Pascal Girard

Modelling Response Time Profiles in the Absence of Drug Concentrations: Definition and Performance Evaluation of the K–PD Model

The plasma concentration–time profile of a drug is essential to explain the relationship between the administered dose and the kinetics of drug action. However, in some cases such as in pre-clinical pharmacology or phase-III clinical studies where it is not always possible to collect all the required PK information, this relationship can be difficult to establish. In these circumstances several authors have proposed simple models that can analyse and simulate the kinetics of the drug action in the absence of PK data. The present work further develops and evaluates the performance of such an approach. A virtual compartment representing the biophase in which the concentration is in equilibrium with the observed effect is used to extract the (pharmaco)kinetic component from the pharmacodynamic data alone. Parameters of this model are the elimination rate constant from the virtual compartment (KDE), which describes the equilibrium between the rate of dose administration and the observed effect, and the second parameter, named EDK50 which is the apparent in vivo potency of the drug at steady state, analogous to the product of EC50, the pharmacodynamic potency, and clearance, the PK “potency” at steady state. Using population simulation and subsequent (blinded) analysis to evaluate this approach, it is demonstrated that the proposed model usually performs well and can be used for predictive simulations in drug development. However, there are several important limitations to this approach. For example, the investigated doses should extend from those producing responses well below the EC50 to those producing ones close to the maximum response, optimally reach steady state response and followed until the response returns to baseline. It is shown that large inter-individual variability on PK–PD parameters will produce biases as well as large imprecision on parameter estimates. It is also clear that extrapolations to dosage routes or schedules other than those used to estimate the parameters should be undertaken with great caution (e.g., in case of non-linearity or complex drug distribution). Consequently, it is advised to apply this approach only when the underlying structural PD and PK are well understood. In any case, K–PD model should definitively not be substituted for the gold standard PK–PD model when correct full model can and should be identified.

Evaluation of uncertainty parameters estimated by different population PK software and methods.

The uncertainty associated with parameter estimations is essential for population model building, evaluation, and simulation. Summarized by the standard error (SE), its estimation is sometimes questionable. Herein, we evaluate SEs provided by different non linear mixed-effect estimation methods associated with their estimation performances. Methods based on maximum likelihood (FO and FOCE in NONMEMTM, nlme in SplusTM, and SAEM in MONOLIX) and Bayesian theory (WinBUGS) were evaluated on datasets obtained by simulations of a one-compartment PK model using 9 different designs. Bootstrap techniques were applied to FO, FOCE, and nlme. We compared SE estimations, parameter estimations, convergence, and computation time. Regarding SE estimations, methods provided concordant results for fixed effects. On random effects, SAEM and WinBUGS, tended respectively to under or over-estimate them. With sparse data, FO provided biased estimations of SE and discordant results between bootstrapped and original datasets. Regarding parameter estimations, FO showed a systematic bias on fixed and random effects. WinBUGS provided biased estimations, but only with sparse data. SAEM and WinBUGS converged systematically while FOCE failed in half of the cases. Applying bootstrap with FOCE yielded CPU times too large for routine application and bootstrap with nlme resulted in frequent crashes. In conclusion, FO provided bias on parameter estimations and on SE estimations of random effects. Methods like FOCE provided unbiased results but convergence was the biggest issue. Bootstrap did not improve SEs for FOCE methods, except when confidence interval of random effects is needed. WinBUGS gave consistent results but required long computation times. SAEM was in-between, showing few under-estimated SE but unbiased parameter estimations.

