Designing population pharmacokinetic studies: performance of mixed designs.

The interplay of the following factors: population design (PDN), the cost function in terms of maximum cost (Max. C) (i.e., maximum number of samples/sample size), sample size, and intersubject variability [restricted (30%) to moderate (60%)] on the estimation of pharmacokinetic parameters from population pharmacokinetic data sets obtained using mixed designs was investigated in a simulation study. A two compartment model with multiple bolus intravenous inputs was assumed, and the residual variability was set at 15%. The sample size (N) investigated ranged from 30 to 200 with the associated cost function varying accordingly with the five individual and sixteen population designs studied. Accurate and precise estimates of structural model parameters were obtained for N > or = 50 (Max. C > or = 150) irrespective of the intersubject variability (ITV) and PDN investigated. When ITV was 30%, all structural model parameters were well estimated irrespective of the PDN. Robust estimates of clearance and its variability were obtained for all N at all levels of ITV with Max. C > or = 90 (PDN > or = 4). Imprecise estimates of ITV in V1, V2, and Q were obtained at 60% ITV irrespective of N, PDN, or Max. C. Positive bias was associated with the estimation of variability in V1, V2, and Q with PDN < or = 4 (Max. C < or = 150). This was due in part to a greater proportion of subjects sampled only once. Correspondingly, residual variability was underestimated. It is of utmost importance to avoid this artifact by ensuring that at least a moderate subset of subjects contributing data to a population pharmacokinetic study contribute data more than once. Given a sample size and ITV, the cost function must be considered in designing a population pharmacokinetic study using mixed designs.     

Factors affecting oral cyclosporin disposition after heart transplantation: bootstrap validation of a population pharmacokinetic model

Objective: To determine factors affecting the population pharmacokinetics of oral cyclosporin (CsA) in cardiac allograft recipients during the first 3 weeks after surgery. Methods: Data were obtained from routine trough monitoring and from two extra samples drawn during a dosing interval on a randomly selected day. Whole blood CsA concentrations were assayed using high-performance liquid chromatography (HPLC). Approximately equal numbers of patients were prescribed Sandimmun (SAN) or Neoral (NEO) CsA formulations. Parameter values of a one-compartment kinetic model with first-order absorption and elimination were sought together with the inter-patient and intra-patient variances using the NONMEM program. Results: Improved fits resulted from using the following expression in the model to adjust apparent bioavailability as a function of post-operative day (POD): f=0.2 + 10 × ABS (POD−5)/[(POD + 7) × 60]. The CsA clearance (CL/f ) was found to be influenced by current body weight (WT). There was an absorption lag time of about 35 min with SAN, but zero lag time with NEO. Oral bioavailability (f ) was increased by about 35% with concomitant diltiazem and about 18% with NEO. The CL/f was10% higher during the daytime than at night. The final pharmacokinetic model was validated using 200 bootstrap samples of the original data. Conclusions: Using a validated population modelling approach, it was found that a number of factors influence the pharmacokinetics of CsA during the early post-operative period in cardiac transplant patients. These influences affecting oral bioavailability and clearance may need to be taken into account for maintaining appropriate concentrations of CsA in the bloodstream. Received: 29 June 1999 / Accepted in revised form: 28 April 2000     

A computationally efficient approach for the design of population pharmacokinetic studies.

A computationally efficient procedure was devised for designing experiments in which population pharmacokinetic parameters are estimated. The method, referred to as the large-sample approach, evaluates the variances of parameter estimates for a population pharmacostatistical model. The procedure utilizes the NONMEM program and requires a single simulation that assumes many, say 1000, subjects. The approach reduced CPU time by about a factor of 50 when compared with the evaluation of the same variances by the direct simulation of experiments. The large-sample and simulation approaches yielded generally similar values for the variances of parameter estimates. The variances calculated by the large-sample approach were, in the case of a simple model, close to the expected variances. The proposed method identified correctly the imprecise parameter estimates but somewhat underestimated their variances.     

Practical recommendations for population PK studies with sampling time errors

Purpose

Population pharmacokinetic (PK) data collected from routine clinical practice offers a rich source of valuable information. However, in observational population PK data, accurate time information for blood samples is often missing, resulting in measurement errors (ME) in the sampling time variable. The goal of this study was to investigate the effects on model parameters when a scheduled time is used instead of the actual blood sampling time, and to propose ME correction methods.

Methods

Simulation studies were conducted based on two major factors: the curvature in PK profiles and the size of ME. As ME correction methods, transform both sides (TBS) models were developed with application of Box-Cox power transformation and Taylor expansion. The TBS models were compared to a conventional population PK model using simulations.

Results

The most important determinant of bias due to time ME was the degree of curvature (nonlinearity) in PK profiles; the smaller the curvature around sampling times, the smaller the associated bias. The second important determinant was the magnitude of ME; the larger the ME, the larger the bias. The proposed TBS models performed better than a conventional population PK modeling when curvature and ME were substantial.

