Jon Wakefield

The Bayesian Analysis of Population Pharmacokinetic Models

Abstract Pharmacokinetics is the study of the time course of a drug and its metabolites following its introduction into the body. Population pharmacokinetic studies are becoming increasingly important as an aid to drug development. The data from such studies typically consist of dose histories, drug concentrations with associated sampling times, and often covariate measurements such as the age and weight of each subject. These studies aim to provide an understanding of the pharmacokinetics of the drug in question and so lead to an informed choice of dosage regimen. Such an understanding includes determining those covariates that are important predictors of fundamental pharmacokinetic parameters, such as clearance, defined as the volume of plasma cleared of drug in a unit of time. Determining those subpopulations (e.g., the elderly) with altered kinetics has implications for the choice of an appropriate dosage regimens, because predictive concentration profiles arising from a particular regimen in differen...

Modelling daily multivariate pollutant data at multiple sites

This paper considers the spatiotemporal modelling of four pollutants measured daily at eight monitoring sites in London over a 4-year period. Such multiple-pollutant data sets measured over time at multiple sites within a region of interest are typical. Here, the modelling was carried out to provide the exposure for a study investigating the health effects of air pollution. Alternative objectives include the design problem of the positioning of a new monitoring site, or for regulatory purposes to determine whether environmental standards are being met. In general, analyses are hampered by missing data due, for example, to a particular pollutant not being measured at a site, a monitor being inactive by design (e.g. a 6-day monitoring schedule) or because of an unreliable or faulty monitor. Data of this type are modelled here within a dynamic linear modelling framework, in which the dependences across time, space and pollutants are exploited. Throughout the approach is Bayesian, with implementation via Markov chain Monte Carlo sampling. Copyright 2002 Royal Statistical Society.

ISSUES IN THE STATISTICAL ANALYSIS OF SMALL AREA HEALTH DATA

The availability of geographically indexed health and population data, with advances in computing, geographical information systems and statistical methodology, have opened the way for serious exploration of small area health statistics based on routine data. Such analyses may be used to address specific questions concerning health in relation to sources of pollution, to investigate clustering of disease or for hypothesis generation. We distinguish four types of analysis: disease mapping; geographic correlation studies; the assessment of risk in relation to a prespecified point or line source, and cluster detection and disease clustering. A general framework for the statistical analysis of small area studies will be considered. This framework assumes that populations at risk arise from inhomogeneous Poisson processes. Disease cases are then realizations of a thinned Poisson process where the risk of disease depends on the characteristics of the person, time and spatial location. Difficulties of analysis and interpretation due to data inaccuracies and aggregation will be addressed with particular reference to ecological bias and confounding. The use of errors-in-variables modelling in small area analyses will be discussed.

Population modelling in drug development.

In this paper we discuss the vital role that population (hierarchical) modelling can play within the drug development process. Specifically, population pharmacokinetic/pharmacodynamic models can provide reliable predictions of an individualized dose-exposure-response relationship. A predictive model of this kind can be used to simulate and hence design clinical trials, find initial dosage regimens satisfying an optimality criterion on the population distribution of responses, and individualized regimens satisfying such a criterion conditional on individual features, such as sex, age, etc. Throughout we emphasize prediction and advocate mechanistic as opposed to empirical modelling, and argue that the Bayesian approach is particularly natural in this setting.

The Bayesian Modeling of Covariates for Population Pharmacokinetic Models

Abstract Pharmacokinetic (PK) models describe how the concentrations of a drug and its metabolite vary with time. Population PK models identify and quantify sources of between-individual variability in observed concentrations. Crucial to this aim is the identification of those covariates (i.e., individual-specific characteristics) responsible for explaining the variability. In this article we discuss how covariate modeling can be carried out for population PK models. We argue that the importance of a particular covariate can be discussed only with reference to the specific use for which the model is intended. Covariate modeling is important in population PK studies as it aids in determining dosage recommendations for specific covariate-defined populations. We describe a Bayesian predictive procedure that places covariate modeling in the context of dosage determination. In problems such as these it is crucial to incorporate relevant prior information. For covariate selection we extend the approach of Georg...

