WinBugs

Spiegelhalter D, Thomas A, Best N. 2000. WinBugs version 1.3 user manual. Available from http //www.nrc-bsu.cam.ac.uk/bug s... 

Lawson, Browne and Vidal Rodeiro Disease Mapping With WinBUGS and MLwiN Lui Statistical Estimation of Epidemiological Risk Marubini and Valsecchi Analysing Survival Data from Clinical Trials and Observation Studies... 

Duffull, S., Kirkpatrick, C., Green, B., and Holford, N., Analysis of population pharmacokinetic data using NONMEM and WinBUGS, Journal of Biopharmaceutical Statistics, Vol. 15, No. 1, 2005, pp. 53-73. 

Mixed effects models under a Bayesian framework have been widely studied and used with the use of Markov chain Monte Carlo methods (10). These methods have gained particular popularity as complex problems became easily formulated using the WinBUGS software (11). See Congdon (12) for an extensive coverage of topics and examples and implementation in WinBUGS. 

It is worth mentioning at this stage that the three-stage hierarchical model used in Bayesian analyses when undertaken within the framework provided by WinBUGS requires that normal distributions are parameterized as mean and precision. Precision is the inverse of variance. For example, when defining the prior for the population parameter vector 0, the multivariate normal distribution would be parameterized as the mean vector fi and the inverse of the variance-covariance matrix X such that,... 

This parameterization would also hold for Eq. (5.3), (5.4), and (5.6). Hereafter the notation of WinBUGS is adopted and where possible examples of WinBUGS code are provided. Readers are referred to Fryback et al. (8) for an introduction to WinBUGS (see especially the appendixes for reference to how to run WinBUGS), Duffull et al. (6) for an introductory population PK example, and Lunn et al. (9) for a more in-depth treatment. 

A more objective method is to investigate the Gelman-Rubin diagnostics for chain convergence. This procedure is automated within WinBUGS. This method compares the between-chains and within-chain variability in a similar spirit to an analysis of variance. Samples are required from at least two chains that are started... 

Many Bayesian analyses utilize so-called noninformative priors (see examples in the WinBUGS manual (17)). The principal belief underlying their wide utility is to retain objectivity in relation to the current analysis. Should prior evidence influence the analysis of the current experiment, then the objectivity of the current analysis may be questioned, due to the subjective nature of priors and methods for their elicitation. In a philosophical sense, it might also be argued that it is equally nonobjective to ignore all previous evidence, no matter how applicable or strong the evidence might be. 

Although there are a large number of methods that can be used for model discrimination, we only consider methods that can be implemented easily in WinBUGS (Version 1.4 or earlier) with minimal extra coding. 

Version 1.4 of WinBUGS greatly eases the computational burden by providing DIC as a standard output in the statistical samples toolbox. For users of Version 1.3, the complexity of the model (parameter wise) can more simply be calculated as half of the posterior variance of the deviance as... 

The mixture model is assessed for a hypothetical example and an example for WinBUGS code is given in Figure 5.2. Evaluation of the individual model predictions for one- and two-compartment models is shown on lines 5 and 7,... 

FIGURE 5.2 WinBUGS code (Version 1.3) for performing a mixture model. 

Uncertainty/Precision The hypothetical data sets were run with noninforma-tive priors (flat precision of 0.0001). The prior parameter means were set to the simulated means. The two competing models were lit simultaneously in WinBUGS Version 1.4 (17) as a mixture model with a mixing population parameter (mix— in the following notation mix is used in accordance with its use in the WinBUGS code shown in Figure 5.2) drawn from a uniform (0,1) distribution. 

S. B. Duffull, C. M. J. Kirkpatrick, B. Green, and N. H. G. Holford, Analysis of population pharmacokinetic data using NONMEM and WinBUGS. I Biopharm Stat 15 53-73 (2005). 

D. G. Fryback, N. K. Stout, and M. A. Rosenberg, An elementary introdnction to Bayesian computing using WinBUGS. Int I Tech Assess 17 98-113 (2001). 

D. J. Spiegelhalter, A. Thomas, and N. G. Best, WinBUGS Version 1.4 User Manual. Medical Research ConncU Biostatics Unit, Cambridge, UK, 2003. 

S. P. Riley, Pharmacokinetic model selection within a population analysis using NONMEM and WinBUGS, in AAPS Workshop on Bayesian Primer. AAPS, Sait Lake City, UT, 2003. 

Fryback DG, Stout NK, Rosenberg MA (2001) An elementary introduction to Bayesian computing using WinBUGS. International Journal of Technology Assessment in Health Care 17 98-113. 

Lambert PC, Sutton AJ, Bnrton PR, Abrams KR, Jones DR (2005) How vague is vague. A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS. Statistics in Medicine 24 2401-2428. 

BUGSAVinBUGS The distributions of structural parameters are used as inputs random interindividual effects are defined by parametric distributions as well. Markov Chain Monte Carlo (MCMC) methods are used to generate posterior probabilities. WinBUGS is the windows GUI-version of the DOS-based BUGS. 

A library of PK/PD models is available as well as user-defined models structural models may be defined via GUI (Doodle BUGS) in the WinBUGS program... 

Our Bayesian results were obtained in winBUGS, using two parallel chains of 50,000 MCMC samples after a 50,000-sample bum-in. Jones et al. (2011) recently published SAS code, enabling fitting roughly the same homogeneous... 

The use of Bayesian methods to conduct network meta-analysis is rapidly growing. For example, recent publications include the Evidence Synthesis Technical Support Documents series found on the website of the Decision Support Unit (DSU) of the National Institute for Health and Care Excellence [27]. The statistical methods used in these documents were primarily Bayesian, and WinBUGS was used as the main software platform for data analysis. The documents can be downloaded from the site http //www. nicedsu.org.uk/Evidence-Synthesis-TSD-series%282391675%29.htm. 

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