Gordon Graham

Combining MCMC with 'sequential' PKPD modelling

We introduce a method for preventing unwanted feedback in Bayesian PKPD link models. We illustrate the approach using a simple example on a single individual, and subsequently demonstrate the ease with which it can be applied to more general settings. In particular, we look at the three ‘sequential’ population PKPD models examined by Zhang et al. (J Pharmacokinet Pharmacodyn 30:387–404, 2003; J Pharmacokinet Pharmacodyn 30:405–416, 2003), and provide graphical representations of these models to elucidate their structure. An important feature of our approach is that it allows uncertainty regarding the PK parameters to propagate through to inferences on the PD parameters. This is in contrast to standard two-stage approaches whereby ‘plug-in’ point estimates for either the population or the individual-specific PK parameters are required.

Modeling and simulation for clinical trial design involving a categorical response : A phase II case study with naratriptan

AbstractPurpose. The overall aim of the present study was to investigate retrospectively the feasibility and utility of model-based clinical trial simulation as applied to the clinical development of naratriptan with effect measured on a categorical scale. Methods. A PK-PD model for naratriptan was developed by using information gathered from previous naratriptan and sumatriptan preclinical and clinical trials. The phase IIa naratriptan data were used to check the PK-PD model in its ability to describe future data. A further PK-PD model was developed by using the phase IIa naratriptan data, and a phase IIb trial was designed by simulation with the use of Matlab. The design resulting from clinical trial simulation was compared with that derived by using D-optimal design. Results. The PK-PD model showed reasonable agreement with the data observed in the phase IIa naratriptan clinical trial. Clinical trial simulation resulted in a design with four or five arms at 0 mg, 2.5 and/or 5 mg, 10 mg, and 20 mg, PD measurements to be taken at 0, 2, and 4 or 6 h and at least 150 patients per arm. A sub-D-optimal design resulted in two dosing arms at 0 and 10 mg and PD measurements to be taken at 1 and 2 h. Conclusions. Clinical trial simulation is a useful tool for the quantitative assessment of the influence of the controllable factors and is the only tool for the quantitative assessment of the uncontrollable factors on the power of a clinical trial.

The use of a modified Fedorov exchange algorithm to optimise sampling times for population pharmacokinetic experiments

We propose a new algorithm for optimising sampling times for population pharmacokinetic experiments using D-optimality. The algorithm was used in conjunction with the population Fisher information matrix as implemented in MATLAB (PFIM 1.1 and 1.2) to evaluate population pharmacokinetic designs. The new algorithm based on the classical Fedorov exchange algorithm optimises the determinant of the population Fisher information matrix. The performance of the new algorithm has been compared with other existing algorithms including simplex, simulated annealing and adaptive random search. The new algorithm performed better especially when dealing with complex designs at the expense of longer computing times.

Determination of an optimal dosage regimen using a Bayesian decision analysis of efficacy and adverse effect data

One of the aims of Phase II clinical trials is to determine the dosage regimen(s) that will be investigated during a confirmatory Phase III clinical trial. During Phase II, pharmacodynamic data are collected that enables the efficacy and safety of the drug to be assessed. It is proposed in this paper to use Bayesian decision analysis to determine the optimal dosage regimen based on efficacy and toxicity of the drug oxybutynin used in the treatment of urinary urge incontinence. Such an approach results in a general framework allowing modeling, inference and decision making to be carried out. For oxybutynin, the repeated measurement efficacy and toxicity data were modeled using nonlinear hierarchical models and inferences were based on posterior probabilities. The optimal decision in this problem was to determine the dosage regimen that maximized the posterior expected utility given the prior information on the model parameters and the patient response data. The utility function was defined using clinical opinion on the satisfactory levels of efficacy and toxicity and then combined by weighting the relative importance of each pharmacodynamic response. Markov chain Monte Carlo (MCMC) methodology implemented in WinBUGS 1.3 was used to obtain posterior estimates of the model parameters, probabilities and utilities.

Population pharmacokinetics and optimal design of paediatric studies for famciclovir

AIMS To develop a population pharmacokinetic model for penciclovir (famciclovir is a prodrug of penciclovir) in adults and children and suggest an appropriate dose for children. Furthermore, to develop a limited sampling design based on sampling windows for three different paediatric age groups (1-2, 2-5 and 5-12 years) using an adequate number of subjects for future pharmacokinetic studies. METHODS Penciclovir plasma data from six different adult and paediatric studies were supplied by Novartis. Population pharmacokinetic modelling was undertaken in NONMEM version VI. Simulations in MATLAB were used to select an oral paediatric dose that gives similar exposure to 500 mg in adults. Optimal sampling times and sampling windows were obtained in MATLAB and simulations in NONMEM were used to select adequate sample sizes for three paediatric age groups. RESULTS A two-compartment, first-order absorption model with an absorption lag time, allometric weight models on V(1), V(2) and Q, and an allometric weight model, age and creatinine clearance as covariates on CL adequately describe the pharmacokinetics of penciclovir in adults and children. Estimated CL (l h(-1) 70 kg(-1)) and V(ss) (l.70 kg(-1)) were 31.2 and 83.1, respectively. An oral dose of 10 mg kg(-1) body weight in children was predicted to give similar exposure as 500 mg in adults. A single sampling windows design (0.25-0.4, 0.5-1, 1.25-1.75, 2.75-3.5 and 7.25-8 h) for five samples per subject and 10 subjects in each of the paediatric age groups is recommended for future studies. CONCLUSIONS A population pharmacokinetic model of penciclovir in adults and children has been developed. A prospective study design, including dose adjustment, cohort size and blood sampling design has been recommended.