Geographical epidemiology of prostate cancer in Great Britain

Prostate cancer incidence has increased during recent years, possibly linked to environmental exposures. Exposure to environmental carcinogens is unlikely to be evenly distributed geographically, which may give rise to variations in disease occurrence that is detectable in a spatial analysis. The aim of our study was to examine the spatial variation of prostate cancer in Great Britain at ages 45–64 years. Spatial variation was examined across electoral wards from 1975–1991. Poisson regression was used to examine regional, urbanisation and socioeconomic effects, while Bayesian mapping techniques were used to assess spatial variability. There was an indication of geographical differences in prostate cancer risk at a regional level, ranging from 0.83 (95% CI: 0.78–0.87) to 1.2 (95% CI: 1.1–1.3) across regions. There was significant heterogeneity in the risk across wards, although the range of relative risks was narrow. More detailed spatial analyses within 4 regions did not indicate any clear evidence of localised geographical clustering for prostate cancer. The absence of any marked geographical variability at a small‐area scale argues against a geographically varying environmental factor operating strongly in the aetiology of prostate cancer.

A comparison of a bayesian population method with two methods as implemented in commercially available software

In this paper we describe and discuss three specific estimation procedures that are available within commercially available population software packages. The first version of NONMEM (1) was released in 1979 and later versions are the standard analysis tools in both industry and academia. Recently, two commercially available pieces of software have become available. PPHARM was released during 1994 and POPKAN was released in 1995. We provide descriptions and critique the FOCE method within NONMEM, the two-step algorithm within PPHARM and the Markov chain Monte Carlo method that is utilized by POPKAN. We use simulated data generated from a monoexponential model to evaluate the parameter estimation capabilities of these methods within the three software tools. In particular we investigate the effect on parameter estimation of increasing both interindividual and intraindividual variability.

Statistical methods for population pharmacokinetic modelling.

A principal aim of population pharmacokinetic studies is to estimate the variance components associated with intra- and inter-individual variability in observed drug concentrations. The explanation of the inter-individual variability in terms of subject-specific covariates is also of great importance. Pharmacokinetic models are nonlinear in the parameters and estimation is not straightforward. Within this paper we review a number of estimation approaches which have been suggested for population pharmacokinetic analyses. We distinguish between Bayesian and non-Bayesian and fully-parametric, semi-parametric and nonparametric methods.

Bayesian individualization via sampling-based methods

We consider the situation where we wish to adjust the dosage regimen of a patient based on (in general) sparse concentration measurements taken on-line. A Bayesian decision theory approach is taken which requires, the specification of an appropriate prior distribution and loss function. A simple method for obtaining samples from the posterior distribution of the pharmacokinetic parameters of the patient is described. In general, these samples are used to obtain a Monte Carlo estimate of the expected loss which is then minimized with respect to the dosage regimen. Some special cases which yield analytic solutions are described. When the prior distribution is based on a population analysis then a method of accounting for the uncertainty in the population parameters is described. Two simulation studies showing how the methods work in practice are presented.

Ecological regression analysis of environmental benzene exposure and childhood leukaemia: sensitivity to data inaccuracies, geographical scale and ecological bias

Benzene is classified as a group 1 human carcinogen by the International Agency for Research on Cancer, and it is now accepted that occupational exposure is associated with an increased risk of various leukaemias. However, occupational exposure accounts for less than 1% of all benzene exposures, the major sources being cigarette smoking and vehicle exhaust emissions. Whether such low level exposures to environmental benzene are also associated with the risk of leukaemia is currently not known. In this study, we investigate the relationship between benzene emissions arising from outdoor sources (predominantly road traffic and petrol stations) and the incidence of childhood leukaemia in Greater London. An ecological design was used because of the rarity of the disease, the difficulty of obtaining individual level measurements of benzene exposure and the availability of data. However, some methodological difficulties were encountered, including problems of case registration errors, the choice of geographical areas for analysis, exposure measurement errors and ecological bias. We use a Bayesian hierarchical modelling framework to address these issues, and we investigate the sensitivity of our inference to various modelling assumptions.