Handling underlying discrete variables with bivariate mixed hidden Markov models in NONMEM.

Non-linear mixed effects models typically deal with stochasticity in observed processes but models accounting for only observed processes may not be the most appropriate for all data. Hidden Markov models (HMMs) characterize the relationship between observed and hidden variables where the hidden variables can represent an underlying and unmeasurable disease status for example. Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs. In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example. The two hidden states included in the model were remission and exacerbation and two observation sources were considered, patient reported outcomes (PROs) and forced expiratory volume (FEV1). Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. The influence of including random and covariate effects of varying magnitudes on the parameters in the model was quantified and a power analysis was performed to compare the power of a single bivariate MHMM with two separate univariate MHMMs. A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks. Parameter precision was high for all parameters with the exception of the variance of the transition rate dictating the transition from remission to exacerbation (relative root mean squared error [RRMSE] > 150%). Parameter precision was better with higher magnitudes of the transition probability parameters. A drug effect was included on the transition rate probability and the precision of the drug effect parameter improved with increasing magnitude of the parameter. The power to detect the drug effect was improved by utilizing a bivariate MHMM model over the univariate MHMM models where the number of subject required for 80% power was 25 with the bivariate MHMM model versus 63 in the univariate MHMM FEV1 model and > 100 in the univariate MHMM PRO model. The results advocates for the use of bivariate MHMM models when implementation is possible.

Reduced and optimized trial designs for drugs described by a target mediated drug disposition model.

Monoclonal antibodies against soluble targets are often rich and include the sampling of multiple analytes over a lengthy period of time. Predictive models built on data obtained in such studies can be useful in all drug development phases. If adequate model predictions can be maintained with a reduced design (e.g. fewer samples or shorter duration) the use of such designs may be advocated. The effect of reducing and optimizing a rich design based on a published study for Omalizumab (OMA) was evaluated as an example. OMA pharmacokinetics were characterized using a target-mediated drug disposition model considering the binding of OMA to free IgE and the subsequent formation of an OMA-IgE complex. The performance of the reduced and optimized designs was evaluated with respect to: efficiency, parameter uncertainty and predictions of free target. It was possible to reduce the number of samples in the study by 30% while still maintaining an efficiency of almost 90%. A reduction in sampling duration by two-thirds resulted in an efficiency of 75%. Omission of any analyte measurement or a reduction of the number of dose levels was detrimental to the efficiency of the designs (efficiency ≤ 51%). However, other metrics were, in some cases, relatively unaffected, showing that multiple metrics may be needed to obtain balanced assessments of design performance.

Model averaging for robust assessment of QT prolongation by concentration-response analysis.

Assessing the QT prolongation potential of a drug is typically done based on pivotal safety studies called thorough QT studies. Model-based estimation of the drug-induced QT prolongation at the estimated mean maximum drug concentration could increase efficiency over the currently used intersection-union test. However, robustness against model misspecification needs to be guaranteed in pivotal settings. The objective of this work was to develop an efficient, fully prespecified model-based inference method for thorough QT studies, which controls the type I error and provides satisfactory test power. This is achieved by model averaging: The proposed estimator of the concentration-response relationship is a weighted average of a parametric (linear) and a nonparametric (monotonic I-splines) estimator, with weights based on mean integrated square error. The desired properties of the method were confirmed in an extensive simulation study, which demonstrated that the proposed method controlled the type I error adequately, and that its power was higher than the power of the nonparametric method alone. The method can be extended from thorough QT studies to the analysis of QT data from pooled phase I studies.

Influence of CYP2B6 516G>T polymorphism and interoccasion variability (IOV) on the population pharmacokinetics of efavirenz in HIV-infected South African children.

