A Bayesian approach to sequential meta‐analysis

As evidence accumulates within a meta‐analysis, it is desirable to determine when the results could be considered conclusive to guide systematic review updates and future trial designs. Adapting sequential testing methodology from clinical trials for application to pooled meta‐analytic effect size estimates appears well suited for this objective. In this paper, we describe a Bayesian sequential meta‐analysis method, in which an informative heterogeneity prior is employed and stopping rule criteria are applied directly to the posterior distribution for the treatment effect parameter. Using simulation studies, we examine how well this approach performs under different parameter combinations by monitoring the proportion of sequential meta‐analyses that reach incorrect conclusions (to yield error rates), the number of studies required to reach conclusion, and the resulting parameter estimates. By adjusting the stopping rule thresholds, the overall error rates can be controlled within the target levels and are no higher than those of alternative frequentist and semi‐Bayes methods for the majority of the simulation scenarios. To illustrate the potential application of this method, we consider two contrasting meta‐analyses using data from the Cochrane Library and compare the results of employing different sequential methods while examining the effect of the heterogeneity prior in the proposed Bayesian approach. Copyright © 2016 John Wiley & Sons, Ltd.     

A Bayesian approach to analysing the cost-effectiveness of two primary care interventions aimed at improving attendance for breast screening

AIMS: To assess the cost-effectiveness of two primary care interventions, a letter and a flag, aimed at improving attendance for breast screening among (i) all women invited for breast screening and (ii) non-attenders. METHODS: A probabilistic decision analytic model was developed using Markov chain Monte Carlo simulation implemented in WinBUGS. The model was populated using economic and effectiveness data collected alongside two randomised controlled trials. RESULTS: For all women invited, the incremental cost-effectiveness ratio (ICER) for the letter compared with no intervention is 27 pounds per additional attendance, and the ICER for the combined letter and flag intervention compared to the letter alone is 171 pounds. The corresponding ICERs for non-attenders are 41 pounds and 90 pounds. The flag intervention is an inefficient option in both settings. A large proportion of the costs fall on the practices (25-67%), depending on the intervention and target population. The total costs incurred do not, however, seem prohibitive.Expected value of perfect information suggests that there is greater value in carrying out further research on the intervention implemented among all women invited for breast screening rather than on non-attenders. CONCLUSIONS: The flag intervention alone does not appear to be an efficient option. The choice between the letter and both interventions combined is subjective, depending on the willingness to pay for an additional screening attendance.     

Using covariates to reduce uncertainty in the economic evaluation of clinical trial data

As part of their practice, policymakers have to make economic evaluations using clinical trial data. Recent interest has been expressed in determining how cost-effectiveness analysis can be undertaken in a regression framework. In this respect, published research basically provides a general method for prognostic factor adjustment in the presence of imbalance, emphasizing sub-group analysis. In this paper, we present an alternative method from a Bayesian approach. We propose the use of covariates in Bayesian health technology assessment in order to reduce uncertainty about the effect of treatments. We show its advantages by comparison with another published method that do not adjust for covariates using simulated data.     

Bayesian estimation,simulation and uncertainty analysis: the cost-effectiveness of ganciclovir prophylaxis in liver transplantation

This paper demonstrates the usefulness of combining simulation with Bayesian estimation methods in analysis of cost-effectiveness data collected alongside a clinical trial. Specifically, we use Markov Chain Monte Carlo (MCMC) to estimate a system of generalized linear models relating costs and outcomes to a disease process affected by treatment under alternative therapies. The MCMC draws are used as parameters in simulations which yield inference about the relative cost-effectiveness of the novel therapy under a variety of scenarios. Total parametric uncertainty is assessed directly by examining the joint distribution of simulated average incremental cost and effectiveness. The approach allows flexibility in assessing treatment in various counterfactual premises and quantifies the global effect of parametric uncertainty on a decision-maker's confidence in adopting one therapy over the other.     

