Martin Bergstrand

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.

Handling Data Below the Limit of Quantification in Mixed Effect Models

The purpose of this study is to investigate the impact of observations below the limit of quantification (BQL) occurring in three distinctly different ways and assess the best method for prevention of bias in parameter estimates and for illustrating model fit using visual predictive checks (VPCs). Three typical ways in which BQL can occur in a model was investigated with simulations from three different models and different levels of the limit of quantification (LOQ). Model A was used to represent a case with BQL observations in an absorption phase of a PK model whereas model B represented a case with BQL observations in the elimination phase. The third model, C, an indirect response model illustrated a case where the variable of interest in some cases decreases below the LOQ before returning towards baseline. Different approaches for handling of BQL data were compared with estimation of the full dataset for 100 simulated datasets following models A, B, and C. An improved standard for VPCs was suggested to better evaluate simulation properties both for data above and below LOQ. Omission of BQL data was associated with substantial bias in parameter estimates for all tested models even for seemingly small amounts of censored data. Best performance was seen when the likelihood of being below LOQ was incorporated into the model. In the tested examples this method generated overall unbiased parameter estimates. Results following substitution of BQL observations with LOQ/2 were in some cases shown to introduce bias and were always suboptimal to the best method. The new standard VPCs was found to identify model misfit more clearly than VPCs of data above LOQ only.

Population Pharmacokinetics of Busulfan in Children: Increased Evidence for Body Surface Area and Allometric Body Weight Dosing of Busulfan in Children

Purpose: To evaluate the best method for dosing busulfan in children, we retrospectively analyzed two different data sets from three different dosing regimens by means of population pharmacokinetics using NONMEM. Experimental Design: The development data set consisted of plasma samples from 94 children, in the age range of 0.4 to 18.8 years, receiving either oral or intravenous busulfan. The external model evaluation data set comprised 24 children, in the age range of 0.1 to 18.9 years, who belonged to the once-daily intravenous busulfan dosing regimen. A one-compartment model with first-order absorption using body surface area (BSA) or allometric body weight (BW) as covariate on clearance (CL) and BW as covariate on volume of distribution (V) were used to describe the results sufficiently. In addition to interindividual variability on all pharmacokinetic parameters, interoccasion variability was included for CL and V. Results: CL values in the present study did not reflect the shape of the CL versus weight curve reported in previous investigations. By external model evaluation, we were able to confirm these findings. Furthermore, bioavailability was calculated to be between 93% and 99% for the development data set. On the basis of the final models, we simulated two dosing schemes according to allometric BW and BSA showing that we estimated to include about 30% more patients into the proposed therapeutic area under the curve (AUC) range of 900 to 1,500 μM*min and could, furthermore, achieve a reduction in the AUC variability when dosed according to the labeled European Medicines Agency (EMA) dosing recommendation. Conclusion: We recommend a BSA or an allometric BW dosing regimen for individualizing busulfan therapy in children to reduce variability in busulfan exposure and to improve safety and efficacy of busulfan treatment. Clin Cancer Res; 17(21); 6867–77. ©2011 AACR.

Population Pharmacokinetic and Pharmacodynamic Modeling of Amodiaquine and Desethylamodiaquine in Women with Plasmodium vivax Malaria during and after Pregnancy

ABSTRACT Amodiaquine is effective for the treatment of Plasmodium vivax malaria, but there is little information on the pharmacokinetic and pharmacodynamic properties of amodiaquine in pregnant women with malaria. This study evaluated the population pharmacokinetic and pharmacodynamic properties of amodiaquine and its biologically active metabolite, desethylamodiaquine, in pregnant women with P. vivax infection and again after delivery. Twenty-seven pregnant women infected with P. vivax malaria on the Thai-Myanmar border were treated with amodiaquine monotherapy (10 mg/kg/day) once daily for 3 days. Nineteen women, with and without P. vivax infections, returned to receive the same amodiaquine dose postpartum. Nonlinear mixed-effects modeling was used to evaluate the population pharmacokinetic and pharmacodynamic properties of amodiaquine and desethylamodiaquine. Amodiaquine plasma concentrations were described accurately by lagged first-order absorption with a two-compartment disposition model followed by a three-compartment disposition of desethylamodiaquine under the assumption of complete in vivo conversion. Body weight was implemented as an allometric function on all clearance and volume parameters. Amodiaquine clearance decreased linearly with age, and absorption lag time was reduced in pregnant patients. Recurrent malaria infections in pregnant women were modeled with a time-to-event model consisting of a constant-hazard function with an inhibitory effect of desethylamodiaquine. Amodiaquine treatment reduced the risk of recurrent infections from 22.2% to 7.4% at day 35. In conclusion, pregnancy did not have a clinically relevant impact on the pharmacokinetic properties of amodiaquine or desethylamodiaquine. No dose adjustments are required in pregnancy.

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.