OBJECTIVE: To investigate the influence of CYP2B6 516G>T polymorphism, as a covariate, and of interoccasion variability (IOV) on the oral clearance (CL/F) of efavirenz (EFV) in treatment-naïve black South African children over a period of 24 months post-antiretroviral therapy (ART) initiation. METHODS: HIV-infected black children (n = 60, aged 3-16 years), with no prior exposure to ART, eligible to commence ART and attending an outpatient clinic were enrolled into this study. Blood samples were taken at mid-dose interval at 1, 3, 6, 12, 18 and 24 months post-ART initiation. EFV plasma samples were determined with an adapted and validated LC/MS/MS method. Genotyping of the CYP2B6 G516T single nucleotide polymorphism (SNP) was performed using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP). NONMEM was used for the population pharmacokinetic modelling. RESULTS: EFV concentrations below 1 µg/mL accounted for 18% (116/649), EFV concentrations >4 µg/mL accounted for 29.5% (192/649) and concentrations within the therapeutic range (1-4 µg/mL) represented 52.5% (341/649) of all the samples determined. The covariates age, weight and CYP2B6 G516Tgenotype were included in the final model with population estimates for CL/F determined as 2.46, 4.60 and 7.33 L/h for the T/T, G/T and G/G genotype groups respectively. CONCLUSIONS: The inclusion of both age and weight to predict accurate EFV CL values for the respective genotype groups within this paediatric population was required, whereas the addition of gender and body surface area did not improve the predictions. The importance of introducing IOV in a PK model for a longitudinal study with sparsely collected data was again highlighted by this investigation.

Evaluation of IPPSE, an alternative method for sequential population PKPD analysis.

The aim of this study is to present and evaluate an alternative sequential method to perform population pharmacokinetic-pharmacodynamic (PKPD) analysis. Simultaneous PKPD analysis (SIM) is generally considered the reference method but may be computationally burdensome and time consuming. Evaluation of alternative approaches aims at speeding up the computation time and stabilizing the estimation of the models, while estimating the model parameters with good enough precision. The IPPSE method presented here uses the individual PK parameter estimates and their uncertainty (SE) to propagate the PK information to the PD estimation step, while the IPP method uses the individual PK parameters only and the PPP&D method utilizes the PK data. Data sets (n = 200) with various study designs were simulated according to a one-compartment PK model and a direct Emax PD model. The study design of each dataset was randomly selected. The same PK and PD models were fitted to the simulated observations using the SIM, IPP, PPP&D and IPPSE methods. The performances of the methods were compared with respect to estimation precision and bias, and computation time. Estimated precision and bias for the IPPSE method were similar to that of SIM and PPP&D, while IPP had higher bias and imprecision. Compared with the SIM method, IPPSE saved more computation time (61%) than PPP&D (39%), while IPP remained the fastest method (86% run time saved). The IPPSE method is a promising alternative for PKPD analysis, combining the advantages of the SIM (higher precision and lower bias of parameter estimates) and the IPP (shorter run time) methods.

Impact of CYP2C8*3 on paclitaxel clearance: a population pharmacokinetic and pharmacogenomic study in 93 patients with ovarian cancer.

The primary purpose of this study was to evaluate the effect of CYP2C8*3 and three genetic ABCB1 variants on the elimination of paclitaxel. We studied 93 Caucasian women with ovarian cancer treated with paclitaxel and carboplatin. Using sparse sampling and nonlinear mixed effects modeling, the individual clearance of unbound paclitaxel was estimated from total plasma paclitaxel and Cremophor EL. The geometric mean of clearance was 385 l h⁻¹ (range 176-726 l h⁻¹). Carriers of CYP2C8*3 had 11% lower clearance than non-carriers, P=0.03. This has not been shown before in similar studies; the explanation is probably the advantage of using both unbound paclitaxel clearance and a population of patients of same gender. No significant association was found for the ABCB1 variants C1236T, G2677T/A and C3435T. Secondarily, other candidate single-nucleotide polymorphisms were explored with possible associations found for CYP2C8*4 (P=0.04) and ABCC1 g.7356253C>G (P=0.04).

Transforming parts of a differential equations system to difference equations as a method for run-time savings in NONMEM.

