Joakim Nyberg

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.

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.

The lasso—a novel method for predictive covariate model building in nonlinear mixed effects models

Covariate models for population pharmacokinetics and pharmacodynamics are often built with a stepwise covariate modelling procedure (SCM). When analysing a small dataset this method may produce a covariate model that suffers from selection bias and poor predictive performance. The lasso is a method suggested to remedy these problems. It may also be faster than SCM and provide a validation of the covariate model. The aim of this study was to implement the lasso for covariate selection within NONMEM and to compare this method to SCM.In the lasso all covariates must be standardised to have zero mean and standard deviation one. Subsequently, the model containing all potential covariate–parameter relations is fitted with a restriction: the sum of the absolute covariate coefficients must be smaller than a value, t. The restriction will force some coefficients towards zero while the others are estimated with shrinkage. This means in practice that when fitting the model the covariate relations are tested for inclusion at the same time as the included relations are estimated. For a given SCM analysis, the model size depends on the P-value required for selection. In the lasso the model size instead depends on the value of t which can be estimated using cross-validation.The lasso was implemented as an automated tool using PsN. The method was compared to SCM in 16 scenarios with different dataset sizes, number of investigated covariates and starting models for the covariate analysis. Hundred replicate datasets were created by resampling from a PK-dataset consisting of 721 stroke patients. The two methods were compared primarily on the ability to predict external data, estimate their own predictive performance (external validation), and on the computer run-time.In all 16 scenarios the lasso predicted external data better than SCM with any of the studied P-values (5%, 1% and 0.1%), but the benefit was negligible for large datasets. The lasso cross-validation provided a precise and nearly unbiased estimate of the actual prediction error. On a single processor, the lasso was faster than SCM. Further, the lasso could run completely in parallel whereas SCM must run in steps.In conclusion, the lasso is superior to SCM in obtaining a predictive covariate model on a small dataset or on small subgroups (e.g. rare genotype). Run in parallel the lasso could be much faster than SCM. Using cross-validation, the lasso provides a validation of the covariate model and does not require the user to specify a P-value for selection.

Simultaneous optimal experimental design on dose and sample times

Optimal experimental design can be used for optimizing new pharmacokinetic (PK)–pharmacodynamic (PD) studies to increase the parameter precision. Several methods for optimizing non-linear mixed effect models has been proposed previously but the impact of optimizing other continuous design parameters, e.g. the dose, has not been investigated to a large extent. Moreover, the optimization method (sequential or simultaneous) for optimizing several continuous design parameters can have an impact on the optimal design. In the sequential approach the time and dose where optimized in sequence and in the simultaneous approach the dose and time points where optimized at the same time. To investigate the sequential approach and the simultaneous approach; three different PK–PD models where considered. In most of the cases the optimization method did change the optimal design and furthermore the precision was improved with the simultaneous approach.

Rapid sample size calculations for a defined likelihood ratio test-based power in mixed-effects models.

Efficient power calculation methods have previously been suggested for Wald test-based inference in mixed-effects models but the only available alternative for Likelihood ratio test-based hypothesis testing has been to perform computer-intensive multiple simulations and re-estimations. The proposed Monte Carlo Mapped Power (MCMP) method is based on the use of the difference in individual objective function values (ΔiOFV) derived from a large dataset simulated from a full model and subsequently re-estimated with the full and reduced models. The ΔiOFV is sampled and summed (∑ΔiOFVs) for each study at each sample size of interest to study, and the percentage of ∑ΔiOFVs greater than the significance criterion is taken as the power. The power versus sample size relationship established via the MCMP method was compared to traditional assessment of model-based power for six different pharmacokinetic and pharmacodynamic models and designs. In each case, 1,000 simulated datasets were analysed with the full and reduced models. There was concordance in power between the traditional and MCMP methods such that for 90% power, the difference in required sample size was in most investigated cases less than 10%. The MCMP method was able to provide relevant power information for a representative pharmacometric model at less than 1% of the run-time of an SSE. The suggested MCMP method provides a fast and accurate prediction of the power and sample size relationship.

Adaptive-Optimal Design in PET Occupancy Studies

Positron emission tomography (PET) is an imaging technique that is used to investigate ligand–receptor binding in the living brain and to determine the time course of plasma concentration/receptor occupancy (RO). The purpose of this work was to demonstrate the added value of an adaptive‐optimal design for PET scan timings and dose selection over traditional study designs involving fixed or educated selections of timings and doses. A kon–koff model relating plasma concentration to PET data was applied to generate the simulated data. Optimization was performed on scanning timings and doses using the D‐optimality criterion. Optimal designs as applied to scanning timings provided unbiased estimates and improved the accuracy of results relative to those of fixed and educated designs. Optimization of both timings and dose provided improvements in accuracy and precision when the initial dose selection was noninformative regarding the time course of RO. These results indicate that adaptive‐optimal designs can provide an efficient experimental design for RO studies using PET, by minimizing the number of subjects required and maximizing information related to the plasma concentration–RO relationship.