Bayesian modelling of multivariate quantitative traits using seemingly unrelated regressions

We investigate a Bayesian approach to modelling the statistical association between markers at multiple loci and multivariate quantitative traits. In particular, we describe the use of Bayesian Seemingly Unrelated Regressions (SUR) whereby genotypes at the different loci are allowed to have non-simultaneous effects on the phenotypes considered with residuals from each regression assumed correlated. We present results from simulations showing that, under rather general conditions that are likely to hold in real situations, the Bayesian SUR approach has increased probability of selecting the true model compared to univariate analyses. Finally, we apply our methods to data from subjects genotyped for 12 SNPs in the apolipoprotein E (APOE) gene. Phenotypes relate to response to treatment with atorvastatin and include changes in total cholesterol, low-density lipoprotein cholesterol, and triglycerides. Missing genotype data are naturally accommodated in our Bayesian framework by imputing them using a nested haplotype phasing algorithm.     

Bayesian model choice and infection route modelling in an outbreak of Norovirus

A data set from an outbreak of gastroenteritis in a school is analysed using a stochastic transmission model. The causative agent of the outbreak is believed to be a Norovirus, spread through person-to-person contact. Particular attention is given to the question of whether or not vomiting episodes enhance the spread of the virus via aerosol transmission. The methodology developed uses Bayesian model choice, implemented with reversible-jump Markov chain Monte Carlo methods. The methodology appears to be highly sensitive to assumptions made concerning the data, which provides some assurance that the conclusions are driven by observations rather than the underlying model and methodology.     

Assessing noninferiority in a three-arm trial using the Bayesian approach

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm trial consists of a placebo, a reference and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with comparing this reference to an experimental treatment. In this paper, we consider the analysis of non-inferiority trials using Bayesian methods which incorporate both parametric as well as semi-parametric models. The resulting testing approach is both flexible and robust. The benefit of the proposed Bayesian methods is assessed via simulation, based on a study examining home-based blood pressure interventions.     

Mixed treatment comparison with multiple outcomes reported inconsistently across trials: evaluation of antivirals for treatment of influenza A and B

We present a mixed treatment meta-analysis of antivirals for treatment of influenza, where some trials report summary measures on at least one of the two outcomes: time to alleviation of fever and time to alleviation of symptoms. The synthesis is further complicated by the variety of summary measures reported: mean time, median time and proportion symptom free at the end of follow-up. We compare several models using the deviance information criteria and the contribution of different evidence sources to the residual deviance to aid model selection. A Weibull model with exchangeable treatment effects that are independent for each outcome but have a common random effect mean for the two outcomes gives the best fit according to these criteria. This model allows us to summarize treatment effect on two outcomes in a single summary measure and draw conclusions as to the most effective treatment. Amantadine and Oseltamivir were the most effective treatments, with the probability of being most effective of 0.56 and 0.37, respectively. Amantadine reduces the duration of symptoms by an estimated 2.8 days, and Oseltamivir 2.6 days, compared with placebo. The models provide flexible methods for synthesis of evidence on multiple treatments in the absence of head-to-head trial data, when different summary measures are used and either different clinical outcomes are reported or where the same outcomes are reported at different or multiple time points.     

Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling

Increasingly complex models are being used to evaluate the cost-effectiveness of medical interventions. We describe the multiple sources of uncertainty that are relevant to such models, and their relation to either probabilistic or deterministic sensitivity analysis. A Bayesian approach appears natural in this context. We explore how sensitivity analysis to patient heterogeneity and parameter uncertainty can be simultaneously investigated, and illustrate the necessary computation when expected costs and benefits can be calculated in closed form, such as in discrete-time discrete-state Markov models. Information about parameters can either be expressed as a prior distribution, or derived as a posterior distribution given a generalized synthesis of available data in which multiple sources of evidence can be differentially weighted according to their assumed quality. The resulting joint posterior distributions on costs and benefits can then provide inferences on incremental cost-effectiveness, best presented as posterior distributions over net-benefit and cost-effectiveness acceptability curves. These ideas are illustrated with a detailed running example concerning the cost-effectiveness of hip prostheses in different age-sex subgroups. All computations are carried out using freely available software for conducting Markov chain Monte Carlo analysis.     

