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Purpose Tepotinib is a highly selective MET inhibitor approved for treatment of non-small cell lung cancer (NSCLC) harboring METex14 skipping alterations. Analyses presented herein evaluated the relationship between tepotinib exposure, and efficacy and safety outcomes. Methods Exposure–efficacy analyses included data from an ongoing phase 2 study (VISION) investigating 500 mg/day tepotinib in NSCLC harboring METex14 skipping alterations. Efficacy endpoints included objective response, duration of response, and progression-free survival. Exposure–safety analyses included data from VISION, plus four completed studies in advanced solid tumors/hepatocellular carcinoma (30–1400 mg). Safety endpoints included edema, serum albumin, creatinine, amylase, lipase, alanine aminotransferase, aspartate aminotransferase, and QT interval corrected using Fridericia’s method (QTcF). Results Tepotinib exhibited flat exposure–efficacy relationships for all endpoints within the exposure range observed with 500 mg/day. Tepotinib also exhibited flat exposure–safety relationships for all endpoints within the exposure range observed with 30–1400 mg doses. Edema is the most frequently reported adverse event and the most frequent cause of tepotinib dose reductions and interruptions; however, the effect plateaued at low exposures. Concentration-QTc analyses using data from 30 to 1400 mg tepotinib resulted in the upper bounds of the 90% confidence interval being less than 10 ms for the mean exposures at the therapeutic (500 mg) and supratherapeutic (1000 mg) doses. Conclusions These analyses provide important quantitative pharmacologic support for benefit/risk assessment of the 500 mg/day dosage of tepotinib as being appropriate for the treatment of NSCLC harboring METex14 skipping alterations. Registration Numbers NCT01014936, NCT01832506, NCT01988493, NCT02115373, NCT02864992.

AO_SCPLOWBSTRACTC_SCPLOWPharmacometric modeling establishes causal quantitative relationship between administered dose, tissue exposures, desired and undesired effects and patients risk factors. These models are employed to de-risk drug development and guide precision medicine decisions. Recent technological advances rendered collecting real-time and detailed data easy. However, the pharmacometric tools have not been designed to handle heterogeneous, big data and complex models. The estimation methods are outdated to solve modern healthcare challenges. We set out to design a platform that facilitates domain specific modeling and its integration with modern analytics to foster innovation and readiness to data deluge in healthcare. New specialized estimation methodologies have been developed that allow dramatic performance advances in areas that have not seen major improvements in decades. New ODE solver algorithms, such as coefficient-optimized higher order integrators and new automatic stiffness detecting algorithms which are robust to frequent discontinuities, give rise to up to 4x performance improvements across a wide range of stiff and non-stiff systems seen in pharmacometric applications. These methods combine with JIT compiler techniques and further specialize the solution process on the individual systems, allowing statically-sized optimizations and discrete sensitivity analysis via forward-mode automatic differentiation, to further enhance the accuracy and performance of the solving and parameter estimation process. We demonstrate that when all of these techniques are combined with a validated clinical trial dosing mechanism and non-compartmental analysis (NCA) suite, real applications like NLME parameter estimation see run times halved while retaining the same accuracy. Meanwhile in areas with less prior optimization of software, like optimal experimental design, we see orders of magnitude performance enhancements. Together we show a fast and modern domain specific modeling framework which lays a platform for innovation via upcoming integrations with modern analytics.

