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Background and Aims: Indirect estimation methods are required for estimating the size of populations where only a proportion of individuals are observed directly, such as problem drug users (PDUs). Capture–recapture and multiplier methods are widely used, but have been criticized as subject to bias. We propose a new approach to estimating prevalence of PDU from numbers of fatal drug‐related poisonings (fDRPs) using linked databases, addressing the key limitations of simplistic 'mortality multipliers'. Methods: Our approach requires linkage of data on a large cohort of known PDUs to mortality registers and summary information concerning additional fDRPs observed outside this cohort. We model fDRP rates among the cohort and assume that rates in unobserved PDUs are equal to rates in the cohort during periods out of treatment. Prevalence is estimated in a Bayesian statistical framework, in which we simultaneously fit regression models to fDRP rates and prevalence, allowing both to vary by demographic factors and the former also by treatment status. Results: We report a case study analysis, estimating the prevalence of opioid dependence in England in 2008/09, by gender, age group and geographical region. Overall prevalence was estimated as 0.82% (95% credible interval = 0.74–0.94%) of 15–64‐year‐olds, which is similar to a published estimate based on capture–recapture analysis. Conclusions: Our modelling approach estimates prevalence from drug‐related mortality data, while addressing the main limitations of simplistic multipliers. This offers an alternative approach for the common situation where available data sources do not meet the strong assumptions required for valid capture–recapture estimation. In a case study analysis, prevalence estimates based on our approach were surprisingly similar to existing capture–recapture estimates but, we argue, are based on a much more objective and justifiable modelling approach. [ABSTRACT FROM AUTHOR]

In designing a randomized controlled trial, it has been argued that trialists should consider existing evidence about the likely intervention effect. One approach is to form a prior distribution for the intervention effect based on a meta-analysis of previous studies and then power the trial on its ability to affect the posterior distribution in a Bayesian analysis. Alternatively, methods have been proposed to calculate the power of the trial to influence the "pooled" estimate in an updated meta-analysis. These two approaches can give very different results if the existing evidence is heterogeneous, summarised using a random effects meta-analysis. We argue that the random effects mean will rarely represent the trialist's target parameter, and so, it will rarely be appropriate to power a trial based on its impact upon the random effects mean. Furthermore, the random effects mean will not generally provide an appropriate prior distribution. More appropriate alternatives include the predictive distribution and shrinkage estimate for the most similar study. Consideration of the impact of the trial on the entire random effects distribution might sometimes be appropriate. We describe how beliefs about likely sources of heterogeneity have implications for how the previous evidence should be used and can have a profound impact on the expected power of the new trial. We conclude that the likely causes of heterogeneity among existing studies need careful consideration. In the absence of explanations for heterogeneity, we suggest using the predictive distribution from the meta-analysis as the basis for a prior distribution for the intervention effect. [ABSTRACT FROM AUTHOR]

Background and Aims Capture-recapture (CRC) analysis is recommended for estimating the prevalence of problem drug use or people who inject drugs (PWID). We aim to demonstrate how naive application of CRC can lead to highly misleading results, and to suggest how the problems might be overcome. Methods We present a case study of estimating the prevalence of PWID in Bristol, UK, applying CRC to lists in contact with three services. We assess: (i) sensitivity of results to different versions of the dominant (treatment) list: specifically, to inclusion of non-incident cases and of those who were referred directly from one of the other services; (ii) the impact of accounting for a novel covariate, housing instability; and (iii) consistency of CRC estimates with drug-related mortality data. We then incorporate formally the drug-related mortality data and lower bounds for prevalence alongside the CRC into a single coherent model. Results Five of 11 models fitted the full data equally well but generated widely varying prevalence estimates, from 2740 [95% confidence interval (CI) = 2670, 2840] to 6890 (95% CI = 3740, 17680). Results were highly sensitive to inclusion of non-incident cases, demonstrating the presence of considerable heterogeneity, and were sensitive to a lesser extent to inclusion of direct referrals. A reduced data set including only incident cases and excluding referrals could be fitted by simpler models, and led to much greater consistency in estimates. Accounting for housing stability improved model fit considerably more than did the standard covariates of age and gender. External data provided validation of results and aided model selection, generating a final estimate of the number of PWID in Bristol in 2011 of 2770 [95% credible interval (Cr-I) = 2570, 3110] or 0.9% (95% Cr-I = 0.9, 1.0%) of the population aged 15-64 years. Conclusions Steps can be taken to reduce bias in capture-recapture analysis, including: careful consideration of data sources, reduction of lists to less heterogeneous subsamples, use of covariates and formal incorporation of external data. [ABSTRACT FROM AUTHOR]

