.0.
Methods: Visual Predictive Checks (VPC) compares the distribution of the observations with the distribution of simulated data by grouping the data into bins. We propose a method that automatically determines the optimal binning. The optimal limits of the bins are obtained by optimizing a modified least-squares criteria using a dynamic programming algorithm. The number of bins is selected using a model selection approach.
Because of possible shrinkage, we suggest replacing the Empirical Bayes Estimates (EBEs) with predicted individual parameters correctly simulated with their conditional distribution. An MCMC procedure is used for this simulation.
In presence of Below the Limit of Quantification (BLQ) data, we propose replacing these BLQ data by data correctly simulated with their conditional distribution. An acceptance-reject procedure is used for this simulation.
Results: We applied the proposed methodology to several real and simulated PK examples: i) when the data presents clusters of different sizes, the proposed binning algorithm perfectly detects the clusters and the resulting VPC is improved, ii) we show that inference on the population distribution should not be based on the EBEs but on simulated parameters which are not affected by any possible shrinkage, iii) we show that residuals computed by replacing the BLQ data with the LOQ present a positive bias. On the other hand, no bias is introduced when imputing the BLQ data with simulated data.
Conclusions: Even if the existing procedures generally used for producing diagnostic plots are satisfactory in standard situations, some improvements appear to be necessary in more difficult situations (sparse data, BLQ data,...). Computational statistics can provide different new valuable tools (simulation procedures, MCMC, optimal segmentation,...) to improve model evaluation.
References:
[1] Karlsson M. and Holford N. "A Tutorial on Visual Predictive Checks", PAGE Meeting, Marseille, 2008.
[2] Comets E., Brendel K. and Mentré M. "Model evaluation in nonlinear mixed effect models, with applications to pharmacokinetics", Jour. SFDS, vol 151, pp. 106-128, 2010.
[3] Hooker A., Karlsson M., Jonsson Niclas, Xpose 4, http://xpose.sourceforge.net
[4] Lavielle M. and the Monolix team "MONOLIX 3.2 User's Guide", http://software.monolix.org/, 2010.