Computer models of biological systems grow more complex as computing power increase. Often these models are defined as differential equations and no analytical solutions exist. Numerical integration is used to approximate the solution; this can be computationally intensive, time consuming and be a large proportion of the total computer runtime. The performance of different integration methods depend on the mathematical properties of the differential equations system at hand. In this paper we investigate the possibility of runtime gains by calculating parts of or the whole differential equations system at given time intervals, outside of the differential equations solver. This approach was tested on nine models defined as differential equations with the goal to reduce runtime while maintaining model fit, based on the objective function value. The software used was NONMEM. In four models the computational runtime was successfully reduced (by 59-96%). The differences in parameter estimates, compared to using only the differential equations solver were less than 12% for all fixed effects parameters. For the variance parameters, estimates were within 10% for the majority of the parameters. Population and individual predictions were similar and the differences in OFV were between 1 and -14 units. When computational runtime seriously affects the usefulness of a model we suggest evaluating this approach for repetitive elements of model building and evaluation such as covariate inclusions or bootstraps.

Population pharmacokinetics of colistin and the relation to survival in critically ill patients infected with colistin susceptible and carbapenem-resistant bacteria.

OBJECTIVES: The aim was to analyse the population pharmacokinetics of colistin and to explore the relationship between colistin exposure and time to death. METHODS: Patients included in the AIDA randomized controlled trial were treated with colistin for severe infections caused by carbapenem-resistant Gram-negative bacteria. All subjects received a 9 million units (MU) loading dose, followed by a 4.5 MU twice daily maintenance dose, with dose reduction if creatinine clearance (CrCL) < 50 mL/min. Individual colistin exposures were estimated from the developed population pharmacokinetic model and an optimized two-sample per patient sampling design. Time to death was evaluated in a parametric survival analysis. RESULTS: Out of 406 randomized patients, 349 contributed pharmacokinetic data. The median (90% range) colistin plasma concentration was 0.44 (0.14-1.59) mg/L at 15 minutes after the end of first infusion. In samples drawn 10 hr after a maintenance dose, concentrations were >2 mg/L in 94% (195/208) and 44% (38/87) of patients with CrCL ≤120 mL/min, and >120 mL/min, respectively. Colistin methanesulfonate sodium (CMS) and colistin clearances were strongly dependent on CrCL. High colistin exposure to MIC ratio was associated with increased hazard of death in the multivariate analysis (adjusted hazard ratio (95% CI): 1.07 (1.03-1.12)). Other significant predictors included SOFA score at baseline (HR 1.24 (1.19-1.30) per score increase), age and Acinetobacter or Pseudomonas as index pathogen. DISCUSSION: The population pharmacokinetic model predicted that >90% of the patients had colistin concentrations >2 mg/L at steady state, but only 66% at 4 hr after start of treatment. High colistin exposure was associated with poor kidney function, and was not related to a prolonged survival.

Pharmacometric Analysis of the Relationship Between Absolute Lymphocyte Count and Expanded Disability Status Scale and Relapse Rate, Efficacy End Points, in Multiple Sclerosis Trials.

The aim of this work was to assess the relationship between the absolute lymphocyte count (ALC), and disability (as measured by the Expanded Disability Status Scale [EDSS]) and occurrence of relapses, 2 efficacy endpoints, respectively, in patients with remitting-relasping multiple sclerosis. Data for ALC, EDSS, and relapse rate were available from 1319 patients receiving placebo and/or cladribine tablets. Pharmacodynamic models were developed to characterize the time course of the endpoints. ALC-related measures were then evaluated as predictors of the efficacy endpoints. EDSS data were best fitted by a model where the logit-linear disease progression is affected by the dynamics of ALC change from baseline. Relapse rate data were best described by the Weibull hazard function, and the ALC change from baseline was also found to be a significant predictor of time to relapse. Presented models have shown that once cladribine exposure driven ALC-derived measures are included in the model, the need for drug effect components is of less importance (EDSS) or disappears (relapse rate). This simplifies the models and theoretically makes them mechanism specific rather than drug specific. Having a reliable mechanism-specific model would allow leveraging historical data across compounds, to support decision making in drug development and possibly shorten the time to market.

Diagnosing model diagnostics.

