Comparison of some practical sampling strategies for population pharmacokinetic studies

Impact of pharmacokinetic-pharmacodynamic model linearization on the accuracy of population information matrix and optimal design

Influence of experimental design on hyperparameter estimates precision when performing a population pharmacokinetic-pharmacodynamic (PK-PD) analysis has been shown by several studies and various approaches have been proposed for optimizing or evaluating such designs. Some of these methods rely on the optimization of a suitable scalar function of the population information matrix. Unfortunately for the nonlinear models encountered in pharmacokinetics or pharmacodynamics the latter is particularly difficult to evaluate. Under some assumptions and after a linearization of the PK-PD model a closed form of this matrix can be obtained which considerably simplifies its calculation but leads to an approximation. The aim of this paper is to evaluate the quality of the latter and its potential impact, when comparing or optimizing population designs and to relate it to Bates and Watts curvature measures. Two models commonly used in PK-PD were considered and nominal hyperparameter values when chosen for each one. Several population designs were studied and the associated population information matrix was computed for each using the approximate procedure and also using a reference method. Design optimizations were calculated under constraints for each model from the reference and approximate population information matrix. Nonlinearity curvatures were also computed for every model and design. The impact of model linearization when calculating the population information matrix was then examined in terms of lower bound accuracies on the hyperparameter estimates, design criterion variation, as well as D-optimal population designs, these results being related to nonlinearity curvature measures. Our results emphasize the influence of the parameter effects curvature when deriving the lower bounds of the hyperparameter estimates precision for a given design from the approximate population information matrix especially for hyperparameters quantifying the PK-PD interindividual variability. No discrepancies were detected between the population D-optimal designs obtained from the approximate and reference matrix despite some minor differences in criterion variation with respect to the design. More pronounced differences were, however, observed when comparing the amplitudes of criterion variation which can lead to errors when calculating design efficiencies. From a practical point of view, a strategy easily applicable by the pharmacokineticist for avoiding such problems in the context of population design optimization or comparison is then proposed.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.

The role of population pharmacokinetics in drug development in light of the Food and Drug Administration's 'Guidance for Industry: population pharmacokinetics'

Population pharmacokinetics (PPK) has evolved from a discipline primarily applied to therapeutic drug monitoring to one that plays a significant role in clinical pharmacology in general and drug development in particular. In February 1999 the US Food and Drug Administration issued a 'Guidance for Industry: Population Pharmacokinetics' that sets out the mechanisms and philosophy of PPK and outlines its role in drug development. The application of PPK to the drug development process plays an important role in the efficient development of safe and effective drugs. PPK knowledge is essential for mapping the response surface, explaining subgroup differences, developing and evaluating competing dose administration strategies, and as an aid in designing future studies. The mapping of the response surface is done to maximise the benefit-risk ratio, so that the impact of the input profile and dose magnitude on beneficial and harmful pharmacological effects can be understood and applied to individual patients. PPK combined with simulation methods provides a tool for estimating the expected range of concentrations from competing dose administration strategies. Once extracted, this knowledge can be applied to labelling or used to assess various future study designs. PPK should be implemented across all phases of drug development. For preclinical studies, PPK can be applied to allometric scaling and toxicokinetic analyses, and is useful for determining 'first time in man' doses and explaining toxicological results. Phase I studies provide initial understanding of the structural model and the effect of possible covariates, and may later be used to evaluate PPK differences between patients and healthy individuals. Phase II studies provide the greatest opportunity to map the response surface. With these PPK models it is possible to gain an improved understanding of the role of the dose on the response surface and of the range of expected responses. In phase III and IV studies, PPK is implemented to further refine the PPK model and to explain unexpected responses. Planning for the implementation of PPK across all phases of drug development is necessary, as well as planning for individual PPK studies. Planning should include: defining important questions, identifying covariates and drug-drug interactions that need to be investigated, and identifying the applications and intended use of the model(s). The plan for each project must have a strategy for data management, data collection, data quality assurance, staff training for data collection, data analysis and model validation.

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.

Inter-study variability in population pharmacokinetic meta-analysis: when and how to estimate it?