Inconsistent trial design and analysis is a key reason that few advances in postoperative pain management have been made from clinical trials analyzing opioid consumption data. This study aimed to compare four different approaches to analyze opioid consumption data. A repeated time-to-event (RTTE) model in NONMEM was used to simulate clinical trials of morphine consumption with and without a hypothetical adjuvant analgesic in doses equivalent to 15-62% reduction in morphine consumption. Trials were simulated with duration of 24-96 h. Monte Carlo simulation and re-estimation were performed to determine sample size required to demonstrate efficacy with 80% power using t test, Mann-Whitney rank sum test, time-to-event (TTE) modeling and RTTE modeling. Precision of efficacy estimates for RTTE models were evaluated in 500 simulations. A sample size of 50 patients was required to detect 37% morphine sparing effect with at least 80% power in a 24 h trial with RTTE modeling whereas the required sample size was 200 for Mann-Whitney, 180 for t-test and 76 for TTE models. Extending the trial duration from 24 to 96 h reduced the required sample size by 3.1 fold with RTTE modeling. Precise estimate of potency was obtained with a RTTE model accounting for both morphine effects and time-varying covariates on opioid consumption. An RTTE analysis approach proved better suited for demonstrating efficacy of opioid sparing analgesics than traditional statistical tests as a lower sample size was required due the ability to account for time-varying factors including PK.

Editor’s Perspective What We Already Know about This Topic What This Article Tells Us That Is New Background Population-based, pharmacokinetic modeling can be used to describe variability in fluid distribution and dilution between individuals and across populations. The authors hypothesized that dilution produced by crystalloid infusion after hemorrhage would be larger in anesthetized than in awake subjects and that population kinetic modeling would identify differences in covariates. Methods Twelve healthy volunteers, seven females and five males, mean age 28 ± 4.3 yr, underwent a randomized crossover study. Each subject participated in two separate sessions, separated by four weeks, in which they were assigned to an awake or an anesthetized arm. After a baseline period, hemorrhage (7 ml/kg during 20 min) was induced, immediately followed by a 25 ml/kg infusion during 20 min of 0.9% saline. Hemoglobin concentrations, sampled every 5 min for 60 min then every 10 min for an additional 120 min, were used for population kinetic modeling. Covariates, including body weight, sex, and study arm (awake or anesthetized), were tested in the model building. The change in dilution was studied by analyzing area under the curve and maximum plasma dilution. Results Anesthetized subjects had larger plasma dilution than awake subjects. The analysis showed that females increased area under the curve and maximum plasma dilution by 17% (with 95% CI, 1.08 to 1.38 and 1.07 to 1.39) compared with men, and study arm (anesthetized increased area under the curve by 99% [0.88 to 2.45] and maximum plasma dilution by 35% [0.71 to 1.63]) impacted the plasma dilution whereas a 10-kg increase of body weight resulted in a small change (less than1% [0.93 to 1.20]) in area under the curve and maximum plasma dilution. Mean arterial pressure was lower in subjects while anesthetized (P < 0.001). Conclusions In awake and anesthetized subjects subjected to controlled hemorrhage, plasma dilution increased with anesthesia, female sex, and lower body weight. Neither study arm nor body weight impact on area under the curve or maximum plasma dilution were statistically significant and therefore no effect can be established.

SummaryTwo full model approaches was compared with respect to their ability to handle missing covariate information. The reference data analysis approach was the full model method in which the covariate effects are estimated conventionally using fixed effects, and missing covariate data is imputed with the median of the non-missing covariate information. This approach was compared to a novel full model method which treats the covariate data as observed data and estimates the covariates as random effects. A consequence of this way of handling the covariates is that no covariate imputation is required and that any missingness in the covariates is handled implicitly. The comparison between the two analysis methods was based on simulated data from a model of height for age z-scores as a function of age. Data was simulated with increasing degrees of randomly missing covariate information (0-90%) and analyzed using each of the two analysis approaches. Not surprisingly, the precision in the parameter estimates from both methods decreased with increasing degrees of missing covariate information. However, while the bias in the parameter estimates increased in a similar fashion for the reference method, the full random effects approach provided unbiased estimates for all degrees of covariate missingness.