Conclusions from clinical trial results that are derived from model-based analyses rely on the model adequately describing the underlying system. The traditionally used diagnostics intended to provide information about model adequacy have seldom discussed shortcomings. Without an understanding of the properties of these diagnostics, development and use of new diagnostics, and additional information pertaining to the diagnostics, there is risk that adequate models will be rejected and inadequate models accepted. Thus, a diagnosis of available diagnostics is desirable.

Time for quantitative clinical pharmacology: a proposal for a pharmacometrics curriculum.

A formal training program in pharmacometrics is essential to train clinical pharmacology scientists. A proposal is made for a pharmacometrics curriculum. The curriculum has components at the undergraduate, graduate and postgraduate levels.

Developmental pharmacokinetics of ciclosporin--a population pharmacokinetic study in paediatric renal transplant candidates.

AIMS: To use population pharmacokinetic modelling to characterize the influence of developmental and demographic factors on the pharmacokinetic variability of ciclosporin. METHODS: Pharmacokinetic modelling was performed in NONMEM using a dataset comprising 162 pretransplant children, aged 0.36-17.5 years. Ciclosporin was given intravenously (3 mg kg(-1)) and orally (10 mg kg(-1)) on separate occasions followed by blood sampling for 24 h. RESULTS: A three-compartment model with first-order absorption without lag-time best described the pharmacokinetics of ciclosporin. The most important covariate affecting systemic clearance (CL) and distribution volume (V) was body weight (BW; scaled allometrically), responsible for a fourfold difference in uncorrected ciclosporin CL and a sixfold difference in ciclosporin V. The other significant covariates, haematocrit, plasma cholesterol and creatinine, were estimated to explain 20-30% of interindividual differences in CL and V of ciclosporin. No age-related changes in oral bioavailability or in BW-normalized V were seen. The BW-normalized CL (CL/BW) declined with age and prepubertal children (<8 years) had an approximately 25% higher CL/BW than did older children. Normalization of CL for allometric BW (BW(3/4)) removed its relationship to age. CONCLUSION: The relationship between CL and allometric BW is consistent with a gradual reduction in relative liver size, until adult values, and a relatively constant CYP3A4 content in the liver from about 6-12 months of age to adulthood. Ciclosporin oral bioavailability, known previously to display large interindividual variability, is not influenced by age. These findings can enable better individualization of ciclosporin dosing in infants, children and adolescents.

A Pharmacometric Framework for Axitinib Exposure, Efficacy, and Safety in Metastatic Renal Cell Carcinoma Patients.

The relationships between exposure, biomarkers (vascular endothelial growth factor (VEGF), soluble VEGF receptors (sVEGFR)-1, -2, -3, and soluble stem cell factor receptor (sKIT)), tumor sum of longest diameters (SLD), diastolic blood pressure (dBP), and overall survival (OS) were investigated in a modeling framework. The dataset included 64 metastatic renal cell carcinoma patients (mRCC) treated with oral axitinib. Biomarker timecourses were described by indirect response (IDR) models where axitinib inhibits sVEGFR-1, -2, and -3 production, and VEGF degradation. No effect was identified on sKIT. A tumor model using sVEGFR-3 dynamics as driver predicted SLD data well. An IDR model, with axitinib exposure stimulating the response, characterized dBP increase. In a time-to-event model the SLD timecourse predicted OS better than exposure, biomarker- or dBP-related metrics. This type of framework can be used to relate pharmacokinetics, efficacy, and safety to long-term clinical outcome in mRCC patients treated with VEGFR inhibitors. (ClinicalTrial.gov identifier NCT00569946.).

Implications for Drug Characterization in Glucose Tolerance Tests Without Insulin: Simulation Study of Power and Predictions Using Model-Based Analysis.