Optimal Design for Multiresponse Pharmacokinetic–Pharmacodynamic Models – Dealing with Unbalanced Designs

This paper addresses the problem of determining D-optimal designs for multiresponse pharmacokinetic–pharmacodynamic (PKPD) experiments where data on each response variable can be collected at different times. Most previous multiresponse model optimal design applications have considered the case where all response variables are measured at the same time points. However in practice it may not be possible to have all responses measured at the same sampling times. We propose an optimal design method to take into account the unbalanced nature of the problem. The method developed was applied to a PKPD problem that involved describing the time course of drug plasma concentrations, heart rate and mean arterial blood pressure for both a fixed effects and mixed effects regression model. Additionally a simulation study was carried out in NONMEM for one such population optimal design problem.

Sample size calculations based on generalized estimating equations for population pharmacokinetic experiments.

ABSTRACT We present a method for calculating the sample size of a pharmacokinetic study analyzed using a mixed effects model within a hypothesis testing framework. A sample size calculation method for repeated measurement data analyzed using generalized estimating equations has been modified for nonlinear models. The Wald test is used for hypothesis testing of pharmacokinetic parameters. A marginal model for the population pharmacokinetic is obtained by linearizing the structural model around the subject specific random effects. The proposed method is general in that it allows unequal allocation of subjects to the groups and accounts for situations where different blood sampling schedules are required in different groups of patients. The proposed method has been assessed using Monte Carlo simulations under a range of scenarios. NONMEM was used for simulations and data analysis and the results showed good agreement.

Methodological approaches to the population analysis of toxicity data

Toxicokinetics is the assessment of systemic exposure in toxicity studies, in which pharmacokinetic data are generated, either as an integral component in the conduct of the nonclinical toxicity studies or in specially designed supportive studies, in order to assess systemic exposure. The data may be used in the interpretation of toxicity findings and contribute to the assessment of the relevance of these findings to clinical safety. Data may be obtained from all animals in a toxicity study, in representative subgroups, in satellite groups or in separate studies. Applying a mixed effects modelling approach in toxicokinetics offers many advantages over the current approach of having satellite groups. Sparse samples for measuring drug/metabolite concentration are collected in all main animals in the majority of studies where toxicological findings are obtained. Such sampling is unlikely to distress the animals, disturb the conduct of a toxicological study or affect the outcome of the study. Many of the outcome measures in toxicological studies are categorical in nature. For example, lesions may be scored on a one to four scale, from none to severe. The analysis of such data is usually carried out using a general mixed modelling approach. We have implemented such models in a nonlinear mixed effects modelling framework which allows us to relate pharmacokinetic response to outcome. A case study is used to illustrate the principles of general mixed effects modelling in toxicokinetics.

Incorporating Correlation in Interindividual Variability for the Optimal Design of Multiresponse Pharmacokinetic Experiments

This paper presents a method for optimal design of multiresponse population pharmacokinetic experiments taking into account correlations between interindividual variances. Expressions for the population Fisher information matrix have been defined for uniresponse and multiresponse pharmacokinetic experiments. A major assumption often made is that the variance–covariance matrix of the interindividual variance components has only diagonal elements so that whenever intersubject covariance elements are present, they are ignored during the design of the experiment. Recently expressions that accounted for these off diagonal elements were developed for uniresponse population pharmacokinetic experiments. The work presented here extends these expressions to multiresponse population pharmacokinetic experiments. These were applied to a population pharmacokinetic model, a population pharmacokinetic–pharmacodynamic model, and a parent–metabolite pharmacokinetic model example. The results obtained showed that optimal designs are different with diagonal omega matrix and full omega matrix and ignoring the off diagonal elements can lead to a design that produces more biased and less precise parameter estimates compared to a design that includes the off diagonal elements. The results also showed correlation between residual components of the responses has an effect on the optimal design.

A program for the optimum design of pharmacokinetic, pharmacodynamic, drug metabolism and drug-drug interaction models

Planning any experiment includes issues such as how many samples are to be taken and their location given some predictor variable. Often a model is used to explain these data; hence including this formally in the design will be beneficial for any subsequent parameter estimation and modelling. A number of criteria for model oriented experiments, which maximise the information content of the collected data are available. In this paper we present a program, Optdes, to investigate the optimal design of pharmacokinetic, pharmacodynamic, drug metabolism and drug-drug interaction models. Using the developed software the location of either a predetermined number of design points (exact designs) or together with the proportion of samples at each point (continuous designs) can be determined. Local as well as Bayesian designs can be optimised by either D- or A-optimality criteria. Although often the optimal design cannot be applied for practical reasons, alternative designs can be readily evaluated.