Edoxaban exposure-response relationships from the phase III study evaluating edoxaban for prevention and treatment of venous thromboembolism (VTE) in patients with acute deep vein thrombosis (DVT) and/or pulmonary embolism (PE) were assessed by parametric time-to-event analysis. Statistical significant exposure-response relationships were recurrent VTE with hazard ratio (HR) based on average edoxaban concentration at steady state (C-av) (HRCav) 50.98 (i.e., change in the HR with every 1 ng/mL increase of C-av); the composite of recurrent DVT and nonfatal PE with HRC(av)50.99; and the composite of recurrent DVT, nonfatal PE, and all-cause mortality HRC(av)50.98, and all death using maximal edoxaban concentration (C-max) with HR (C-max) 50.99. No statistical significant exposure-response relationships were found for clinically relevant bleeding or major adverse cardiovascular event. Results support the recommendation of once-daily edoxaban 60 mg, and a reduced 30 mg dose in patients with moderate renal impairment, body weight

PURPOSE: To characterize the pharmacokinetic-pharmacodynamic (PK-PD) relationship between exposure of morphine and subsequent morphine consumption and to develop simulation tools for model validation.METHODS: Dose, formulation and time of morphine administration was available from a published study in 63 patients receiving intravenous, oral immediate release or oral controlled release morphine on request after hip surgery. The PK-PD relationship between predicted exposure of morphine and morphine consumption was modeled using repeated time to event (RTTE) modeling in NONMEM. To validate the RTTE model, a visual predictive check method was developed with simulated morphine consumption given the exposure of preceding morphine administration.RESULTS: The probability of requesting morphine was found to be significantly related to the exposure of morphine as well as night/day. Oral controlled release morphine was more effective than intravenous and oral immediate release formulations at equivalent average concentrations. Maximum effect was obtained for 8 h by oral controlled release doses ≥ 15 mg, where probability of requesting a new dose was reduced to 20% for a typical patient.CONCLUSION: This study demonstrates the first quantitative link between exposure of morphine and subsequent morphine consumption and introduces an efficient visual predictive check approach with simulation of adaptive dosing.

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 (CLcr) 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 CLcr. Compared with healthy volunteers, inter-compartmental clearance and the CLcr 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.

Population Pharmacokinetic (PK)-Pharmacodynamic (PD) (PKPD) models are increasingly used in drug development and in academic research. Hence designing efficient studies is an important task. Follow ...

Investigate the possibility to directly optimize a clinical trial design for statistical power to detect a drug effect and compare to optimal designs that focus on parameter precision. An improved statistic derived from the general formulation of the Wald approximation was used to predict the statistical power for given trial designs of a disease progression study. The predicted value was compared, together with the classical Wald statistic, to a type I error-corrected model-based power determined via clinical trial simulations. In a second step, a study design for maximal power was determined by directly maximizing the new statistic. The resulting power-optimal designs and their corresponding performance based on empirical power calculations were compared to designs focusing on parameter precision. Comparisons of empirically determined power and the newly developed statistic, showed excellent agreement across all scenarios investigated. This was in contrast to the classical Wald statistic, which consistently over-predicted the reference power with deviations of up to 90 %. Designs maximized using the proposed metric differed from traditional optimal designs and showed equal or up to 20 % higher power in the subsequent clinical trial simulations. Furthermore, the proposed method was used to minimize the number of individuals required to achieve 80 % power through a simultaneous optimization of study size and study design. The targeted power of 80 % was confirmed in subsequent simulation study. A new statistic was developed, allowing for the explicit optimization of a clinical trial design with respect to statistical power.