A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data

We propose a transmission model to estimate the main characteristics of influenza transmission in households. The model details the risks of infection in the household and in the community at the individual scale. Heterogeneity among subjects is investigated considering both individual susceptibility and infectiousness. The model was applied to a data set consisting of the follow-up of influenza symptoms in 334 households during 15 days after an index case visited a general practitioner with virologically confirmed influenza.Estimating the parameters of the transmission model was challenging because a large part of the infectious process was not observed: only the dates when new cases were detected were observed. For each case, the data were augmented with the unobserved dates of the start and the end of the infectious period. The transmission model was included in a 3-levels hierarchical structure: (i) the observation level ensured that the augmented data were consistent with the observed data, (ii) the transmission level described the underlying epidemic process, (iii) the prior level specified the distribution of the parameters. From a Bayesian perspective, the joint posterior distribution of model parameters and augmented data was explored by Markov chain Monte Carlo (MCMC) sampling.The mean duration of influenza infectious period was estimated at 3.8 days (95 per cent credible interval, 95 per cent CI [3.1,4.6]) with a standard deviation of 2.0 days (95 per cent CI [1.1,2.8]). The instantaneous risk of influenza transmission between an infective and a susceptible within a household was found to decrease with the size of the household, and established at 0.32 person day(-1) (95 per cent CI [0.26,0.39]); the instantaneous risk of infection from the community was 0.0056 day(-1) (95 per cent CI [0.0029,0.0087]). Focusing on the differences in transmission between children (less than 15 years old) and adults, we estimated that the former were more likely to transmit than adults (posterior probability larger than 99 per cent), but that the mean duration of the infectious period was similar in children (3.6 days, 95 per cent CI [2.3,5.2]) and adults (3.9 days, 95 per cent CI [3.2,4.9]). The posterior probability that children had a larger community risk was 76 per cent and the posterior probability that they were more susceptible than adults was 79 per cent.     

Reducing Monte Carlo error in the Bayesian estimation of risk ratios using log‐binomial regression models

In cohort studies, binary outcomes are very often analyzed by logistic regression. However, it is well known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a log‐binomial regression model is preferable. On the other hand, the estimation of the regression coefficients of the log‐binomial model is difficult owing to the constraints that must be imposed on these coefficients. Bayesian methods allow a straightforward approach for log‐binomial regression models and produce smaller mean squared errors in the estimation of risk ratios than the frequentist methods, and the posterior inferences can be obtained using the software WinBUGS. However, Markov chain Monte Carlo methods implemented in WinBUGS can lead to large Monte Carlo errors in the approximations to the posterior inferences because they produce correlated simulations, and the accuracy of the approximations are inversely related to this correlation. To reduce correlation and to improve accuracy, we propose a reparameterization based on a Poisson model and a sampling algorithm coded in R. Copyright © 2015 John Wiley & Sons, Ltd.     

Predicting costs over time using Bayesian Markov chain Monte Carlo methods: an application to early inflammatory polyarthritis

This article focuses on the modelling and prediction of costs due to disease accrued over time, to inform the planning of future services and budgets. It is well documented that the modelling of cost data is often problematic due to the distribution of such data; for example, strongly right skewed with a significant percentage of zero-cost observations. An additional problem associated with modelling costs over time is that cost observations measured on the same individual at different time points will usually be correlated. In this study we compare the performance of four different multilevel/hierarchical models (which allow for both the within-subject and between-subject variability) for analysing healthcare costs in a cohort of individuals with early inflammatory polyarthritis (IP) who were followed-up annually over a 5-year time period from 1990/1991. The hierarchical models fitted included linear regression models and two-part models with log-transformed costs, and two-part model with gamma regression and a log link. The cohort was split into a learning sample, to fit the different models, and a test sample to assess the predictive ability of these models. To obtain predicted costs on the original cost scale (rather than the log-cost scale) two different retransformation factors were applied. All analyses were carried out using Bayesian Markov chain Monte Carlo (MCMC) simulation methods.     

