Abstract. 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.

Abstract. 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.

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Taking parameter uncertainty into account is key to make drug development decisions such as testing whether trial endpoints meet defined criteria. Currently used methods for assessing parameter uncertainty in NLMEM have limitations, and there is a lack of diagnostics for when these limitations occur. In this work, a method based on sampling importance resampling (SIR) is proposed, which has the advantage of being free of distributional assumptions and does not require repeated parameter estimation. To perform SIR, a high number of parameter vectors are simulated from a given proposal uncertainty distribution. Their likelihood given the true uncertainty is then approximated by the ratio between the likelihood of the data given each vector and the likelihood of each vector given the proposal distribution, called the importance ratio. Non-parametric uncertainty distributions are obtained by resampling parameter vectors according to probabilities proportional to their importance ratios. Two simulation examples and three real data examples were used to define how SIR should be performed with NLMEM and to investigate the performance of the method. The simulation examples showed that SIR was able to recover the true parameter uncertainty. The real data examples showed that parameter 95 % confidence intervals (CI) obtained with SIR, the covariance matrix, bootstrap and log-likelihood profiling were generally in agreement when 95 % CI were symmetric. For parameters showing asymmetric 95 % CI, SIR 95 % CI provided a close agreement with log-likelihood profiling but often differed from bootstrap 95 % CI which had been shown to be suboptimal for the chosen examples. This work also provides guidance towards the SIR workflow, i.e.,which proposal distribution to choose and how many parameter vectors to sample when performing SIR, using diagnostics developed for this purpose. SIR is a promising approach for assessing parameter uncertainty as it is applicable in many situations where other methods for assessing parameter uncertainty fail, such as in the presence of small datasets, highly nonlinear models or meta-analysis.Electronic supplementary materialThe online version of this article (doi:10.1007/s10928-016-9487-8) contains supplementary material, which is available to authorized users.

Quantifying the uncertainty around endpoints used for decision-making in drug development is essential. In nonlinear mixed-effects models (NLMEM) analysis, this uncertainty is derived from the uncertainty around model parameters. Different methods to assess parameter uncertainty exist, but scrutiny towards their adequacy is low. In a previous publication, sampling importance resampling (SIR) was proposed as a fast and assumption-light method for the estimation of parameter uncertainty. A non-iterative implementation of SIR proved adequate for a set of simple NLMEM, but the choice of SIR settings remained an issue. This issue was alleviated in the present work through the development of an automated, iterative SIR procedure. The new procedure was tested on 25 real data examples covering a wide range of pharmacokinetic and pharmacodynamic NLMEM featuring continuous and categorical endpoints, with up to 39 estimated parameters and varying data richness. SIR led to appropriate results after 3 iterations on average. SIR was also compared with the covariance matrix, bootstrap and stochastic simulations and estimations (SSE). SIR was about 10 times faster than the bootstrap. SIR led to relative standard errors similar to the covariance matrix and SSE. SIR parameter 95% confidence intervals also displayed similar asymmetry to SSE. In conclusion, the automated SIR procedure was successfully applied over a large variety of cases, and its user-friendly implementation in the PsN program enables an efficient estimation of parameter uncertainty in NLMEM.Electronic supplementary materialThe online version of this article (doi:10.1007/s10928-017-9542-0) contains supplementary material, which is available to authorized users.

The market of new psychoactive substances (NPS) is characterized by a high turnover and thus provides several challenges for analytical toxicology. The analysis of urine samples often requires detailed knowledge about metabolism given that parent compounds may either be present only in small amounts or may not even be excreted. Hence, knowledge of the metabolism of NPS is a prerequisite for the development of reliable analytical methods. The main aim of this work was to elucidate for the first time the pooled human liver S9 fraction metabolism of the nine d-lysergic acid diethylamide (LSD) derivatives 1-acetyl-LSD (ALD-52), 1-propionyl-LSD (1P-LSD), 1-butyryl-LSD (1B-LSD), N 6-ethyl-nor-LSD (ETH-LAD), 1-propionyl-N 6-ethyl-nor-LSD (1P-ETH-LAD), N 6-allyl-nor-LSD (AL-LAD), N-ethyl-Ncyclopropyl lysergamide (ECPLA), (2'S,4'S)-lysergic acid 2,4-dimethylazetidide (LSZ), and lysergic acid morpholide (LSM-775) by means of liquid chromatography coupled to high resolution tandem mass spectrometry. Identification of the monooxygenase enzymes involved in the initial metabolic steps was performed using recombinant human enzymes and their contribution confirmed by inhibition experiments. Overall, N-dealkylation, hydroxylation, as well as combinations of these steps predominantly catalyzed by CYP1A2 and CYP3A4 were found. For ALD-52, 1P-LSD, and 1B-LSD deacylation to LSD was observed. The obtained mass spectral data of all metabolites is essential for reliable analytical detection particularly in urinalysis and for differentiation of the LSD-like compounds as biotransformations also led to structurally identical metabolites. However, in urine of rats after the administration of expected recreational doses and using standard urine screening approaches, parent drugs or metabolites could not be detected.

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.

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 mM Ã 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. Ó2011 AACR.