Andrew C. Hooker

Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models.

Informative diagnostic tools are vital to the development of useful mixed-effects models. The Visual Predictive Check (VPC) is a popular tool for evaluating the performance of population PK and PKPD models. Ideally, a VPC will diagnose both the fixed and random effects in a mixed-effects model. 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. However, the diagnostic value of a VPC can be hampered by binning across a large variability in dose and/or influential covariates. VPCs can also be misleading if applied to data following adaptive designs such as dose adjustments. The prediction-corrected VPC (pcVPC) offers a solution to these problems while retaining the visual interpretation of the traditional VPC. 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 principal benefit with the pcVPC has been explored by application to both simulated and real examples of PK and PKPD models. 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 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.

Quantitative Magnetic Resonance Imaging Analysis of Neovasculature Volume in Carotid Atherosclerotic Plaque

Background—Neovasculature within atherosclerotic plaques is believed to be associated with infiltration of inflammatory cells and plaque destabilization. The aim of the present investigation was to determine whether the amount of neovasculature present in advanced carotid plaques can be noninvasively measured by dynamic, contrast-enhanced MRI. Methods and Results—A total of 20 consecutive patients scheduled for carotid endarterectomy were recruited to participate in an MRI study. Images were obtained at 15-second intervals, and a gadolinium contrast agent was injected coincident with the second of 10 images in the sequence. The resulting image intensity within the plaque was tracked over time, and a kinetic model was used to estimate the fractional blood volume. For validation, matched sections from subsequent endarterectomy were stained with ULEX and CD-31 antibody to highlight microvessels. Finally, all microvessels within the matched sections were identified, and their total area was computed as a fraction of the plaque area. Results were obtained from 16 participants, which showed fractional blood volumes ranging from 2% to 41%. These levels were significantly higher than the histological measurements of fractional vascular area. Nevertheless, the 2 measurements were highly correlated, with a correlation coefficient of 0.80 (P <0.001). Conclusions—Dynamic contrast-enhanced MRI provides an indication of the extent of neovasculature within carotid atherosclerotic plaque. MRI therefore provides a means for prospectively studying the link between neovasculature and plaque vulnerability.

Conditional Weighted Residuals (CWRES): A Model Diagnostic for the FOCE Method

PurposePopulation model analyses have shifted from using the first order (FO) to the first-order with conditional estimation (FOCE) approximation to the true model. However, the weighted residuals (WRES), a common diagnostic tool used to test for model misspecification, are calculated using the FO approximation. Utilizing WRES with the FOCE method may lead to misguided model development/evaluation. We present a new diagnostic tool, the conditional weighted residuals (CWRES), which are calculated based on the FOCE approximation.Materials and MethodsCWRES are calculated as the FOCE approximated difference between an individual’s data and the model prediction of that data divided by the root of the covariance of the data given the model.ResultsUsing real and simulated data the CWRES distributions behave as theoretically expected under the correct model. In contrast, in certain circumstances, the WRES have distributions that greatly deviate from the expected, falsely indicating model misspecification. CWRES/WRES comparisons can also indicate if the FOCE estimation method will improve the results of an FO model fit to data.ConclusionsUtilization of CWRES could improve model development and evaluation and give a more accurate picture of if and when a model is misspecified when using the FO or FOCE methods.

Modeling and Simulation Workbench for NONMEM: Tutorial on Pirana, PsN, and Xpose

Several software tools are available that facilitate the use of the NONMEM software and extend its functionality. This tutorial shows how three commonly used and freely available tools, Pirana, PsN, and Xpose, form a tightly integrated workbench for modeling and simulation with NONMEM. During the tutorial, we provide some guidance on what diagnostics we consider most useful in pharmacokinetic model development and how to construct them using these tools.

Robust population pharmacokinetic experiment design

The population approach to estimating mixed effects model parameters of interest in pharmacokinetic (PK) studies has been demonstrated to be an effective method in quantifying relevant population drug properties. The information available for each individual is usually sparse. As such, care should be taken to ensure that the information gained from each population experiment is as efficient as possible by designing the experiment optimally, according to some criterion. The classic approach to this problem is to design “good” sampling schedules, usually addressed by the D-optimality criterion. This method has the drawback of requiring exact advanced knowledge (expected values) of the parameters of interest. Often, this information is not available. Additionally, if such prior knowledge about the parameters is misspecified, this approach yields designs that may not be robust for parameter estimation. In order to incorporate uncertainty in the prior parameter specification, a number of criteria have been suggested. We focus on ED-optimality. This criterion leads to a difficult numerical problem, which is made tractable here by a novel approximation of the expectation integral usually solved by stochastic integration techniques. We present two case studies as evidence of the robustness of ED-optimal designs in the face of misspecified prior information. Estimates from replicate simulated population data show that such misspecified ED-optimal designs recover parameter estimates that are better than similarly misspecified D-optimal designs, and approach estimates gained from D-optimal designs where the parameters are correctly specified.