Population pharmacokinetic analysis is being increasingly applied to individual data collected in different studies and pooled in a single database. However, individual pharmacokinetic parameters may change randomly from one study to another. In this article, we show by simulation that neglecting inter-study variability (ISV) does not introduce any bias for the fixed parameters or for the residual variability but may result in an overestimation of inter-individual (IIV) variability, depending on the magnitude of the ISV. Two random study-effect (RSE) estimation methods were investigated: (i) estimation, in a single step, of the three-nested random effects (inter-study, inter-individual and residual variability); (ii) estimation of residual variability and a mixture of ISV and IIV in the first step, then separation of ISV from IIV in the second. The one-stage RSE model performed well for population parameter assessment, whereas, the two-stage model yielded good estimates of IIV only with a rich sampling design. Finally, irrespective of the method used, ISV estimates were valid only when a large number of studies was pooled. The analysis of one real data set illustrated the use of an ISV model. It showed that the fixed parameter estimates were not modified, whether an RSE model was used or not, probably because of the homogeneity of the experimental designs of the studies, and suggest no study-effect in this example.

Population pharmacokinetics of methylphenidate in children with attention-deficit hyperactivity disorder

Sources of individual variation in plasma methylphenidate (MP) concentrations during usual clinical use are not established. This was evaluated in a series of patients receiving clinical treatment with MP. A single plasma MP concentration was determined in each of 273 children and adolescents ages 5 to 18 years (mean: 11.1 years) who were clinically good responders to MP for the treatment of attention-deficit hyperactivity disorder. MP was given on a twice-daily schedule (mean dose: 25 mg/day) in 40% of patients and three times daily (mean dose: 39.3 mg/day) in 60%. A nonlinear regression model was applied to estimate overall population values of MP clearance and elimination half-life (t1/2), assuming a one-component model with first-order absorption and elimination, and further assuming that clearance is linearly related to body weight. The model incorporated each patient's dosage size and schedule, body weight, and time of the plasma sample. Iterated solutions of best fit were: t1/2, 4.5 hours (95% confidence interval [CI]: 3.1-8.1 hours), and apparent clearance, 90.7 ml/min/kg (95% CI: 74.6-106.7 ml/min/kg). The model explained 43% of the overall variance in MP concentrations (r2 = 0.43, p < .001). In a small subsample (N = 16), a second plasma sample was drawn at the same time of day and at the same dose; the correlation between the two concentration values was 0.83. The relatively noninvasive approach used in this study allows the assessment of pharmacokinetic properties of medications under conditions of appropriate clinical use in special populations such as children, adolescents, and the elderly.

Robust optimal design for the estimation of hyperparameters in population pharmacokinetics

The expectation of the determinant of the inverse of the population Fisher information matrix is proposed as a criterion to evaluate and optimize designs for the estimation of population pharmacokinetic (PK) parameters. Given a PK model, a measurement error model, a parametric distribution of the parameters and a prior distribution representing the belief about the hyperparameters to be estimated, the EID criterion is minimized in order to find the optimal population design. In this approach, a group is defined as a number of subjects to whom the same sampling schedule (i.e., the number of samples and their timing) is applied. The constraints, which are defined a priori, are the number of groups, the size of each group and the number of samples per subject in each group. The goal of the optimization is to determine the optimal sampling times in each group. This criterion is applied to a one-compartment open model with first-order absorption. The error model is either homoscedastic or heteroscedastic with constant coefficient of variation. Individual parameters are assumed to arise from a lognormal distribution with mean vector M and covariance matrix C. Uncertainties about the M and C are accounted for by a prior distribution which is normal for M and Wishart for C. Sampling times are optimized by using a stochastic gradient algorithm. Influence of the number of different sampling schemes, the number of subjects per sampling schedule, the number of samples per subject in each sampling scheme, the uncertainties on M and C and the assumption about the error model and the dose have been investigated.

The application of population pharmacokinetics to the drug development process

Population pharmacokinetics is playing an increasing role in clinical drug development. An overview of the population approach, including software and the advantages and limitations of the approach compared to the traditional approach to pharmacokinetic studies, is given. This paper also documents how the area has evolved over the past 15 years and addresses some of the issues that have arisen over the design and conduct of population studies. Finally, some alternative applications of the population approach are given for areas other than clinical drug development.

Optimal statistical design for toxicokinetic studies

Optimal statistical design strategies are applied to toxicokinetic experiments, for determining proper allocations of subjects and/or spacings of sampling times under a variety of nonlinear concentration-time models. The strategies include: (i) optimal allocations of subjects assuming the placement of time points is fixed, (ii) optimal spacing of design time points while assuming an equal allocation of subjects per time points and (iii) allocations/time-point spacings optimized jointly. Emphasis is placed on the first case, where a variance-minimization method is illustrated for optimizing the allocations when estimating specific toxicokinetic parameters. Appeals to forms of D-optimality are also considered, for cases when no specific toxicokinetic parameter is of specialized interest.