David Lunn

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.

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.

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.

Gene Transfer Corrects Acute GM2 Gangliosidosis—Potential Therapeutic Contribution of Perivascular Enzyme Flow

The GM2 gangliosidoses are fatal lysosomal storage diseases principally affecting the brain. Absence of β-hexosaminidase A and B activities in the Sandhoff mouse causes neurological dysfunction and recapitulates the acute Tay-Sachs (TSD) and Sandhoff diseases (SD) in infants. Intracranial coinjection of recombinant adeno-associated viral vectors (rAAV), serotype 2/1, expressing human β-hexosaminidase α (HEXA) and β (HEXB) subunits into 1-month-old Sandhoff mice gave unprecedented survival to 2 years and prevented disease throughout the brain and spinal cord. Classical manifestations of disease, including spasticity-as opposed to tremor-ataxia-were resolved by localized gene transfer to the striatum or cerebellum, respectively. Abundant biosynthesis of β-hexosaminidase isozymes and their global distribution via axonal, perivascular, and cerebrospinal fluid (CSF) spaces, as well as diffusion, account for the sustained phenotypic rescue-long-term protein expression by transduced brain parenchyma, choroid plexus epithelium, and dorsal root ganglia neurons supplies the corrective enzyme. Prolonged survival permitted expression of cryptic disease in organs not accessed by intracranial vector delivery. We contend that infusion of rAAV into CSF space and intraparenchymal administration by convection-enhanced delivery at a few strategic sites will optimally treat neurodegeneration in many diseases affecting the nervous system.The GM2 gangliosidoses are fatal lysosomal storage diseases principally affecting the brain. Absence of β-hexosaminidase A and B activities in the Sandhoff mouse causes neurological dysfunction and recapitulates the acute Tay-Sachs (TSD) and Sandhoff diseases (SD) in infants. Intracranial coinjection of recombinant adeno-associated viral vectors (rAAV), serotype 2/1, expressing human β-hexosaminidase α (HEXA) and β (HEXB) subunits into 1-month-old Sandhoff mice gave unprecedented survival to 2 years and prevented disease throughout the brain and spinal cord. Classical manifestations of disease, including spasticity-as opposed to tremor-ataxia-were resolved by localized gene transfer to the striatum or cerebellum, respectively. Abundant biosynthesis of β-hexosaminidase isozymes and their global distribution via axonal, perivascular, and cerebrospinal fluid (CSF) spaces, as well as diffusion, account for the sustained phenotypic rescue-long-term protein expression by transduced brain parenchyma, choroid plexus epithelium, and dorsal root ganglia neurons supplies the corrective enzyme. Prolonged survival permitted expression of cryptic disease in organs not accessed by intracranial vector delivery. We contend that infusion of rAAV into CSF space and intraparenchymal administration by convection-enhanced delivery at a few strategic sites will optimally treat neurodegeneration in many diseases affecting the nervous system.

Markov Chain Monte Carlo Techniques for Studying Interoccasion and Intersubject Variability: Application to Pharmacokinetic Data

SUMMARY Values of pharmacokinetic parameters may seem to vary randomly between dosing occasions. An accurate explanation of the pharmacokinetic behaviour of a particular drug within a population therefore requires two major sources of variability to be accounted for, namely interoccasion variability and intersubject variability. A hierarchical model that recognizes these two sources of variation has been developed. Standard Bayesian techniques were applied to this statistical model, and a mathematical algorithm based on a Gibbs sampling strategy was derived. The accuracy of this algorithms determination of the interoccasion and intersubject variation in pharmacokinetic parameters was evaluated from various population analyses of several sets of simulated data. A comparison of results from these analyses with those obtained from parallel maximum likelihood analyses (NONMEM) showed that, forsimple problems, the outputs from the two algorithms agreed well, whereas for more complex situations the NONMEM approach may be less accurate. Statistical analyses of a multioccasion data set of pharmacokinetic measurements on the drug metoprolol (the measurements being of concentrations of drug in blood plasma from human subjects) revealed substantial interoccasion variability for all structural model parameters. For some parameters, interoccasion variability appears to be the primary source of pharmacokinetic variation.