In antihyperglycemic drug development, drug effects are usually characterized using glucose provocations. Analyzing provocation data using pharmacometrics has shown powerful, enabling small studies. In preclinical drug development, high power is attractive due to the experiment sizes; however, insulin is not always available, which potentially impacts power and predictive performance. This simulation study was performed to investigate the implications of performing model-based drug characterization without insulin. The integrated glucose-insulin model was used to simulate and re-estimated oral glucose tolerance tests using a crossover design of placebo and study compound. Drug effects were implemented on seven different mechanisms of action (MOA); one by one or in two-drug combinations. This study showed that exclusion of insulin may severely reduce the power to distinguish the correct from competing drug effect, and to detect a primary or secondary drug effect, however, it did not affect the predictive performance of the model.

Item Response Theory to Quantify Longitudinal Placebo and Paliperidone Effects on PANSS Scores in Schizophrenia.

As biomarkers are lacking, multi-item questionnaire-based tools like the Positive and Negative Syndrome Scale (PANSS) are used to quantify disease severity in schizophrenia. Analyzing composite PANSS scores as continuous data discards information and violates the numerical nature of the scale. Here a longitudinal analysis based on Item Response Theory is presented using PANSS data from phase III clinical trials. Latent disease severity variables were derived from item-level data on the positive, negative, and general PANSS subscales each. On all subscales, the time course of placebo responses were best described with Weibull models, and dose-independent functions with exponential models to describe the onset of the full effect were used to describe paliperidone's effect. Placebo and drug effect were most pronounced on the positive subscale. The final model successfully describes the time course of treatment effects on the individual PANSS item-levels, on all PANSS subscale levels, and on the total score level.

Application of Item Response Theory to Modeling of Expanded Disability Status Scale in Multiple Sclerosis.

In this study, we report the development of the first item response theory (IRT) model within a pharmacometrics framework to characterize the disease progression in multiple sclerosis (MS), as measured by Expanded Disability Status Score (EDSS). Data were collected quarterly from a 96-week phase III clinical study by a blinder rater, involving 104,206 item-level observations from 1319 patients with relapsing-remitting MS (RRMS), treated with placebo or cladribine. Observed scores for each EDSS item were modeled describing the probability of a given score as a function of patients' (unobserved) disability using a logistic model. Longitudinal data from placebo arms were used to describe the disease progression over time, and the model was then extended to cladribine arms to characterize the drug effect. Sensitivity with respect to patient disability was calculated as Fisher information for each EDSS item, which were ranked according to the amount of information they contained. The IRT model was able to describe baseline and longitudinal EDSS data on item and total level. The final model suggested that cladribine treatment significantly slows disease-progression rate, with a 20% decrease in disease-progression rate compared to placebo, irrespective of exposure, and effects an additional exposure-dependent reduction in disability progression. Four out of eight items contained 80% of information for the given range of disabilities. This study has illustrated that IRT modeling is specifically suitable for accurate quantification of disease status and description and prediction of disease progression in phase 3 studies on RRMS, by integrating EDSS item-level data in a meaningful manner.

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.

Implementing Pharmacogenomics in Europe: Design and Implementation Strategy of the Ubiquitous Pharmacogenomics Consortium.

Despite scientific and clinical advances in the field of pharmacogenomics (PGx), application into routine care remains limited. Opportunely, several implementation studies and programs have been initiated over recent years. This article presents an overview of these studies and identifies current research gaps. Importantly, one such gap is the undetermined collective clinical utility of implementing a panel of PGx-markers into routine care, because the evidence base is currently limited to specific, individual drug-gene pairs. The Ubiquitous Pharmacogenomics (U-PGx) Consortium, which has been funded by the European Commission's Horizon-2020 program, aims to address this unmet need. In a prospective, block-randomized, controlled clinical study (PREemptive Pharmacogenomic testing for prevention of Adverse drug REactions [PREPARE]), pre-emptive genotyping of a panel of clinically relevant PGx-markers, for which guidelines are available, will be implemented across healthcare institutions in seven European countries. The impact on patient outcomes and cost-effectiveness will be investigated. The program is unique in its multicenter, multigene, multidrug, multi-ethnic, and multihealthcare system approach.

Model describing the relationship between pharmacokinetics and hematologic toxicity of the epirubicin-docetaxel regimen in breast cancer patients.