Information on the incidence of Chlamydia trachomatis (CT) is essential for models of the effectiveness and cost-effectiveness of screening programmes. We developed two independent estimates of CT incidence in women in England: one based on an incidence study, with estimates ‘recalibrated’ to the general population using data on setting-specific relative risks, and allowing for clearance and re-infection during follow-up; the second based on UK prevalence data, and information on the duration of CT infection. The consistency of independent sources of data on incidence, prevalence and duration, validates estimates of these parameters. Pooled estimates of the annual incidence rate in women aged 16–24 and 16–44 years for 2001–2005 using all these data were 0·05 [95% credible interval (CrI) 0·035–0·071] and 0·021 (95% CrI 0·015–0·028), respectively. Although, the estimates apply to England, similar methods could be used in other countries. The methods could be extended to dynamic models to synthesize, and assess the consistency of data on contact and transmission rates. [ABSTRACT FROM AUTHOR]

Planning, implementation and evaluation of public health policies to control the human immunodeficiency virus (HIV) epidemic require regular monitoring of disease burden. This includes the proportion living with HIV, whether diagnosed or not, and the rate of new infections in the general population and in specific risk groups and regions. Estimation of these quantities is not straightforward: data informing them directly are not typically available, but a wealth of indirect information from surveillance systems and ad hoc studies can inform functions of these quantities. In this paper we show how the estimation problem can be successfully solved through a Bayesian evidence synthesis approach, relaxing the focus on "best available" data to which classical methods are typically restricted. This more comprehensive and flexible use of evidence has led to the adoption of our proposed approach as the official method to estimate HIV prevalence in the United Kingdom since 2005. [ABSTRACT FROM AUTHOR]

Our objective in this study was to estimate the probability that a Chlamydia trachomatis (CT) infection will cause an episode of clinical pelvic inflammatory disease (PID) and the reduction in such episodes among women with CT that could be achieved by annual screening. We reappraised evidence from randomized controlled trials of screening and controlled observational studies that followed untreated CT-infected and -uninfected women to measure the development of PID. Data from these studies were synthesized using a continuous-time Markov model which takes into account the competing risk of spontaneous clearance of CT. Using a 2-step piecewise homogenous Markov model that accounts for the distinction between prevalent and incident infections, we investigated the possibility that the rate of PID due to CT is greater during the period immediately following infection. The available data were compatible with both the homogenous and piecewise homogenous models. Given a homogenous model, the probability that a CT episode will cause clinical PID was 0.16 (95% credible interval (CrI): 0.06, 0.25), and annual screening would prevent 61% (95% CrI: 55, 67) of CT-related PID in women who became infected with CT. Assuming a piecewise homogenous model with a higher rate during the first 60 days, corresponding results were 0.16 (95% CrI: 0.07, 0.26) and 55% (95% CrI: 32, 72), respectively. [ABSTRACT FROM PUBLISHER]