The relationships between drug exposure and the composite risk of cardiovascular (CV) death, myocardial infarction (MI), and stroke as well as the risk of TIMI major bleeding were estimated following long-term treatment with ticagrelor 60 or 90 mg twice daily in 20,942 patients with prior MI. These analyses support the primary reported efficacy and safety evaluations by showing that there were clear separations from placebo early in treatment with both doses, regardless of ticagrelor exposure, for both endpoints. In addition, the exposure-response analyses provided new insight into the contribution of individual exposure levels, rather than dose, as a predictor of events and accounted for differences in the baseline risk between patients. The predicted risks of CV death/MI/stroke were similar despite an increase in the median predicted ticagrelor average steady-state concentration from 606 nmol/L with ticagrelor 60 mg to 998 nmol/L with ticagrelor 90 mg (hazard ratios vs placebo of 0.83 and 0.81, respectively). The corresponding predicted risk of TIMI major bleeding slightly increased (hazard ratios vs placebo of 2.4 and 2.6, respectively). Apart from Japanese patients, showing a lower risk of CV death/MI/stroke, the response to ticagrelor was consistent across the study population, as supported by the combination of relatively flat exposure-response relationships in the studied exposure range, similar sensitivity to ticagrelor exposure, and small exposure differences. Consequently, the present analyses support the selection of the 60-mg dose for all demographic subgroups of patients studied.

With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.

We have previously shown how screening experiments for neuropathic pain can be optimised taking into account parameter and model uncertainty. Here we demonstrate how optimised protocols can be used to screen and rank candidate molecules. The concept is illustrated by pregabalin as a new chemical entity and gabapentin as a reference compound. ED-optimality was applied to a logistic regression model describing the relationship between drug exposure and response to evoked pain in the complete Freund's adjuvant (CFA) model in rats. Design variables for optimisation of the experimental protocol included dose levels and sampling times. Prior information from the reference compound was used in conjunction with relative in vitro potency as priors. Results from simulated scenarios were then combined with fitting of experimental data to estimate precision and bias of model parameters for the empirical and optimised designs. The pharmacokinetics of pregabalin was described by a two-compartment model. The expected value of EC(50) of pregabalin was 637.5 ng ml(-1). Model-based analysis of the data yielded median (range) of EC(50) values of 1,125 (898-2412) ng ml(-1) for the empirical protocol and 755 (189-756) ng ml(-1) for the optimised design. In contrast to current practice, optimal design entails different sampling schedule across dose levels. ED-optimised designs should become standard practice in the screening of candidate molecules. It ensures lower bias when estimating the drug potency, facilitating accurate ranking and selection of compounds for further development.

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.

A simulation-based comparison study on the relative merits of dose-control trials (DCTs) with exposure–response analysis versus concentration-control trials (CCTs) for drugs with narrow therapeutic index showed that DCT designs are more informative about the exposure–response relationship. The authors revisit the question employing optimal design methodology and propose strategies for designing ethically attractive trials for these drugs, balancing between individual–collective risk and informativeness. An optimal study was performed considering a hypothetical immunosuppressant agent with 2 clinical end points. Different scenarios were optimized applying cost-based designs (unwanted events vs number of subjects/ trial or maximal individual risk). Dose/exposure targets and number of subjects per trial/arm were optimized. Prior information inclusion on baseline risks was evaluated. DCTs were more informative, needing smaller studies to provide the same information as CCTs. Using the number of unwanted events—rather than subjects—as cost resulted in ethically more attractive designs. Including prior baseline risk information reduced the number of subject/events and allowed the use of targets closer to the optimal. Designing dose-finding trials for some narrow therapeutic index drugs may be improved by using DCTs with exposure–response analysis, cost-based designs, prior information, and optimal design analysis providing information on the ethical trade-off between individual risk and information gain.

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 (V(max) and K(m)) was collected from previously reported studies, and every V(max)/K(m) 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 (C(0)) for the incubation between 0.01 and 100 μM. The optimization was performed by finding the sample times and C(0) 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 (RMSE30%) of both V(max) and K(m) 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.