A model of vascular tumour growth in mice combining longitudinal tumour size data with histological biomarkers

Optimising the delivery of antiangiogenic drugs requires the development of drug-disease models of vascular tumour growth that incorporate histological data indicative of cytostatic action. In this study, we formulated a model to analyse the dynamics of tumour progression in nude mice xenografted with HT29 or HCT116 colorectal cancer cells. In 30 mice, tumour size was periodically measured, and percentages of hypoxic and necrotic tissue were assessed using immunohistochemistry techniques on tumour samples after euthanasia. The simultaneous analysis of histological data together with longitudinal tumour size data prompted the development of a semi-mechanistic model integrating random effects of parameters. In this model, the peripheral non-hypoxic tissue proliferates according to a generalised-logistic equation where the maximal tumour size is represented by a variable called carrying capacity. The ratio of the whole tumour size to the carrying capacity was used to define the hypoxic stress. As this stress increases, non-hypoxic tissue turns hypoxic. Hypoxic tissue does not stop proliferating, but hypoxia constitutes a transient stage before the tissue becomes necrotic. As the tumour grows, the carrying capacity increases owing to the process of angiogenesis. The model is shown to correctly predict tumour growth dynamics as well as percentages of necrotic and hypoxic tissues within the tumour. We show how the model can be used as a theoretical tool to investigate the effects of antiangiogenic treatments on tumour growth. This model provides a tool to analyse tumour size data in combination with histological biomarkers such as the percentages of hypoxic and necrotic tissue and is shown to be useful for gaining insight into the effects of antiangiogenic drugs on tumour growth and composition.

Etoposide pharmacokinetics and survival in patients with small cell lung cancer: A multicentre study

PURPOSEnTo investigate the prognostic value of systemic exposure to etoposide (Area Under the concentration Curve (AUC(VP16))) on overall survival (OS) in patients with small cell lung cancer (SCLC).nnnPATIENTS AND METHODSnData from 52 patients with limited stage (n=17) or metastatic (n=35) SCLC were analysed. They received at least two courses of etoposide (120mg/(m(2)day) on 3 days) combined with either doxorubicin-ifosfamide (AVI, n=29) or platinum compounds (carboplatin: n=16; cisplatin: n=7). Population pharmacokinetic-pharmacodynamic (PK-PD) study was performed using NON-linear Mixed Effect Model (NONMEM) and Splus software with univariate and multivariate analyses.nnnRESULTSnEtoposide plasma concentration vs. time was described by a two compartment model. Etoposide clearance (CL) was significantly dependant on serum creatinine (Scr). Ifosfamide (IFO) coadministration increased etoposide clearance by 28% (median CL(VP16): 2.42L/h vs. 1.89L/h, p<0.0005) leading to a reduced systemic exposure (median AUC(VP16): 260mgh/L vs. 339mgh/L). No influence of body surface area (BSA) on CL(VP16) was observed. Median percent decrease of absolute neutrophil count (ANC) after the first chemotherapy course was greater when etoposide 24h concentration was above 0.33mg/L (88% vs. 0%, p=0.028). Median OS was significantly longer in patients treated without ifosfamide (11.0 months vs. 7.0 months, p=0.049) and in patients with CL(VP16)<2.22L/h (14 months vs. 7 months, p=0.013) and AUC(VP16)>254.8mgh/L (11 months vs. 7 months, p=0.048). The independent prognostic factors regarding OS were LDH, CL(VP16) and AUC(VP16).nnnCONCLUSIONnIn this study it was found that CL(VP16) is reduced in patients with elevated serum creatinine, whilst ifosfamide coadministration increases CL(VP16) and reduces AUC(VP16), demonstrating the interaction between VP16 and ifosfamide. CL(VP16) and AUC(VP16) correlate significantly with overall survival of patients with SCLC patients receiving etoposide regimens.

