Whenever the predictions within a bin differ largely due to different values of other independent variables (e.g., dose, covariates), the diagnosis may be hampered or misleading. In many cases, this can be done by comparing different percentiles of the observed data to percentiles of simulated data. Ideally, a VPC will diagnose both the fixed and random effects in a mixed-effects model. This is thought to make the interpretation of VPCs less subjective. The size of the confidence intervals acts as a reference to better judge what is likely to be a true deviation between observations and model predictions. By calculating the percentiles of interest for each of the simulated replicates of the original dataset design, a nonparametric confidence interval can be generated for the predicted percentiles ( 5). The fact that VPCs are created by simulations of a large number of replicates of the original dataset design can be utilized to improve the interpretability of the VPC. Different widths of the prediction intervals can be assessed depending on the objective and the sample size of the original data (e.g., 5th to 95th percentileвЂ‰в‡’вЂ‰90% interpercentile range). The interpercentile range between the outer percentiles of all the simulated data is often referred to as a prediction interval. Typically, the median and 2.5th and 97.5th percentiles are presented. The percentiles are calculated either for each unique value of the independent ( x-axis) variable or for a bin across the independent variable. Percentiles of the simulated data are compared to the corresponding percentiles of the observed data. A VPC is based on multiple simulations with the model of interest and the design structure of the observed data (i.e., dosing, timing, and number of samples). The principle of the VPC is to assess graphically whether simulations from a model of interest are able to reproduce both the central trend and variability in the observed data, when plotted versus an independent variable (typically time). The popularity of VPCs can be attributed to two main advantages of the approach: the principle behind the diagnostic is simple and easily communicated to both modelers and other modeling stakeholders, and by the retention of the original time-course profile and the y-axis units, the VPC graphs are illustrated on a relevant and easily appreciated scale which can be powerful in guiding the modeler to the origin of a potential model misspecification. Since the mid-90s, simulation-based diagnostic principles have grown in popularity ( 3), and an especially popular diagnostic tool is the so-called Visual Predictive Check (VPC 4вЂ“ 6). There are many kinds of diagnostic tools applicable to mixed-effects models ( 2). In order to generate reliable conclusions and predictions, good diagnostic tools to evaluate the predictive performance of the models are vital ( 2). Population pharmacokinetic (PK) and pharmacodynamic (PD) models are used increasingly in pharmaceutical research ( 1). The pcVPC was in contrast to traditional VPCs shown to be readily applicable to data from studies with a priori and/or a posteriori dose adaptations. The investigated examples demonstrate that pcVPCs have an enhanced ability to diagnose model misspecification especially with respect to random effects models in a range of situations. The principal benefit with the pcVPC has been explored by application to both simulated and real examples of PK and PKPD models.

In a pcVPC, the variability coming from binning across independent variables is removed by normalizing the observed and simulated dependent variable based on the typical population prediction for the median independent variable in the bin. The prediction-corrected VPC (pcVPC) offers a solution to these problems while retaining the visual interpretation of the traditional VPC. VPCs can also be misleading if applied to data following adaptive designs such as dose adjustments. However, the diagnostic value of a VPC can be hampered by binning across a large variability in dose and/or influential covariates. In many cases, this can be done by comparing different percentiles of the observed data to percentiles of simulated data, generally grouped together within bins of an independent variable. The Visual Predictive Check (VPC) is a popular tool for evaluating the performance of population PK and PKPD models. Informative diagnostic tools are vital to the development of useful mixed-effects models.

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