PURPOSE: The aims of the present study were (1) to characterize the pharmacokinetics of both component drugs and (2) to describe the relationship between the pharmacokinetics and the dose-limiting hematologic toxicity for the epirubicin (EPI)/docetaxel (DTX) regimen in breast cancer patients. PATIENTS AND METHODS: Forty-four patients with advanced disease received EPI and DTX every 3 weeks for up to nine cycles. The initial doses (EPI/DTX) were 75/70 mg/m(2). Based on leukocyte (WBC) and platelet counts, the subsequent doses were, stepwise, either escalated (maximum, 120/100 mg/m(2)) or reduced (minimum, 40/50 mg/m(2)). Hematologic toxicity was monitored in all patients, whereas pharmacokinetics was studied in 16 patients. A semiphysiological model, including physiological parameters as well as drug-specific parameters, was used to describe the time course of WBC count following treatment. RESULTS: In the final pharmacokinetic model, interoccasion variability was estimated to be less than interindividual variability in the clearances for both drugs. The sum of the individual EPI and DTX areas under concentration-time curve correlated stronger to WBC survival fraction than did the corresponding sum of doses. A pharmacokinetic-pharmacodynamic (PK-PD) model with additive effects of EPI and DTX could adequately describe the data. CONCLUSION: The final PK-PD model might provide a tool for calculation of WBC time course, and hence, for prediction of nadir day and duration of leukopenia in breast cancer patients treated with the EPI/DTX regimen.

Population analysis of the pharmacokinetics and the haematological toxicity of the fluorouracil-epirubicin-cyclophosphamide regimen in breast cancer patients.

PURPOSE: The aims of the study were (a) to characterise the pharmacokinetics (PK), including inter-individual variability (IIV) and inter-occasion variability (IOV) as well as covariate relationships and (b) to characterise the relationship between the PK and the haematological toxicity of the component drugs of the fluorouracil (5-FU)-epirubicin (EPI)-cyclophosphamide (CP) regimen in breast cancer patients. PATIENTS AND METHODS: Data from 140 breast cancer patients, either within one of different studies or in routine clinical management, were included in the analyses. The patients were all treated with the fluorouracil-epirubicin-cyclophosphamide (FEC) regimen every third week for 3-12 courses, either in standard doses, i.e. 600/60/600 mg/m(2) of 5-FU, EPI and CP, respectively, or according to a dose escalation/reduction protocol (tailored dosing). PK data were available from 84 of the patients, whereas time-courses of haematological toxicity were available from 87 patients. The data analysis was carried out using mixed effects models within the NONMEM program. RESULTS: The PK of 5-FU, EPI and 4-hydroxy-cyclophosphamide (4-OHCP), the active metabolite of CP, were described with a one-compartment model with saturable elimination, a three-compartment linear model and a two-compartment linear model, respectively. No clinical significant correlation was found between PK across drugs. The unexplained variability in clearance was found to be less within patients, between courses (inter-occasion variability, IOV) than between patients (inter-individual variability, IIV) for EPI and 5-FU. For 4-OHCP, however, the IIV diminished by approximately 45% when significant covariates were included and the final population model predicts an IIV that is equal to IOV. Significant covariates for elimination capacity parameters were serum albumin (5-FU, EPI and 4-OHCP), creatinine clearance (5-FU), bilirubin (EPI) and body surface area (BSA) (4-OHCP). Elimination capacity of 5-FU and EPI was not related to BSA and for none of the studied drugs did body weight explain the PK variability. The time-course of haematological toxicity after treatment was well described by a semi-physiological model that assumes additive haematological toxicity between CP and EPI with negligible contribution from 5-FU. The influence of G-CSF could be incorporated into the model in a mechanistic manner as shortening the maturation time to 43% of the normal duration and increasing the mitotic activity to 269% of normal activity. CONCLUSIONS: The models presented describe the dose-concentration-toxicity relationships for the FEC therapy and may provide a basis for implementation and comparison of different individualisation strategies based on covariates, therapeutic drug monitoring and/or pharmacodynamic (PD) feedback. The PD model extends on previous semi-mechanistic models in that it also takes G-CSF administration into account.