Why should clinicians care about Bayesian methods?

There is a growing awareness of Bayesian methods within the medical research community, and increasing discussion of their potential applications. This interest has, however, so far failed to convert into the routine use of such methods by working clinicians. I argue that attempts to encourage the use of Bayesian methods by highlighting the deficiencies of conventional (frequentist) inference have not succeeded because these deficiencies typically have minor practical consequences, while their more serious effects can usually be explained away by appeal to other statistical issues. As a result, Bayesian methods have not appeared to offer practical pay-offs big enough to justify the cost of acquiring the necessary expertise. In an attempt to remove this “cost–benefit” hurdle, I outline a simple Bayesian technique that can be used alongside frequentist methods to address an issue of routine practical concern to working clinicians: the credibility of new research findings.     

Markov models and Bayesian methods in image analysis

Markov random field models and Bayesian methods have provided answers to various contemporary problems in Image Analysis. We give a very brief introduction to the topic. In particular, we highlight the use of Bayesian methods in classifying the image into different classes.     

Bayesian methods for analysing ringing data

A major recent development in statistics has been the use of fast computational methods of Markov chain Monte Carlo. These procedures allow Bayesian methods to be used in quite complex modelling situations. In this paper, we shall use a range of real data examples involving lapwings, shags, teal, dippers, and herring gulls, to illustrate the power and range of Bayesian techniques. The topics include: prior sensitivity; the use of reversible-jump MCMC for constructing model probabilities and comparing models, with particular reference to models with random effects; model-averaging; and the construction of Bayesian measures of goodness-of-fit. Throughout, there will be discussion of the practical aspects of the work - for instance explaining when and when not to use the BUGS package.     

Bayesian methods for analysing ringing data

A major recent development in statistics has been the use of fast computational methods of Markov chain Monte Carlo. These procedures allow Bayesian methods to be used in quite complex modelling situations. In this paper, we shall use a range of real data examples involving lapwings, shags, teal, dippers, and herring gulls, to illustrate the power and range of Bayesian techniques. The topics include: prior sensitivity; the use of reversible-jump MCMC for constructing model probabilities and comparing models, with particular reference to models with random effects; model-averaging; and the construction of Bayesian measures of goodness-of-fit. Throughout, there will be discussion of the practical aspects of the work - for instance explaining when and when not to use the BUGS package.     

Assessing safety at the end of clinical trials using system organ classes: A case and comparative study

Recent approaches to the statistical analysis of adverse event (AE) data in clinical trials have proposed the use of groupings of related AEs, such as by system organ class (SOC). These methods have opened up the possibility of scanning large numbers of AEs while controlling for multiple comparisons, making the comparative performance of the different methods in terms of AE detection and error rates of interest to investigators. We apply two Bayesian models and two procedures for controlling the false discovery rate (FDR), which use groupings of AEs, to real clinical trial safety data. We find that while the Bayesian models are appropriate for the full data set, the error controlling methods only give similar results to the Bayesian methods when low incidence AEs are removed. A simulation study is used to compare the relative performances of the methods. We investigate the differences between the methods over full trial data sets, and over data sets with low incidence AEs and SOCs removed. We find that while the removal of low incidence AEs increases the power of the error controlling procedures, the estimated power of the Bayesian methods remains relatively constant over all data sizes. Automatic removal of low-incidence AEs however does have an effect on the error rates of all the methods, and a clinically guided approach to their removal is needed. Overall we found that the Bayesian approaches are particularly useful for scanning the large amounts of AE data gathered.     

Bayesian point null hypothesis testing via the posterior likelihood ratio

This paper gives an exposition of the use of the posterior likelihood ratio for testing point null hypotheses in a fully Bayesian framework. Connections between the frequentist P-value and the posterior distribution of the likelihood ratio are used to interpret and calibrate P-values in a Bayesian context, and examples are given to show the use of simple posterior simulation methods to provide Bayesian tests of common hypotheses.     

