Nicky Best

WinBUGS – A Bayesian modelling framework: Concepts, structure, and extensibility

WinBUGS is a fully extensible modular framework for constructing and analysing Bayesian full probability models. Models may be specified either textually via the BUGS language or pictorially using a graphical interface called DoodleBUGS. WinBUGS processes the model specification and constructs an object-oriented representation of the model. The software offers a user-interface, based on dialogue boxes and menu commands, through which the model may then be analysed using Markov chain Monte Carlo techniques. In this paper we discuss how and why various modern computing concepts, such as object-orientation and run-time linking, feature in the softwares design. We also discuss how the framework may be extended. It is possible to write specific applications that form an apparently seamless interface with WinBUGS for users with specialized requirements. It is also possible to interface with WinBUGS at a lower level by incorporating new object types that may be used by WinBUGS without knowledge of the modules in which they are implemented. Neither of these types of extension require access to, or even recompilation of, the WinBUGS source-code.

The BUGS project: Evolution, critique and future directions

BUGS is a software package for Bayesian inference using Gibbs sampling. The software has been instrumental in raising awareness of Bayesian modelling among both academic and commercial communities internationally, and has enjoyed considerable success over its 20-year life span. Despite this, the software has a number of shortcomings and a principal aim of this paper is to provide a balanced critical appraisal, in particular highlighting how various ideas have led to unprecedented flexibility while at the same time producing negative side effects. We also present a historical overview of the BUGS project and some future perspectives.

A comparison of Bayesian spatial models for disease mapping

With the advent of routine health data indexed at a fine geographical resolution, small area disease mapping studies have become an established technique in geographical epidemiology. The specific issues posed by the sparseness of the data and possibility for local spatial dependence belong to a generic class of statistical problems involving an underlying (latent) spatial process of interest corrupted by observational noise. These are naturally formulated within the framework of hierarchical models, and over the past decade, a variety of spatial models have been proposed for the latent level(s) of the hierarchy. In this article, we provide a comprehensive review of the main classes of such models that have been used for disease mapping within a Bayesian estimation paradigm, and report a performance comparison between representative models in these classes, using a set of simulated data to help illustrate their respective properties. We also consider recent extensions to model the joint spatial distribution of multiple disease or health indicators. The aim is to help the reader choose an appropriate structural prior for the second level of the hierarchical model and to discuss issues of sensitivity to this choice.

Interpreting Posterior Relative Risk Estimates in Disease-Mapping Studies

There is currently much interest in conducting spatial analyses of health outcomes at the small-area scale. This requires sophisticated statistical techniques, usually involving Bayesian models, to smooth the underlying risk estimates because the data are typically sparse. However, questions have been raised about the performance of these models for recovering the “true” risk surface, about the influence of the prior structure specified, and about the amount of smoothing of the risks that is actually performed. We describe a comprehensive simulation study designed to address these questions. Our results show that Bayesian disease-mapping models are essentially conservative, with high specificity even in situations with very sparse data but low sensitivity if the raised-risk areas have only a moderate (< 2-fold) excess or are not based on substantial expected counts (> 50 per area). Semiparametric spatial mixture models typically produce less smoothing than their conditional autoregressive counterpart when there is sufficient information in the data (moderate-size expected count and/or high true excess risk). Sensitivity may be improved by exploiting the whole posterior distribution to try to detect true raised-risk areas rather than just reporting and mapping the mean posterior relative risk. For the widely used conditional autoregressive model, we show that a decision rule based on computing the probability that the relative risk is above 1 with a cutoff between 70 and 80% gives a specific rule with reasonable sensitivity for a range of scenarios having moderate expected counts (~ 20) and excess risks (~1.5- to 2-fold). Larger (3-fold) excess risks are detected almost certainly using this rule, even when based on small expected counts, although the mean of the posterior distribution is typically smoothed to about half the true value.

Bayesian analysis of population PK/PD models: general concepts and software.

Markov chain Monte Carlo (MCMC) techniques have revolutionized the field of Bayesian statistics by enabling posterior inference for arbitrarily complex models. The now widely used WinBUGS software has, over the years, made the methodology accessible to a great many applied scientists, in all fields of research. Despite this, serious application of MCMC methods within the field of population PK/PD has been comparatively limited. We appreciate that for many applied pharmacokineticists the prospect of conducting a Bayesian analysis will require numerous alien concepts to be taken on board and it may be difficult to justify investing the time and effort required in order to understand them (especially since the approach is so computer-intensive). For this reason we provide here a thorough (but often informal) discussion of all aspects of Bayesian inference as they apply specifically to population PK/PD. We also acknowledge that while the WinBUGS software is general purpose, model specification for some types of problem, population PK/PD being a prime example, can be very difficult, to the extent that a specialized interface for describing the problem at hand is often a practical necessity. In the latter part of this paper we describe such an interface, namely PKBugs. A principal aim of the paper is to offer sufficient technical background, in an easy to follow format, that the reader may develop both the confidence and know-how to make appropriate use of the PKBugs/WinBUGS framework (or similar software) for their own data analysis needs, should they choose to adopt a Bayesian approach.

Generic reversible jump MCMC using graphical models

Markov chain Monte Carlo techniques have revolutionized the field of Bayesian statistics. Their power is so great that they can even accommodate situations in which the structure of the statistical model itself is uncertain. However, the analysis of such trans-dimensional (TD) models is not easy and available software may lack the flexibility required for dealing with the complexities of real data, often because it does not allow the TD model to be simply part of some bigger model. In this paper we describe a class of widely applicable TD models that can be represented by a generic graphical model, which may be incorporated into arbitrary other graphical structures without significantly affecting the mechanism of inference. We also present a decomposition of the reversible jump algorithm into abstract and problem-specific components, which provides infrastructure for applying the method to all models in the class considered. These developments represent a first step towards a context-free method for implementing TD models that will facilitate their use by applied scientists for the practical exploration of model uncertainty. Our approach makes use of the popular WinBUGS framework as a sampling engine and we illustrate its use via two simple examples in which model uncertainty is a key feature.

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.

Use of space-time models to investigate the stability of patterns of disease.

Background The use of Bayesian hierarchical spatial models has become widespread in disease mapping and ecologic studies of health–environment associations. In this type of study, the data are typically aggregated over an extensive time period, thus neglecting the time dimension. The output of purely spatial disease mapping studies is therefore the average spatial pattern of risk over the period analyzed, but the results do not inform about, for example, whether a high average risk was sustained over time or changed over time. Objective We investigated how including the time dimension in disease-mapping models strengthens the epidemiologic interpretation of the overall pattern of risk. Methods We discuss a class of Bayesian hierarchical models that simultaneously characterize and estimate the stable spatial and temporal patterns as well as departures from these stable components. We show how useful rules for classifying areas as stable can be constructed based on the posterior distribution of the space–time interactions. We carry out a simulation study to investigate the sensitivity and specificity of the decision rules we propose, and we illustrate our approach in a case study of congenital anomalies in England. Results Our results confirm that extending hierarchical disease-mapping models to models that simultaneously consider space and time leads to a number of benefits in terms of interpretation and potential for detection of localized excesses.