Conclusions

Time ME in sampling time can lead to bias on the parameter estimators. The following practical recommendations are provided: 1) when the curvature of PK profiles is small, conventional population PK modeling is robust to even large ME; and 2) when the curvature is moderate or large, the proposed methodology reduces bias in parameter estimates.     

A note on population pharmacokinetic studies with a single sampling design

The choice of sampling time point in a population pharmacokinetic study with severe limitation on the number of samples per study subject (single sampling design) is critical in obtaining reliable parameter estimates. The authors have investigated the relationship between the timing as well as the degree of distribution of a sampling point among study subjects and the reliability of the estimates of pharmacokinetic parameters in a population pharmacokinetic study. This was achieved through a simulation, assuming an intravenously administered drug whose pharmacokinetic profile follows a 1-compartment model. The convergence rate of the NLMIXED procedure as well as the values of bias and MSE for the estimated parameters showed great variability depending on the sampling schedules. The results indicate that, in the case of a single sampling design, the sampling points should be distributed as widely as possible over a time range along the concentration-time profile to obtain reliable parameter estimates.     

A pragmatic approach to the design of population pharmacokinetic studies

The publication of a seminal article on nonlinear mixed-effect modeling led to a revolution in pharmacokinetics (PKs) with the introduction of the population approach. Since then, interest in obtaining accurate and precise estimates of population PK parameters has led to work on population PK study design that extended previous work on optimal sampling designs for individual PK parameter estimation. The issues and developments in the design of population PK studies are reviewed as a prelude to investigating, via simulation, the performance of 2 approaches (population Fisher information matrix D-optimal design and informative block [profile] randomized [IBR] design) for designing population PK studies. The results of our simulation study indicate that the designs based on the 2 approaches yielded efficient parameter estimates. The designs based on the 2 approaches performed similarly, and in some cases designs based on the IBR approach were slightly better. The ease with which the IBR designs can be generated makes them preferable in drug development, where pragmatism and time are of great consideration. We, therefore, refer to the IBR designs as pragmatic designs. Pragmatic designs that achieve high efficiency in the estimation parameters should be used in the design of population PK studies, and simulation should be used to determine the efficiency of the designs.     

A computationally efficient approach for the design of population pharmacokinetic studies

A computationally efficient procedure was devised for designing experiments in which population pharmacokinetic parameters are estimated. The method, referred to as the large-sample approach, evaluates the variances of parameter estimates for a population pharmacostatistical model. The procedure utilizes the NONMEM program and requires a single simulation that assumes many, say 1000, subjects. The approach reduced CPU time by about a factor of 50 when compared with the evaluation of the same variances by the direct simulation of experiments. The large-sample and simulation approaches yielded generally similar values for the variances of parameter estimates. The variances calculated by the large-sample approach were, in the case of a simple model, close to the expected variances. The proposed method identified correctly the imprecise parameter estimates but somewhat underestimated their variances.This work was supported by the Medical Research Council of Canada.     

Interrater agreement with a standard scheme for classifying medication errors.

PURPOSE: The interrater agreement for and reliability of the National Coordinating Council for Medication Error Reporting and Prevention (NCC MERP) index for categorizing medication errors were determined. METHODS: A letter was sent by the U.S. Pharmacopeia to all 550 contacts in the MEDMARX system user database. Participants were asked to categorize 27 medication scenarios using the NCC MERP index and were randomly assigned to one of three tools (the index alone, a paper-based algorithm, or a computer-based algorithm) to assist in categorization. Because the NCC MERP index accounts for harm and cost, and because categories could be interpreted as substantially similar, study results were analyzed after the nine error categories were collapsed to six. The interrater agreement was measured using Cohen's kappa value. RESULTS: Of 119 positive responses, 101 completed surveys were returned for a response rate of 85%. There were no significant differences in baseline demographics among the three groups. The overall interrater agreement for the participants, regardless of group assignment, was substantial at 0.61 (95% confidence interval [CI], 0.41-0.81). There was no difference among the kappa values of the three study groups and the tools used to aid in medication error classification. When the index was condensed from nine categories to six, the interrater agreement increased with a kappa value of 0.74 (95% CI, 0.56-0.90). CONCLUSION: Overall interrater agreement for the NCC MERP index for categorizing medication errors was substantial. The tool provided to assist with categorization did not influence overall categorization. Further refining of the scale could improve the usefulness and validity of medication error categorization.     