The current state of Bayesian methods in nonclinical pharmaceutical statistics: Survey results and recommendations from the DIA/ASA-BIOP Nonclinical Bayesian Working Group

The use of Bayesian methods to support pharmaceutical product development has grown in recent years. In clinical statistics, the drive to provide faster access for patients to medical treatments has led to a heightened focus by industry and regulatory authorities on innovative clinical trial designs, including those that apply Bayesian methods. In nonclinical statistics, Bayesian applications have also made advances. However, they have been embraced far more slowly in the nonclinical area than in the clinical counterpart. In this article, we explore some of the reasons for this slower rate of adoption. We also present the results of a survey conducted for the purpose of understanding the current state of Bayesian application in nonclinical areas and for identifying areas of priority for the DIA/ASA-BIOP Nonclinical Bayesian Working Group. The survey explored current usage, hurdles, perceptions, and training needs for Bayesian methods among nonclinical statisticians. Based on the survey results, a set of recommendations is provided to help guide the future advancement of Bayesian applications in nonclinical pharmaceutical statistics.     

Bayesian analysis of complementary Poisson rate parameters with data subject to misclassification

We formulate closed-form Bayesian estimators for two complementary Poisson rate parameters using double sampling with data subject to misclassification and error free data. We also derive closed-form Bayesian estimators for two misclassification parameters in the modified Poisson model we assume. We use our results to determine credible sets for the rate and misclassification parameters. Additionally, we use MCMC methods to determine Bayesian estimators for three or more rate parameters and the misclassification parameters. We also perform a limited Monte Carlo simulation to examine the characteristics of these estimators. We demonstrate the efficacy of the new Bayesian estimators and highest posterior density regions with examples using two real data sets.     

Case study in the Bayesian analysis of a cost‐effectiveness trial in the evaluation of health care technologies: Depression

We present a case study based on a depression study that will illustrate the use of Bayesian statistics in the economic evaluation of cost‐effectiveness data, demonstrate the benefits of the Bayesian approach (whilst honestly recognizing any deficiencies) with respect to frequentist methods, and provide details of using the methods, including computer code where appropriate. Copyright © 2003 John Wiley & Sons, Ltd.     

Markov models and Bayesian methods in image analysis

Markov random field models and Bayesian methods have provided answers to various contemporary problems in image analysis. We give a very brief introduction to the topic. In particular, we highlight the use of Bayesian methods in classifying the image into different classes. Some other current developments are also described and their relationship with other chapters in this volume is indicated. Some future directions are also outlined.     

A bayesian alternative to the sign test in the presence of ties

Bayesian alternatives to the sign test are proposed which incorporate the number of ties observed. These alternatives arise from different strategies in dealing with the number of ties. One strategy is incorporating the true proportion of ties into the hypotheses of interest. The Bayesian methods are compared to each other and to the typical sign test in a simulation study. Also, the new methods are compared to another version of the sign test proposed by Coakley and Heise (1996). This new version of the sign test was shown to perform especially well in situations where the probability of observing a tie is very high. Although one of the Bayesian methods appears to perform best overall in the simulation study, its performance is not dominating and the easy to use typical sign test generally performs very well.     

Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta‐analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study‐to‐study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide‐induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the “3Rs initiative” to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd.     

On the correspondence between frequentist and Bayesian tests

Modern theory for statistical hypothesis testing can broadly be classified as Bayesian or frequentist. Unfortunately, one can reach divergent conclusions if Bayesian and frequentist approaches are applied in parallel to analyze the same data set. This is a serious impasse since there is a lack of consensus on when to use one approach in detriment of the other. However, this conflict can be resolved. The present paper shows the existence of a perfect equivalence between Bayesian and frequentist methods for testing. Hence, Bayesian and frequentist decision rules can always be calibrated, in both directions, in order to present concordant results.     

On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods

Competing risks models are of great importance in reliability and survival analysis. They are often assumed to have independent causes of failure in literature, which may be unreasonable. In this article, dependent causes of failure are considered by using the Marshall–Olkin bivariate Weibull distribution. After deriving some useful results for the model, we use ML, fiducial inference, and Bayesian methods to estimate the unknown model parameters with a parameter transformation. Simulation studies are carried out to assess the performances of the three methods. Compared with the maximum likelihood method, the fiducial and Bayesian methods could provide better parameter estimation.     