A novel Bayesian continuous piecewise linear log-hazard model,with estimation and inference via reversible jump Markov chain Monte Carlo

We present a reversible jump Bayesian piecewise log-linear hazard model that extends the Bayesian piecewise exponential hazard to a continuous function of piecewise linear log hazards. A simulation study encompassing several different hazard shapes, accrual rates, censoring proportion, and sample sizes showed that the Bayesian piecewise linear log-hazard model estimated the true mean survival time and survival distributions better than the piecewsie exponential hazard. Survival data from Wake Forest Baptist Medical Center is analyzed by both methods and the posterior results are compared.     

A Bayesian approach to competing risks analysis with masked cause of death

Cause‐specific analyses under a competing risks framework have received considerable attention in the statistical literature. Such analyses are useful for comparing mortality patterns across racial and/or age groups. Earlier work in the statistical literature focused on the situation when the cause of death is known. A challenging twist to the problem arises when the cause of death is not known exactly, but can be narrowed down to a set of potential causes that do not necessarily act independently. This phenomenon, referred to as masking, is often the result of incomplete or partial information on death certificates and/or lack of routine autopsy on every patient. In this article we propose a semiparametric Bayesian approach for analyzing competing risks survival data with masked cause of death. The models proposed do not assume independence among the causes, and are valid for an arbitrary number of causes. Further, the Bayesian approach is flexible in allowing a general pattern of missingness for the cause of death. We illustrate our methodology using breast cancer data from the Detroit Surveillance, Epidemiology, and End Results registry. Copyright © 2010 John Wiley & Sons, Ltd.     

A Bayesian framework for health economic evaluation in studies with missing data

Health economics studies with missing data are increasingly using approaches such as multiple imputation that assume that the data are “missing at random.” This assumption is often questionable, as—even given the observed data—the probability that data are missing may reflect the true, unobserved outcomes, such as the patients' true health status. In these cases, methodological guidelines recommend sensitivity analyses to recognise data may be “missing not at random” (MNAR), and call for the development of practical, accessible approaches for exploring the robustness of conclusions to MNAR assumptions. Little attention has been paid to the problem that data may be MNAR in health economics in general and in cost‐effectiveness analyses (CEA) in particular. In this paper, we propose a Bayesian framework for CEA where outcome or cost data are missing. Our framework includes a practical, accessible approach to sensitivity analysis that allows the analyst to draw on expert opinion. We illustrate the framework in a CEA comparing an endovascular strategy with open repair for patients with ruptured abdominal aortic aneurysm, and provide software tools to implement this approach.     

The choice of prior distribution for a covariance matrix in multivariate meta‐analysis: a simulation study

Bayesian meta‐analysis is an increasingly important component of clinical research, with multivariate meta‐analysis a promising tool for studies with multiple endpoints. Model assumptions, including the choice of priors, are crucial aspects of multivariate Bayesian meta‐analysis (MBMA) models. In a given model, two different prior distributions can lead to different inferences about a particular parameter. A simulation study was performed in which the impact of families of prior distributions for the covariance matrix of a multivariate normal random effects MBMA model was analyzed. Inferences about effect sizes were not particularly sensitive to prior choice, but the related covariance estimates were. A few families of prior distributions with small relative biases, tight mean squared errors, and close to nominal coverage for the effect size estimates were identified. Our results demonstrate the need for sensitivity analysis and suggest some guidelines for choosing prior distributions in this class of problems. The MBMA models proposed here are illustrated in a small meta‐analysis example from the periodontal field and a medium meta‐analysis from the study of stroke. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysing Italian voluntary abortion data using a Bayesian approach to the time series decomposition