Methods and software tools for design evaluation in population pharmacokinetics–pharmacodynamics studies

Population pharmacokinetic (PK)-pharmacodynamic (PKPD) models are increasingly used in drug development and in academic research; hence, designing efficient studies is an important task. Following the first theoretical work on optimal design for nonlinear mixed-effects models, this research theme has grown rapidly. There are now several different software tools that implement an evaluation of the Fisher information matrix for population PKPD. We compared and evaluated the following five software tools: PFIM, PkStaMp, PopDes, PopED and POPT. The comparisons were performed using two models, a simple-one compartment warfarin PK model and a more complex PKPD model for pegylated interferon, with data on both concentration and response of viral load of hepatitis C virus. The results of the software were compared in terms of the standard error (SE) values of the parameters predicted from the software and the empirical SE values obtained via replicated clinical trial simulation and estimation. For the warfarin PK model and the pegylated interferon PKPD model, all software gave similar results. Interestingly, it was seen, for all software, that the simpler approximation to the Fisher information matrix, using the block diagonal matrix, provided predicted SE values that were closer to the empirical SE values than when the more complicated approximation was used (the full matrix). For most PKPD models, using any of the available software tools will provide meaningful results, avoiding cumbersome simulation and allowing design optimization.

Population Pharmacokinetic Model for Docetaxel in Patients with Varying Degrees of Liver Function: Incorporating Cytochrome P450 3A Activity Measurements

The relationship between cytochrome P4503A4 (CYP3A4) activity and docetaxel clearance in patients with varying degrees of liver function (LF) was evaluated. Docetaxel 40, 50, or 75 mg/m2 was administered to 85 patients with advanced cancer; 23 of 77 evaluable patients had abnormalities in LF tests. Baseline CYP3A activity was assessed using the erythromycin breath test (ERMBT). Pharmacokinetic studies and toxicity assessments were performed during cycle 1 of therapy and population modeling was performed using NONMEM. Docetaxel unbound clearance was lower (317 vs. 470 l/h) and more variable in patients with LF abnormalities compared to patients with normal LF. Covariates evaluated accounted for 83% of variability on clearance in patients with liver dysfunction, with CYP3A4 activity accounting for 47% of variation; covariates accounted for only 23% of variability in patients with normal LF. The clinical utility of the ERMBT may lie in identifying safe docetaxel doses for patients with LF abnormalities.

PopED: An extended, parallelized, nonlinear mixed effects models optimal design tool

Several developments have facilitated the practical application and increased the general use of optimal design for nonlinear mixed effects models. These developments include new methodology for utilizing advanced pharmacometric models, faster optimization algorithms and user friendly software tools. In this paper we present the extension of the optimal design software PopED, which incorporates many of these recent advances into an easily useable enhanced GUI. Furthermore, we present new solutions to problems related to the design of experiments such as: faster and more robust FIM calculations and optimizations, optimizing over cost/utility functions and diagnostic tools and plots to evaluate design performance. Examples for; (i) Group size optimization and efficiency translation, (ii) Cost/constraint optimization, (iii) Optimizations with different FIM approximations and (iv) optimization with parallel computing demonstrate the new features in PopED and underline the potential use of this tool when designing experiments.

Simultaneous population optimal design for pharmacokinetic-pharmacodynamic experiments

Multiple outputs or measurement types are commonly gathered in biological experiments. Often, these experiments are expensive (such as clinical drug trials) or require careful design to achieve the desired information content. Optimal experimental design protocols could help alleviate the cost and increase the accuracy of these experiments. In general, optimal design techniques ignore between-individual variability, but even work that incorporates it (population optimal design) has treated simultaneous multiple output experiments separately by computing the optimal design sequentially, first finding the optimal design for one output (eg, a pharmacokinetic [PK] measurement) and then determining the design for the second output (eg, a pharmacodynamic [PD] measurement). Theoretically, this procedure can lead to biased and imprecise results when the second model parameters are also included in the first model (as in PK-PD models). We present methods and tools for simultaneous population D-optimal experimental designs, which simultaneously compute the design of multiple output experiments, allowing for correlation between model parameters. We then apply these methods to simulated PK-PD experiments. We compare the new simultaneous designs to sequential designs that first compute the PK design, fix the PK parameters, and then compute the PD design in an experiment. We find that both population designs yield similar results in designs for low sample number experiments, with simultaneous designs being possibly superior in situations in which the number of samples is unevenly distributed between outputs. Simultaneous population D-optimality is a potentially useful tool in the emerging field of experimental design.

Model Evaluation of Continuous Data Pharmacometric Models: Metrics and Graphics

This article represents the first in a series of tutorials on model evaluation in nonlinear mixed effect models (NLMEMs), from the International Society of Pharmacometrics (ISoP) Model Evaluation Group. Numerous tools are available for evaluation of NLMEM, with a particular emphasis on visual assessment. This first basic tutorial focuses on presenting graphical evaluation tools of NLMEM for continuous data. It illustrates graphs for correct or misspecified models, discusses their pros and cons, and recalls the definition of metrics used.