Because the sepsis-induced pharmacokinetic (PK) modifications need to be considered in aminoglycoside dosing, the present study aimed to develop a population PK model for amikacin (AMK) in severe sepsis and to subsequently propose an optimal sampling strategy suitable for Bayesian estimation of the drug PK parameters. Concentration-time profiles for AMK were obtained from 88 critically ill septic patients during the first 24 hours of antibiotic treatment. The population PK model was developed using a nonlinear mixed effects modeling approach. Covariate analysis included demographic data, pathophysiological characteristics, and comedication. Optimal sampling times were selected based on a robust Bayesian design criterion. Taking into account clinical constraints, a two-point sampling approach was investigated. A two-compartment model with first-order elimination best fitted the AMK concentrations. Population PK estimates were 19.2 and 9.34 L for the central and peripheral volume of distribution and 4.31 and 2.21 L/h for the intercompartmental and total body clearance. Creatinine clearance estimated using the Cockcroft-Gault equation was retained in the final model. The two optimal sampling times were 1 hour and 6 hours after onset of the drug infusion. Predictive performance of individual Bayes estimates computed using the proposed optimal sampling strategy was reported: mean prediction errors were less than 5% and root mean square errors were less than 30%. The present study confirmed the significant influence of the creatinine clearance on the PK disposition of AMK during the first hours of treatment in critically ill septic patients. Based on the population estimates, an optimal sampling strategy suitable for Bayesian estimation of the drug PK parameters was developed, meeting the need of clinical practice.

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.

Optimal design has been used in the past mainly to optimize sampling schedules for clinical trials. Optimization on design variables other than sampling times has been published in the literature only once before. This study shows, as an example, optimization on the length of treatment periods to obtain reliable estimates of drug effects on longterm disease progression studies. Disease progression studies are high in cost, effort, and time; therefore, optimization of treatment length is highly recommended to avoid failure or loss of information. Results are provided for different drug effects (eg, protective and symptomatic) and for different lengths of studies and sampling schedules. The merits of extending the total study length versus inclusion of more samples per participants are investigated. The authors demonstrate that if no observations are taken during the washout period, a trial can lose up to 40% of its efficiency. Furthermore, when optimization of treatment length is performed using multiple possible drug effect models simultaneously, these studies show high power in discriminating between different drug effect 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.

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 k(on)-k(off) 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.

Inter occasion variability (IOV) is of importance to consider in the development of a design where individual pharmacokinetic or pharmacodynamic parameters are of interest. IOV may adversely affect the precision of maximum a posteriori (MAP) estimated individual parameters, yet the influence of inclusion of IOV in optimal design for estimation of individual parameters has not been investigated. In this work two methods of including IOV in the maximum a posteriori Fisher information matrix (FIMMAP) are evaluated: (i) MAP(occ)-the IOV is included as a fixed effect deviation per occasion and individual, and (ii) POPocc-the IOV is included as an occasion random effect. Sparse sampling schedules were designed for two test models and compared to a scenario where IOV is ignored, either by omitting known IOV (Omit) or by mimicking a situation where unknown IOV has inflated the IIV (Inflate). Accounting for IOV in the FIMMAP markedly affected the designs compared to ignoring IOV and, as evaluated by stochastic simulation and estimation, resulted in superior precision in the individual parameters. In addition MAP(occ) and POPocc accurately predicted precision and shrinkage. For the investigated designs, the MAP(occ) method was on average slightly superior to POPocc and was less computationally intensive.

International audience; : Population Pharmacokinetic (PK)-Pharmacodynamic (PD) (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 effect 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 five software tools: PFIM, PkStaMP, PopDes, PopED, and POPT. The comparisons were performed using two models: i) a simple one compartment warfarin PK model; ii) a more complex PKPD model for Pegylated-interferon (peg-interferon) with both concentration and response of viral load of hepatitis C virus (HCV) data. The results of the software were compared in terms of the standard error values of the parameters (SE) predicted from the software and the empirical SE values obtained via replicated clinical trial simulation and estimation. For the warfarin PK model and the peg-interferon PKPD model all software gave similar results. Of interest 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 optimisation.