After the approval of the law on voluntary abortion in Italy, the Italian health care system started to practice voluntary abortion before the third month of pregnancy. Since 1980, the Italian Institute of Statistics (ISTAT) has collected data on the abortion frequency per month and per administrative local areas. Although a preliminary analysis of the data showed that, after an initial increase, the number of abortions progressively lowered over years, there is no insight on the existence of periodicity in the time series and on the local effects related to the regional habits and social environments. The aim of our study is therefore to extract local trends and periodicity from the data collected by ISTAT, by combining a 'structural model' of the time series and Bayesian statistics. This paper describes both the adopted stochastic model and its Bayesian estimation through a Markov chain Monte Carlo approach on the Italian abortion data. Abortion data are analysed both at national level and in each of the 95 Italian local areas. At the national level this analysis allows extraction of a trend component that clearly shows that the voluntary abortion trend has decreased constantly since June-July 1983 until the end of the study. The periodic component shows an astonishing regularity too, suggesting that the Italian people have a seasonal preference for voluntary abortion. In particular, abortions are concentrated in the central part of the year (April-August). Finally, at the local level this analysis allows us to find similarities/differences between different areas in trends and/or in seasonal preferences.     

Bayesian modelling of the dynamics of hepatotoxicity

Hepatotoxicity (liver damage) is a common problem in drug treatment trials but is observed only indirectly through biomarkers measured in the blood. This creates the need to infer an individual's unobserved liver function dynamically using blood tests and other patient baseline characteristics. Major statistical challenges include high dimensionality, irregular time observation points over patients, presence of missing observations, and noise involved in measurement and biological processes. This article introduces a class of multivariate Bayesian dynamic stochastic models for detecting and forecasting changes in an individual's liver function in two situations: without and with drug. These models separate measurement error from variation inherent in a biological process, and describe the underlying process of liver detoxification, whereby, drug affects liver function which in turn induces changes in observed analytes. We apply the Bayesian methodology to make an inference. A clinical toxicity study is examined, together with simulated data. The results suggest that changes in observed analytes can be captured by the proposed models.     

Bayesian inference for unidirectional misclassification of a binary response trait

When assessing association between a binary trait and some covariates, the binary response may be subject to unidirectional misclassification. Unidirectional misclassification can occur when revealing a particular level of the trait is associated with a type of cost, such as a social desirability or financial cost. The feasibility of addressing misclassification is commonly obscured by model identification issues. The current paper attempts to study the efficacy of inference when the binary response variable is subject to unidirectional misclassification. From a theoretical perspective, we demonstrate that the key model parameters possess identifiability, except for the case with a single binary covariate. From a practical standpoint, the logistic model with quantitative covariates can be weakly identified, in the sense that the Fisher information matrix may be near singular. This can make learning some parameters difficult under certain parameter settings, even with quite large samples. In other cases, the stronger identification enables the model to provide more effective adjustment for unidirectional misclassification. An extension to the Poisson approximation of the binomial model reveals the identifiability of the Poisson and zero‐inflated Poisson models. For fully identified models, the proposed method adjusts for misclassification based on learning from data. For binary models where there is difficulty in identification, the method is useful for sensitivity analyses on the potential impact from unidirectional misclassification.     

Hierarchical Bayesian spatial modelling of small-area rates of non-rare disease

We present Bayesian hierarchical spatial models for the analysis of the geographical distribution of a non-rare disease or event. The work is motivated by the need for ascertaining regional variations in health services outcomes and resource use and for assessing the potential sources of these variations. The models discussed herein readily accommodate random spatial effects and covariate effects. We discuss Bayesian inferential framework and implementation of a hybrid Markov chain Monte Carlo method for full Bayesian model inference. The methods are illustrated through an analysis of regional variation in chronic lung disease (CLD) rates among neonatal intensive care unit (NICU) patients across Canada. Specifically, we first present a random effects binomial model for spatially correlated CLD rates, with random spatial effects accounting for latent or covariate effects. These random spatial effects depict regional or spatial variation in chronic lung disease occurrence. We then extend this model to include covariates. With this extension, we assess residual spatial effects and the extent to which risk factors such as illness severity at NICU admission, low birth weight, and very low birth weight influence the CLD rate variation.