Predictive values of hCG clearance for risk of methotrexate resistance in low-risk gestational trophoblastic neoplasias

BACKGROUNDnEarly identification of patients at high risk for chemoresistance among those treated with methotrexate (MTX) for low-risk gestational trophoblastic neoplasia (GTN) is needed. We modeled human chorionic gonadotropin (hCG) decline during MTX therapy using a kinetic population approach to calculate individual hCG clearance (CL(hCG)) and assessed the predictive value of CL(hCG) for MTX resistance.nnnPATIENTS AND METHODSnA total of 154 patients with low-risk GTN treated with 8-day MTX regimen were retrospectively studied. NONMEM was used to model hCG decrease equations between day 0 and day 40 of chemotherapy. Receiver operating characteristic curve analysis defined the best CL(hCG) threshold. Univariate/multivariate survival analyses determined the predictive value of CL(hCG) and compared it with published predictive factors.nnnRESULTSnA monoexponential equation best modeled hCG decrease: hCG(t) = 3900 x e(-0.149 x t). Median CL(hCG) was 0.57 l/day (quartiles: 0.37-0.74). Only choriocarcinoma pathology [yes versus no: hazard ratio (HR) = 6.01; 95% confidence interval (CI) 2.2-16.6; P < 0.001] and unfavorable CL(hCG) quartile (< or =0.37 versus >0.37 l/day: HR = 6.75; 95% CI 2.7-16.8; P < 0.001) were significant independent predictive factors of MTX resistance risk.nnnCONCLUSIONnIn the second largest cohort of low-risk GTN patients reported to date, choriocarcinoma pathology and CL(hCG) < or =0.37 l/day were major independent predictive factors for MTX resistance risk.

Physiologically Based Model of Acute Ischemic Stroke

In the treatment of acute ischemic stroke most of the clinical trials have failed, contrasting with promising results in the preclinical stages. This continuing discrepancy suggests some misconceptions in the understanding of acute ischemic stroke. One possible method for identifying the shortcomings of present-day approaches is to integrate all the available knowledge into a single mathematical model and to subject that model to challenges via simulations with available experimental data. As a first stage, then, the authors developed a simplified model, defining the structure and the different parameters that represent the phenomena that occur during the hyperacute phase of ischemic stroke. First, the different critical points of the evolution of ischemic stroke, based on the available evidence on the pathophysiology of stroke, were identified. Those key steps were then related to the quantitative data obtained by magnetic resonance imaging and positron emission tomography scan. These two techniques allow the measurement of diverse key markers of cerebral metabolism: cerebral blood flow (CBF), oxygen extraction factor, cerebral metabolism rate of oxygen, and the apparent diffusion coefficient of water, among others. Those markers were organized together through mathematical equations, and changed over time in order to describe the evolution of an acute ischemic stroke. At each time during the evolution of stroke those parameters are summarized in a parameter called survival delay. This parameter made possible the definition of three different states for tissues—functional, infarcted, salvageable—as end point. Once the model was designed, simulations were performed to explore its internal validity. Simulation results were consistent with the reality of acute ischemic stroke and did not reveal any major drawbacks in the use of the model. The more rapid the decrease in CBF, the larger is the final infarcted area. The model also allowed for the characterization of two types of tissue in the penumbra: tissues with an initial metabolic impairment and tissues altered owing to the closeness of the ischemic area. The results of this experiment were consistent with what is known of acute ischemic stroke. The model integrated different markers of acute ischemic stroke into a single entity in order to mimic acute ischemic stroke, and has been shown to have a reasonable degree of internal validity.

Population pharmacokinetics and pharmacodynamics of hydroxyurea in sickle cell anemia patients, a basis for optimizing the dosing regimen