Fully Bayesian hierarchical modelling in two stages, with application to meta‐analysis

Meta-analysis is often undertaken in two stages, with each study analysed separately in stage 1 and estimates combined across studies in stage 2. The study-specific estimates are assumed to arise from normal distributions with known variances equal to their corresponding estimates. In contrast, a one-stage analysis estimates all parameters simultaneously. A Bayesian one-stage approach offers additional advantages, such as the acknowledgement of uncertainty in all parameters and greater flexibility. However, there are situations when a two-stage strategy is compelling, e.g. when study-specific analyses are complex and/or time consuming. We present a novel method for fitting the full Bayesian model in two stages, hence benefiting from its advantages while retaining the convenience and flexibility of a two-stage approach. Using Markov chain Monte Carlo methods, posteriors for the parameters of interest are derived separately for each study. These are then used as proposal distributions in a computationally efficient second stage. We illustrate these ideas on a small binomial data set; we also analyse motivating data on the growth and rupture of abdominal aortic aneurysms. The two-stage Bayesian approach closely reproduces a one-stage analysis when it can be undertaken, but can also be easily carried out when a one-stage approach is difficult or impossible.

The pharmacokinetics of saquinavir: a Markov chain Monte Carlo population analysis.

Saquinavir is an HIV proteinase inhibitor marketed as a treatment for HIV infection. The drug has potent (Ki ∼ 0.1 nM) antiviral activity and acts by inhibiting the processing of gag and gagpol polyproteins, thus blocking the maturation of replicated viral particles. By assuming standard two-compartment disposition kinetics in combination with a variety of absorption processes we have identified two structural models that perform well with respect to describing the pharmacokinetic behavior of saquinavir when administered to healthy human volunteers from various Phase I studies. These structural models have been implemented for population analysis of these Phase I data via the Bayesian Markov chain Monte Carlo approach. We conclude that saquinavir exhibits complex and highly variable behavior, but can be modeled adequately using a two-compartment zero-order absorption model. There is also an indication that saquinavir kinetics may be time-dependent.

Bayesian hierarchical approach to estimate insulin sensitivity by minimal model.

We adopted Bayesian analysis in combination with hierarchical (population) modelling to estimate simultaneously population and individual insulin sensitivity (SI) and glucose effectiveness (SG) with the minimal model of glucose kinetics using data collected during insulin-modified intravenous glucose tolerance test (IVGTT) and made comparison with the standard non-linear regression analysis. After fasting overnight, subjects with newly presenting Type II diabetes according to World Health Organization criteria (n =65; 53 males, 12 females; age, 54 +/- 9 years; body mass index, 30.4 +/- 5.2 kg/m2; means+/-S.D.) underwent IVGTT consisting of a 0.3 g of glucose bolus/kg of body weight given at time zero for 2 min, followed by 0.05 unit of insulin/kg of body weight at 20 min. Bayesian inference was carried out using vague prior distributions and log-normal distributions to guarantee non-negativity and, thus, physiological plausibility of model parameters and associated credible intervals. Bayesian analysis gave estimates of SI in all subjects. Non-linear regression analysis failed in four cases, where Bayesian analysis-derived SI was located in the lower quartile and was estimated with lower precision. The population means of SI and SG provided by Bayesian analysis and non-linear regression were identical, but the interquartile range given by Bayesian analysis was tighter by approx. 20% for SI and by approx. 15% for SG. Individual insulin sensitivities estimated by the two methods were highly correlated ( rS=0.98; P <0.001). However, the correlation in the lower 20% centile of the insulin-sensitivity range was significantly lower than the correlation in the upper 80% centile ( rS=0.71 compared with rS=0.99; P <0.001). We conclude that the Bayesian hierarchical analysis is an appealing method to estimate SI and SG, as it avoids parameter estimation failures, and should be considered when investigating insulin-resistant subjects.