Why a Bayesian approach to safety analysis in pharmacovigilance is important

Large databases of routinely collected data are a valuable source of information for detecting potential associations between drugs and adverse events (AE). A pharmacovigilance system starts with a scan of these databases for potential signals of drug-AE associations that will subsequently be examined by experts to aid in regulatory decision-making. The signal generation process faces some key challenges: (1) an enormous volume of drug-AE combinations need to be tested (i.e. the problem of multiple testing); (2) the results are not in a format that allows the incorporation of accumulated experience and knowledge for future signal generation; and (3) the signal generation process ignores information captured from other processes in the pharmacovigilance system and does not allow feedback. Bayesian methods have been developed for signal generation in pharmacovigilance, although the full potential of these methods has not been realised. For instance, Bayesian hierarchical models will allow the incorporation of established medical and epidemiological knowledge into the priors for each drug-AE combination. Moreover, the outputs from this analysis can be incorporated into decision-making tools to help in signal validation and posterior actions to be taken by the regulators and companies. We discuss in this paper the apparent advantage of the Bayesian methods used in safety signal generation and the similarities and differences between the two widely used Bayesian methods. We will also propose the use of Bayesian hierarchical models to address the three key challenges and discuss the reasons why Bayesian methodology still have not been fully utilised in pharmacovigilance activities.     

Generalised data augmentation and posterior inferences

This paper explores the use of data augmentation in settings beyond the standard Bayesian one. In particular, we show that, after proposing an appropriate generalised data-augmentation principle, it is possible to extend the range of sampling situations in which fiducial methods can be applied by constructing Markov chains whose stationary distributions represent valid posterior inferences on model parameters. Some properties of these chains are presented and a number of open questions are discussed. We also use the approach to draw out connections between classical and Bayesian approaches in some standard settings.     

Sequential Monte Carlo with transformations

This paper examines methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. For this, we use sequential Monte Carlo samplers, introducing the innovation of using deterministic transformations to move particles effectively between target distributions with different dimensions. This approach, combined with adaptive methods, yields an extremely flexible and general algorithm for Bayesian model comparison that is suitable for use in applications where the acceptance rate in reversible jump Markov chain Monte Carlo is low. We use this approach on model comparison for mixture models, and for inferring coalescent trees sequentially, as data arrives.     

Bayesian hierarchical models for adaptive basket trial designs

Basket trials evaluate a single drug targeting a single genetic variant in multiple cancer cohorts. Empirical findings suggest that treatment efficacy across baskets may be heterogeneous. Most modern basket trial designs use Bayesian methods. These methods require the prior specification of at least one parameter that permits information sharing across baskets. In this study, we provide recommendations for selecting a prior for scale parameters for adaptive basket trials by using Bayesian hierarchical modeling. Heterogeneity among baskets attracts much attention in basket trial research, and substantial heterogeneity challenges the basic assumption of exchangeability of Bayesian hierarchical approach. Thus, we also allowed each stratum-specific parameter to be exchangeable or nonexchangeable with similar strata by using data observed in an interim analysis. Through a simulation study, we evaluated the overall performance of our design based on statistical power and type I error rates. Our research contributes to the understanding of the properties of Bayesian basket trial designs.     

The reliability and validity of Bayesian measures for hospital profiling: a Monte Carlo assessment

There is a growing trend towards the production of “hospital report-cards” in which hospitals with higher than acceptable mortality rates are identified. Several commentators have advocated for the use of Bayesian methods for health care report cards. Earlier research has demonstrated that there is poor concordance between different Bayesian methods. The current study used Monte Carlo simulation methods to examine the reliability and validity of four different Bayesian measures of hospital performance. Estimates of the reliability of the different measures ranged from a low of 0.89 to a high of 0.99. Estimates of the validity of the four measures ranged from a low of 0.58 to a high of 0.65. Thus, while the four measures of hospital performance demonstrated high reliability, the validity of each method was at most moderate. It is hypothesized that the low validity is due in part to the limited sample sizes that are typically available for hospital report cards.     

Energy performance evaluation of OECD countries using Bayesian stochastic frontier analysis and Bayesian network classifiers

More recently a large amount of interest has been devoted to the use of Bayesian methods for deriving parameter estimates of the stochastic frontier analysis. Bayesian stochastic frontier analysis (BSFA) seems to be a useful method to assess the efficiency in energy sector. However, BSFA results do not expose the multiple relationships between input and output variables and energy efficiency. This study proposes a framework to make inferences about BSFA efficiencies, recognizing the underlying relationships between variables and efficiency, using Bayesian network (BN) approach. BN classifiers are proposed as a method to analyze the results obtained from BSFA.