BackgroundHydroxyurea (HU) is the first approved pharmacological treatment of sickle cell anemia (SCA). The objectives of this study were to develop population pharmacokinetic(PK)-pharmacodynamic(PD) models for HU in order to characterize the exposure-efficacy relationships and their variability, compare two dosing regimens by simulations and develop some recommendations for monitoring the treatment.MethodsThe models were built using population modelling software NONMEM VII based on data from two clinical studies of SCA adult patients receiving 500-2000 mg of HU once daily. Fetal hemoglobin percentage (HbF%) and mean corpuscular volume (MCV) were used as biomarkers for response. A sequential modelling approach was applied. Models were evaluated using simulation-based techniques. Comparisons of two dosing regimens were performed by simulating 10000 patients in each arm during 12 months.ResultsThe PK profiles were described by a bicompartmental model. The median (and interindividual coefficient of variation (CV)) of clearance was 11.6 L/h (30%), the central volume was 45.3 L (35%). PK steady-state was reached in about 35 days. For a given dosing regimen, HU exposure varied approximately fivefold among patients. The dynamics of HbF% and MCV were described by turnover models with inhibition of elimination of response. In the studied range of drug exposures, the effect of HU on HbF% was at its maximum (median Imax was 0.57, CV was 27%); the effect on MCV was close to its maximum, with median value of 0.14 and CV of 49%. Simulations showed that 95% of the steady-state levels of HbF% and MCV need 26 months and 3 months to be reached, respectively. The CV of the steady-state value of HbF% was about 7 times larger than that of MCV. Simulations with two different dosing regimens showed that continuous dosing led to a stronger HbF% increase in some patients.ConclusionsThe high variability of response to HU was related in part to pharmacokinetics and to pharmacodynamics. The steady-state value of MCV at month 3 is not predictive of the HbF% value at month 26. Hence, HbF% level may be a better biomarker for monitoring HU treatment. Continuous dosing might be more advantageous in terms of HbF% for patients who have a strong response to HU.Trial RegistrationThe clinical studies whose data are analysed and reported in this work were not required to be registered in France at their time. Both studies were approved by local ethics committees (of Mondor Hospital and of Kremlin-Bicetre Hospital) and written informed consent was obtained from each patient.

Model-based design of rituximab dosage optimization in follicular non-Hodgkin's lymphoma

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECTnThe concentration-effect relationship of rituximab in follicular lymphoma (FL) was previously described using pharmacokinetic-pharmacodynamic (PK-PD) modelling. The influence of genetic polymorphism of FCGR3A on rituximab efficacy in FL patients was included in this PK-PD model. Previous studies suggest that increasing the dose of rituximab and/or the number of infusions may lead to a better clinical response in FL.nnnWHAT THIS STUDY ADDSnThe previously validated PK-PD model can be used to design an optimized rituximab dose regimen in FL patients. Clinical trial simulation shows the potential clinical benefits of changes in rituximab dose. Optimization of the rituximab dose regimen cannot compensate for the lower response of FCGR3A-158F carriers compared with that of FCGR3A-158VV patients. AIMS Rituximab has dramatically improved the survival of patients with non-Hodgkins lymphoma (NHL). However, studies have suggested that the dose regimen currently used (i.e. 375u2003mgu2003m(-2) ) could be optimized. The aims of this study were to quantify the benefits of the new dose regimen for rituximab in follicular NHL (FL) patients using a previously validated PK-PD model and to design clinical trials investigating optimization of rituximab dosage.nnnMETHODSnA PK-PD model was used to predict progression-free survival (PFS) of FL patients treated by rituximab alone in asymptomatic FL, and those treated by rituximab combined with chemotherapy (R-CHOP) in relapsed/resistant FL. This model accounts for the influence of a polymorphism in FCGR3A, the gene encoding the FcγRIIIa receptor, on clinical efficacy. Several induction and maintenance dose regimens using rituximab alone or in combination with conventional chemotherapy (CHOP) were tested. The benefits of rituximab dose adjustment for F carriers were investigated. The numbers of subjects required for the design of two-armed clinical trials were calculated using model-predicted PFS at a power of 80%.nnnRESULTSnThe model predicted a potential benefit of 1500u2003mgu2003m(-2) maintenance doses of rituximab for both rituximab monotherapy and R-CHOP. The model shows that the PFS of FCGR3A-F carriers remains lower than that of homozygous FCGR3A-VV patients, even with markedly increased rituximab doses.nnnCONCLUSIONnOur results suggest a benefit of increasing doses of rituximab in FL, both during induction and maintenance. These results need to be confirmed in controlled clinical trials.