Application of the Optimal Design Approach to Improve a Pretransplant Drug Dose Finding Design for Ciclosporin

A time and sampling intensive pretransplant test dose design was to be reduced, but at the same time optimized so that there was no loss in the precision of predicting the individual pharmacokinetic (PK) estimates of posttransplant dosing. The following variables were optimized simultaneously: sampling times, ciclosporin dose, time of second dose, infusion duration, and administration order, using a published ciclosporin population PK model as prior information. The original design was reduced from 22 samples to 6 samples/patient and both doses (intravenous oral) were administered within 8 hours. Compared with the prior information given by the published ciclosporin population PK model, the expected standard deviations (SDs) of the individual parameters for clearance and bioavailability could be reduced by, on average, 40% under the optimized sparse designs. The gain of performing the original rich design compared with the optimal reduced design, considering the standard errors of the parameter estimates, was found to be minimal. This application demonstrates, in a practical clinical scenario, how optimal design techniques may be used to improve diagnostic procedures given available software and methods.

Population pharmacokinetics of edoxaban in patients with symptomatic deep-vein thrombosis and/or pulmonary embolism-the Hokusai-VTE phase 3 study

AIMS This study characterized the population pharmacokinetics of edoxaban in patients with symptomatic deep-vein thrombosis and/or pulmonary embolism in the Hokusai-VTE phase 3 study. The impact of the protocol-specified 50% dose reductions applied to patients with body weight ≤ 60 kg, creatinine clearance (CL(cr)) of 30 to 50 ml min(-1) or concomitant P-glycoprotein inhibitor on edoxaban exposure was assessed using simulations. METHODS The sparse data from Hokusai-VTE, 9531 concentrations collected from 3707 patients, were pooled with data from 13 phase 1 studies. In the analysis, the covariate relationships used for dose reductions were estimated and differences between healthy subjects and patients as well as additional covariate effects of age, race and gender were explored based on statistical and clinical significance. RESULTS A linear two-compartment model with first order absorption preceded by a lag time best described the data. Allometrically scaled body weight was included on disposition parameters. Apparent clearance was parameterized as non-renal and renal. The latter increased non-linearly with increasing CL(cr). Compared with healthy volunteers, inter-compartmental clearance and the CL(cr) covariate effect were different in patients (+64.6% and +274%). Asian patients had a 22.6% increased apparent central volume of distribution. The effect of co-administration of P-glycoprotein inhibitors seen in phase 1 could not be confirmed in the phase 3 data. Model-based simulations revealed lower exposure in dose-reduced compared with non-dose-reduced patients. CONCLUSIONS The adopted dose-reduction strategy resulted in reduced exposure compared with non-dose-reduced, thereby overcompensating for covariate effects. The clinical impact of these differences on safety and efficacy remains to be evaluated.

Optimization of the intravenous glucose tolerance test in T2DM patients using optimal experimental design.

Intravenous glucose tolerance test (IVGTT) provocations are informative, but complex and laborious, for studying the glucose-insulin system. The objective of this study was to evaluate, through optimal design methodology, the possibilities of more informative and/or less laborious study design of the insulin modified IVGTT in type 2 diabetic patients. A previously developed model for glucose and insulin regulation was implemented in the optimal design software PopED 2.0. The following aspects of the study design of the insulin modified IVGTT were evaluated; (1) glucose dose, (2) insulin infusion, (3) combination of (1) and (2), (4) sampling times, (5) exclusion of labeled glucose. Constraints were incorporated to avoid prolonged hyper- and/or hypoglycemia and a reduced design was used to decrease run times. Design efficiency was calculated as a measure of the improvement with an optimal design compared to the basic design. The results showed that the design of the insulin modified IVGTT could be substantially improved by the use of an optimized design compared to the standard design and that it was possible to use a reduced number of samples. Optimization of sample times gave the largest improvement followed by insulin dose. The results further showed that it was possible to reduce the total sample time with only a minor loss in efficiency. Simulations confirmed the predictions from PopED. The predicted uncertainty of parameter estimates (CV) was low in all tested cases, despite the reduction in the number of samples/subject. The best design had a predicted average CV of parameter estimates of 19.5%. We conclude that improvement can be made to the design of the insulin modified IVGTT and that the most important design factor was the placement of sample times followed by the use of an optimal insulin dose. This paper illustrates how complex provocation experiments can be improved by sequential modeling and optimal design.

Optimal experimental design for assessment of enzyme kinetics in a drug discovery screening environment

A penalized expectation of determinant (ED)-optimal design with a discrete parameter distribution was used to find an optimal experimental design for assessment of enzyme kinetics in a screening environment. A data set for enzyme kinetic data (Vmax and Km) was collected from previously reported studies, and every Vmax/Km pair (n = 76) was taken to represent a unique drug compound. The design was restricted to 15 samples, an incubation time of up to 40 min, and starting concentrations (C0) for the incubation between 0.01 and 100 μM. The optimization was performed by finding the sample times and C0 returning the lowest uncertainty (S.E.) of the model parameter estimates. Individual optimal designs, one general optimal design and one, for laboratory practice suitable, pragmatic optimal design (OD) were obtained. In addition, a standard design (STD-D), representing a commonly applied approach for metabolic stability investigations, was constructed. Simulations were performed for OD and STD-D by using the Michaelis-Menten (MM) equation, and enzyme kinetic parameters were estimated with both MM and a monoexponential decay. OD generated a better result (relative standard error) for 99% of the compounds and an equal or better result [(root mean square error (RMSE)] for 78% of the compounds in estimation of metabolic intrinsic clearance. Furthermore, high-quality estimates (RMSE < 30%) of both Vmax and Km could be obtained for a considerable number (26%) of the investigated compounds by using the suggested OD. The results presented in this study demonstrate that the output could generally be improved compared with that obtained from the standard approaches used today.