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

In spite of the evidence regarding high variability in the response to evoked pain, little attention has been paid to its impact on the screening of drugs for inflammatory and neuropathic pain. In this study, we explore the feasibility of introducing optimality concepts to experimental protocols, enabling estimation of parameter and model uncertainty. Pharmacokinetic (PK) and pharmacodynamic data from different experiments in rats were pooled and modelled using nonlinear mixed effects modelling. Pain data on gabapentin and placebo-treated animals were generated in the complete Freund's adjuvant model of neuropathic pain. A logistic regression model was applied to optimise sampling times and dose levels to be used in an experimental protocol. Drug potency (EC(50)) and interindividual variability (IIV) were considered the parameters of interest. Different experimental designs were tested and validated by SSE (stochastic simulation and estimation) taking into account relevant exposure ranges. The pharmacokinetics of gabapentin was described by a two-compartment PK model with first order absorption (CL = 0.159 l h(-1), V(2) = 0.118 l, V(3) = 0.253 l, Ka = 0.26 h(-1), Q = 1.22 l h(-1)). Drug potency (EC(50)) for the anti-allodynic effects was estimated to be 1400 ng ml(-1). Protocol optimisation improved bias and precision of the EC50 by 6 and 11.9. %, respectively, whilst IIV estimates showed improvement of 31.89 and 14.91 %, respectively. Our results show that variability in behavioural models of evoked pain response leads to uncertainty in drug potency estimates, with potential impact on the ranking of compounds during screening. As illustrated for gabapentin, ED-optimality concepts enable analysis of discrete data taking into account experimental constraints.

In population modeling two sources of variability are commonly included; inter individual variability and residual variability. Rich sampling optimal design (more samples than model parameters) using these models will often result in a sampling schedule where some measurements are taken at exactly the same time point, thereby maximizing the signal-to-noise ratio. This behavior is a result of not appropriately taking into account error generation mechanisms and is often clinically unappealing and may be avoided by including intrinsic variability, i.e. serially correlated residual errors. In this paper we extend previous work that investigated optimal designs of population models including serial correlation using stochastic differential equations to optimal design with the more robust, and analytic, AR(1) autocorrelation model. Further, we investigate the importance of correlation strength, design criteria and robust designs. Finally, we explore the optimal design properties when estimating parameters with and without serial correlation. In the investigated examples the designs and estimation performance differs significantly when handling serial correlation.

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.

We propose a new method for optimal experimental design of population pharmacometric experiments based on global search methods using interval analysis; all variables and parameters are represented as intervals rather than real numbers. The evaluation of a specific design is based on multiple simulations and parameter estimations. The method requires no prior point estimates for the parameters, since the parameters can incorporate any level of uncertainty. In this respect, it is similar to robust optimal design. Representing sampling times and covariates like doses by intervals gives a direct way of optimizing with rigorous sampling and dose intervals that can be useful in clinical practice. Furthermore, the method works on underdetermined problems for which traditional methods typically fail.

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 k(on)-k(off) 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.

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.

High-spin states in 183 Pt have been studied for the first time using the reactions 154 Sm( 34 S, 5n) and 170 Yb( 16 O,3n). Rotational bands built on the Nilsson configurations 1 2 − [521], 7 2 − [514] and 9 2 + [624] were observed up to spin values of 39 2 − 49 2 h . Quasiparticle alignments and band crossing frequencies were investigated in these bands. A large signature splitting was observed in the νi 13 2 - band structure . The experimental results were compared with total routhian surface calculations, in which the shape of the nucleus could be followed as a function of rotational frequency for different quasiparticle configurations.

Excited states in 123La have been established for the first time using γ-ray spectroscopy, thus extending the systematics of lanthanum isotopes further out from the line of β-stability. Bands built on the Nilsson orbitals [404] 9 2 , [550] 1 2 , and most likely also [422] 3 2 are observed. In the last two cases only the favoured signature is seen, while in the first case both signatures are observed in a strongly coupled band. States in 123La are observed up to a maximum spin of tentatively 59 2 . The configuration dependence of the first band crossing frequency indicates the presence of higher-order terms in the proton pairing. According to calculations, deformation effects are not sufficient to reproduce the observed shift in crossing frequencies.