利用SPSS估算血管外给药的药动学参数

目的 利用SPSS估算血管外给药室模型的药动学参数。方法使用SPSS的非线性回归(nonlinear regression)拟合模拟的两室模型血管外给药的药-时数据;依据95％置信区间决定是否在模型中保留滞后时间(tlag)项。结果SPSS估算的药动学参数：住确可靠;根据tlag95％置信区间决定是否在模型中保留flag项是合理的。结论SPSS适用于估算血管外给药室模型的药动学参数。     

Closed-chamber inhalation pharmacokinetic studies with hexamethyldisiloxane in the rat

Gas uptake methods together with physiologically based pharmacokinetic (PBPK) modeling have been used to assess metabolic parameters and oral absorption rates for a wide variety of volatile organic compounds. We applied these techniques to study the in vivo metabolism of hexamethyldisiloxane (HMDS), a volatile siloxane with low blood/air (partition coefficient PB approximately 1.00) and high fat/blood partitioning (partition coefficient PF approximately 300). In contrast to other classes of metabolized volatiles, metabolic parameters could only be estimated from closed-chamber results with confidence by evaluating both closed-chamber disappearance curves and constant concentration inhalation studies. The constant-concentration inhalation results refine the estimate of the blood/air partition coefficient and constrain model structure for storage of the lipophilic compound in blood and tissues. The gas uptake results, from Fischer 344 rats (male, 8-9 wk old) exposed to initial HMDS air concentrations from 500 to 5000 ppm, were modeled with a 5-tissue PBPK model. Excellent fits were obtained with diffusion-limited uptake of HMDS in fat and a lipid storage pool in the blood. Metabolism, restricted to the liver, was described as a single saturable process (V(max) = 113.6 micro mol/h/kg; K(m) = 42.6 micro mol/L) and was affected by inhibitors (diethyldithiocarbamate) or inducers (phenobarbital) of cytochrome P-450s. Exhalation kinetics of HMDS after oral/intraperitoneal administration showed low bioavailability and significant lag times, also quite different from results of other classes of volatile hydrocarbons. In general, estimates of metabolic clearance by gas uptake studies were improved by simultaneous examination of time-course results from constant concentration inhalation studies. This conclusion is likely to hold for any volatile lipophilic compound with low blood/air partitioning.     

Review of pharmacokinetic and pharmacodynamic interaction studies with citalopram.

Citalopram is a selective serotonin reuptake inhibitor that is N-demethylated to N-desmethylcitalopram partially by CYP2C19 and partially by CYP3A4 and N-desmethylcitalopram is further N-demethylated by CYP2D6 to the likewise inactive metabolite di-desmethylcitalopram. The two metabolites are not active. The fact that citalopram is metabolised by more than one CYP means that inhibition of its biotransformation by other drugs is less likely. Besides citalopram has a wide margin of safety, so even if there was a considerable change in serum concentration then this would most likely not be of clinical importance. In vitro citalopram does not inhibit CYP or does so only very moderately. A number of studies in healthy subjects and patients have confirmed, that this also holds true in vivo. Thus no change in pharmacokinetics or only very small changes were observed when citalopram was given with CYP1A2 substrates (clozapine and therophylline), CYP2C9 (warfarin), CYP2C19 (imipramine and mephenytoin), CYP2D6 (sparteine, imipramine and amitriptyline) and CYP3A4 (carbamazepine and triazolam). At the pharmacodynamic level there have been a few documented cases of serotonin syndrome with citalopram and moclobemide and buspirone. It is concluded that citalopram is neither the source nor the cause of clinically important drug-drug interactions.     

Evaluation of methods for estimating population pharmacokinetic parameters. III. Monoexponential model: Routine clinical pharmacokinetic data

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual kinetic variability, and residual variability, including intraindividual variability and measurement error. Individual pharmacokinetics are estimated by fitting a pharmacokinetic model to individual data. Population pharmacokinetic parameters have traditionally been estimated by doing this separately for each individual, and then combining the individual parameter estimates, the Standard Two Stage (STS) approach. Another approach, NONMEM, appropriately pools data across individuals and is therefore less dependent on individual parameter estimates. This study provides further evidence of NONMEM's validity and usefulness by comparing both approaches on simulated routine-type pharmacokinetic data arising from a monoexponential model. The estimates of population parameters (notably those describing interindividual variability) provided by the STS method are poorer than those provided by NONMEM, especially when there is considerable residual error. Further, NONMEM's estimates of population parameters do not require that the data be restricted to special types of routine data such as those obtained only at steady state, or only at peak or trough, nor do the estimates improve with such data. NONMEM's estimates do improve, however, when a data set is enhanced by the addition of single-observation-per-individual type data. Thus, population parameters can be estimated efficiently from data that simulate real clinical pharmacokinetic conditions.     

Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-menten model: Routine clinical pharmacokinetic data

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual intraindividual variability plus measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters are estimated either by fitting all individual's data together as though there were no individual kinetic differences (the naive pooled data approach), or by fitting each individual's data separately, and then combining the individual parameter estimates (the two-stage approach). A third approach, NONMEM, takes a middle course between these, and avoids shortcomings of each of them. A data set consisting of 124 steady-state phenytoin concentration-dosage pairs from 49 patients, obtained in the routine course of their therapy, was analyzed by each method. The resulting population parameter estimates differ considerably (population mean Km, for example, is estimated as 1.57, 5.36, and 4.44 g/ml by the naive pooled data, two-stage, and NONMEM approaches, respectively). Simulations of the data were analyzed to investigate these differences. The simulations indicate that the pooled data approach fails to estimate variabilities and produces imprecise estimates of mean kinetics. The two-stage appproach produces good estimates of mean kinetics, but biased and imprecise estimates of interindividual variability. NONMEM produces accurate and precise estimates of all parameters, and also reasonable confidence intervals for them. This performance is exactly what is expected from theoretical considerations and provides empirical support for the use of NONMEM when estimating population pharmacokinetics from routine type patient data.Work supported in part by NIH Grants GM 26676 and GM 26691.     

Practical experience and issues in designing and performing population pharmacokinetic/pharmacodynamic studies

An expert meeting to discuss issues relating to the design of population pharmacokinetic/pharmacodynamic (PK/PD) studies was held in Brussels in March 1995, under the auspices of the European Co-operation in Science and Technology (COST), Medicine (B1) programme. The purpose of the meeting was to discuss the experts' experience in designing and performing population PK/PD studies. The topics discussed were current practice, logistical issues, ensuring the accuracy of data, covariate assessment, communication, and protocol design.The main conclusions from the meeting were: 1) a population PK/PD analysis should be one of the objectives of a clinical trial and should not compromise the other objectives; 2) it is particularly important to communicate the purpose of the population PK/PD analysis to the investigators and to convince them of the importance of accurately recording dosing and sampling times; 3) some prior knowledge of the PK and PD models and covariate relationships is necessary for the analysis of sparse phase III data; 4) computer simulation and optimal design measures may be useful in defining sampling times; 5) population methods and objectives must be specified as completely as possible in the protocol. Participants: L. Aarons (UK), L. Balant (Switzerland), P. Bechtel (France), R. Bruno (France), P. Burtin (Switzerland), C. Dubruc (France), E. Fuseau (UK), J. Gabrielsson (Sweden), U. Gundert-Remy (Germany), R. Jochemsen (France), M. Karlsson (Sweden), C. Laveille (France), I. Meineke (Germany), F. Mentré (France), P. Morselli (France), G. Paintaud (France), A. Racine-Poon (Switzerland), J. Rodriguez (Spain), F. Rombout (The Netherlands), M. Rowland (UK), J.-L. Steimer (Switzerland), A. Van Peer (Belgium), S. Vozeh (Switzerland), W. Weber (Germany), B. Wittke (Switzerland)The views expressed by the participants do not necessarily reflect those of the organizations they represent.All authors were members of the COST-B1 Working Party on Population Approaches     

Etoposide encapsulated in positively charged liposomes: pharmacokinetic studies in mice and formulation stability studies.

Etoposide is an antineoplastic agent which acts by forming a ternary complex with topoisomerase II and DNA, causing DNA breaks and cell death. In recent studies we have demonstrated that encapsulation in liposomes increases the antitumour efficacy and reduces the adverse effects associated with etoposide. The present study was thus conducted to evaluate whether encapsulation in cationic liposomes altered the pharmacokinetics of etoposide and to study the effect of cholesterol incorporation on the stability of the liposomes. Etoposide-encapsulated unilammellar liposomes were synthesized by thin film hydration followed by extrusion. The drug was administered to Swiss albino mice at a dose of 10 mg kg(-1). The concentration of the drug in plasma was analysed at different time points till 360 min after injection, using a h.p.l.c. method. The terbium chloride-dipicolinic acid interaction method was applied to study the stability of the formulation in mouse serum and also following storage at 0( composite function)C over a period of time. The effect of the free and liposomal drug on myelosuppression was evaluated at 10 mg m(-2)and 40 mg m(-2)dose levels by quantifying blood cell counts on day 15 and day 21 following a 5 day course of therapy. Encapsulation in cationic liposomes increased the area under the concentration vs time curve to 42.98 microghml(-1)from 24.18 microghml(-1)in the case of the free drug. Half-life (beta) was 58. 62 and 186 min in the case of free and liposomal etoposide, respectively. In the stability studies, incorporation of cholesterol progressively stabilized the formulation in serum. The use of sucrose at increasing concentrations as a cryoprotectant also increased the shelf stability of the formulation at 0( composite function)C. Toxicity studies using a dose of pure drug revealed that though myelosuppression was evident in both liposomal- and free drug-treated groups on day 15 it was reversed by day 21 following initiation of therapy. The present findings suggest that liposomes could serve as an alternative mode of delivery for etoposide.