Mechanistic Modeling of a Magnetic Marker Monitoring Study Linking Gastrointestinal Tablet Transit, In Vivo Drug Release, and Pharmacokinetics

Magnetic marker monitoring (MMM) is a new technique for visualizing transit and disintegration of solid oral dosage forms through the gastrointestinal (GI) tract. The aim of this work was to develop a modeling approach for gaining information from MMM studies using data from a food interaction study with felodipine extended‐release (ER) formulation. The interrelationship between tablet location in the GI tract, in vivo drug release, and felodipine disposition was modeled. A Markov model was developed to describe the tablets movement through the GI tract. Tablet location within the GI tract significantly affected drug release and absorption through the gut wall. Food intake decreased the probability of tablet transition from the stomach, decreased the rate with which released felodipine left the stomach, and increased the fraction absorbed across the gut wall. In conclusion, the combined information of tablet location in the GI tract, in vivo drug release, and plasma concentration can be utilized in a mechanistically informative way with integrated modeling of data from MMM studies.

Comparisons of Analysis Methods for Proof-of-Concept Trials

Drug development struggles with high costs and time consuming processes. Hence, a need for new strategies has been accentuated by many stakeholders in drug development. This study proposes the use of pharmacometric models to rationalize drug development. Two simulated examples, within the therapeutic areas of acute stroke and type 2 diabetes, are utilized to compare a pharmacometric model–based analysis to a t‐test with respect to study power of proof‐of‐concept (POC) trials. In all investigated examples and scenarios, the conventional statistical analysis resulted in several fold larger study sizes to achieve 80% power. For a scenario with a parallel design of one placebo group and one active dose arm, the difference between the conventional and pharmacometric approach was 4.3‐ and 8.4‐fold, for the stroke and diabetes example, respectively. Although the model‐based power depend on the model assumptions, in these scenarios, the pharmacometric model–based approach was demonstrated to permit drastic streamlining of POC trials.

A mechanism-Based Approach for Absorption Modeling: The Gastro-Intestinal Transit Time (GITT) Model

Absorption models used in the estimation of pharmacokinetic drug characteristics from plasma concentration data are generally empirical and simple, utilizing no prior information on gastro-intestinal (GI) transit patterns. Our aim was to develop and evaluate an estimation strategy based on a mechanism-based model for drug absorption, which takes into account the tablet movement through the GI transit. This work is an extension of a previous model utilizing tablet movement characteristics derived from magnetic marker monitoring (MMM) and pharmacokinetic data. The new approach, which replaces MMM data with a GI transit model, was evaluated in data sets where MMM data were available (felodipine) or not available (diclofenac). Pharmacokinetic profiles in both datasets were well described by the model according to goodness-of-fit plots. Visual predictive checks showed the model to give superior simulation properties compared with a standard empirical approach (first-order absorption rate + lag-time). This model represents a step towards an integrated mechanism-based NLME model, where the use of physiological knowledge and in vitro–in vivo correlation helps fully characterize PK and generate hypotheses for new formulations or specific populations.

Population pharmacokinetics of tacrolimus in pediatric liver transplantation : early posttransplantation clearance

Background: Tacrolimus is an immunosuppressant with a narrow therapeutic window, with considerable pharmacokinetic variability. Getting sufficient concentrations in pediatric liver transplantation is imperative, but it has proven difficult in the immediate posttransplantation period in particular. A predictive pharmacokinetic model could be the basis for development of a novel initial dose schedule, and therapeutic drug monitoring with Bayesian methodology. Methods: The predictive capacity of 2 previously developed population pharmacokinetic models of tacrolimus in pediatric liver transplant recipients was tested in 20 new patients using Bayesian forecasting. Predictive performance was poor in the immediate posttransplant period with tacrolimus pharmacokinetics changing rapidly. A new population pharmacokinetic model, focusing on the immediate posttransplant period, was subsequently developed in 73 patients. Results: An increase in the apparent clearance of tacrolimus in the first few weeks after transplant was evident. Typical apparent clearance of tacrolimus was 0.148 L·h−1·kg−0.75 immediately after transplantation, increasing to a maximum of 1.37 L·h−1·kg−0.75. Typical apparent distribution volume was 27.2 L/kg. Internal and external validation studies confirmed the predictive capabilities of the developed model. Simulation studies reveal that in 60% of subjects the current initial standard dose without subsequent dosage adjustments overshoot the desired trough concentration range of 10–20 ng/mL. An alternative dosing schedule was developed based on allometric scaling with an initial loading dose followed by a maintenance dose increasing with time. Conclusions: A population pharmacokinetic model for tacrolimus was developed, to better describe the early posttransplantation phase. This model has the potential to aid therapeutic drug monitoring and was also used to suggest a revised dosing scheme in the intended population.

A semi-mechanistic modeling strategy for characterization of regional absorption properties and prospective prediction of plasma concentrations following administration of new modified release formulations

ABSTRACTPurposeTo outline and test a new modeling approach for prospective predictions of absorption from newly developed modified release formulations based on in vivo studies of gastro intestinal (GI) transit, drug release and regional absorption for the investigational drug AZD0837.MethodsThis work was a natural extension to the companion article “A semi-mechanistic model to link in vitro and in vivo drug release for modified release formulations”. The drug release model governed the amount of substance released in distinct GI regions over time. GI distribution of released drug substance, region specific rate and extent of absorption and the influence of food intake were estimated. The model was informed by magnetic marker monitoring data and data from an intubation study with local administration in colon.ResultsDistinctly different absorption properties were characterized for different GI regions. Bioavailability over the gut-wall was estimated to be high in duodenum (70%) compared to the small intestine (25%). Colon was primarily characterized by a very slow rate of absorption.ConclusionsThe established model was largely successful in predicting plasma concentration following administration of three newly developed formulations for which no clinical data had been applied during model building.