Predictors of prescription errors involving anticancer chemotherapy agents

AIMnThe majority of medication errors that harm patients relate to the prescribing process. Our study aimed to identify the predictors of prescription errors involving anticancer chemotherapy agents.nnnMETHODSnAll consecutive antineoplastic prescriptions from June 2006 to May 2008 were analysed, with medication errors being captured. Potential risk factors for medication prescribing errors were defined in relation to the patient, chemotherapy regimen and hospital organisation. The relationship between these risk factors and observed medication errors or dose medication errors was assessed by univariate and multivariate logistic-regression analyses.nnnRESULTSnAmong the 17,150 chemotherapy prescriptions, 540 contained at least one error (3.15%). The following independent predictors of risk of medication errors were identified: patients with a body surface area >2m(2) (odds ratio (OR): 1.3, 95% confidence interval (CI) 1.01-1.67, p=0.04), protocols with more than three drugs (OR: 1.91, 95%CI 1.59-2.31, p<0.001), protocols involving carboplatin (OR: 2.33, 95%CI 1.85-2.95, p<0.001), protocols requiring at least one modification by the physician (OR: 1.32, 95%CI 1.09-1.61, p=0.005), inpatient care (OR: 1.58, 95%CI 1.28-1.93, p<0.001) and prescriptions by a resident physician (OR: 1.83, 95%CI 1.50-2.22, p<0.001). The risk of medication dose prescribing errors was significantly associated with three independent factors: protocols involving carboplatin (OR: 4.47, 95%CI 3.45-5.79, p<0.001), protocols with more than three drugs (OR: 2.4, 95%CI 1.92-3.00, p<0.001) and protocols requiring at least one modification (OR: 1.33, 95%CI 1.04-1.69, p=0.02).nnnCONCLUSIONnIn this epidemiologic study, the independent risk factors identified should be targeted for preventive measures in order to improve anticancer agent prescriptions and reduce the risk of medication errors.

Development of a drug–disease simulation model for rituximab in follicular non‐Hodgkin's lymphoma

AIMnRituximab has dramatically improved the survival of patients with non-Hodgkins lymphomas (NHL), but the dosing regimen currently used should be optimized. However, the concentration-effect relationship of rituximab has never been described by pharmacokinetic-pharmacodynamic (PK-PD) modelling, precluding the simulation of new dosing regimens. The aim of this study was to develop a PK-PD model of rituximab in relapsed/resistant follicular NHL (FL).nnnMETHODSnA model describing the relationship between rituximab concentrations and progression-free survival (PFS) was developed using data extracted from the pivotal study, which evaluated 151 relapsed/resistant FL patients. The influence of FCGR3A genetic polymorphism on the efficacy of rituximab was quantified using data from 87 relapsed/resistant FL patients. The predictive performance of the model was analysed using two independent datasets: a study that evaluated rituximab combined with chemotherapy [rituximab, cyclophosphamide, vincristine, adriamycin and prednisone (R-CHOP)] in 334 relapsed/resistant FL patients and a study that evaluated rituximab monotherapy in 47 asymptomatic FL patients with known FCGR3A genotype.nnnRESULTSnFor R-CHOP, observed and model-predicted PFS (90% confidence interval) at 24 months were 0.50 and 0.48 (0.40, 0.56), respectively, for the observation arm, and 0.62 and 0.59 (0.50, 0.65), respectively, for the rituximab maintenance arm. For rituximab monotherapy, observed and predicted PFS at 24 months were 0.67 and 0.63, respectively, for FCGR3A-V/V patients, and 0.41 and 0.36 (0.25, 0.49), respectively, for FCGR3A-F carriers.nnnCONCLUSIONSnOur model provides a satisfactory prediction of PFS at 24 months. It can be used to simulate new dosing regimens of rituximab in populations of FL patients and should improve the design of future clinical trials.