Understanding infectious disease dynamics and the effect on prevalence and incidence is crucial for public health policies. Disease incidence and prevalence are typically not observed directly and increasingly are estimated through the synthesis of indirect information from multiple data sources. We demonstrate how an evidence synthesis approach to the estimation of human immunodeficiency virus (HIV) prevalence in England and Wales can be extended to infer the underlying HIV incidence. Diverse time series of data can be used to obtain yearly “snapshots” (with associated uncertainty) of the proportion of the population in 4 compartments: not at risk, susceptible, HIV positive but undiagnosed, and diagnosed HIV positive. A multistate model for the infection and diagnosis processes is then formulated by expressing the changes in these proportions by a system of differential equations. By parameterizing incidence in terms of prevalence and contact rates, HIV transmission is further modeled. Use of additional data or prior information on demographics, risk behavior change and contact parameters allows simultaneous estimation of the transition rates, compartment prevalences, contact rates, and transmission probabilities. [ABSTRACT FROM PUBLISHER]

There is good empirical evidence that specific flaws in the conduct of randomized controlled trials are associated with exaggeration of treatment effect estimates. Mixed treatment comparison meta-analysis, which combines data from trials on several treatments that form a network of comparisons, has the potential both to estimate bias parameters within the synthesis and to produce bias-adjusted estimates of treatment effects. We present a hierarchical model for bias with common mean across treatment comparisons of active treatment versus control. It is often unclear, from the information that is reported, whether a study is at risk of bias or not. We extend our model to estimate the probability that a particular study is biased, where the probabilities for the ‘unclear’ studies are drawn from a common beta distribution. We illustrate these methods with a synthesis of 130 trials on four fluoride treatments and two control interventions for the prevention of dental caries in children. Whether there is adequate allocation concealment and/or blinding are considered as indicators of whether a study is at risk of bias. Bias adjustment reduces the estimated relative efficacy of the treatments and the extent of between-trial heterogeneity. [ABSTRACT FROM AUTHOR]

We present models for the combined analysis of evidence from randomized controlled trials categorized as being at either low or high risk of bias due to a flaw in their conduct. We formulate a bias model that incorporates between-study and between-meta-analysis heterogeneity in bias, and uncertainty in overall mean bias. We obtain algebraic expressions for the posterior distribution of the bias-adjusted treatment effect, which provide limiting values for the information that can be obtained from studies at high risk of bias. The parameters of the bias model can be estimated from collections of previously published meta-analyses. We explore alternative models for such data, and alternative methods for introducing prior information on the bias parameters into a new meta-analysis. Results from an illustrative example show that the bias-adjusted treatment effect estimates are sensitive to the way in which the meta-epidemiological data are modelled, but that using point estimates for bias parameters provides an adequate approximation to using a full joint prior distribution. A sensitivity analysis shows that the gain in precision from including studies at high risk of bias is likely to be low, however numerous or large their size, and that little is gained by incorporating such studies, unless the information from studies at low risk of bias is limited. We discuss approaches that might increase the value of including studies at high risk of bias, and the acceptability of the methods in the evaluation of health care interventions. [ABSTRACT FROM AUTHOR]

Meta-analysis has been well-established for many years, but has been largely confined to pooling evidence on pair-wise contrasts. Broader forms of synthesis have also been described, apparently re-invented in disparate fields, each time taking different computational approaches. The potential value of Bayesian estimation of a joint posterior parameter distribution and simultaneously sampling from it for decision analysis has also been appreciated. However, applications have been relatively few in number, sometimes stylized, and presented mainly to a statistical methods audience. As a result, the potential for multiparameter evidence synthesis in both epidemiology and health technology assessment has remained largely unrecognized. The advent of flexible software for Bayesian Markov chain Monte Carlo in the shape of WinBUGS has the made these earlier strands of work more widely available. Researchers can now carry out synthesis at a realistic level of complexity. The Bristol programme has not only contributed to a growing body of literature on how to synthesize different evidence structures, but also on how to check the consistency of multiple information sources and how to use the resulting models to prioritize future research. [ABSTRACT FROM AUTHOR]

Inferential approaches based on the synthesis of diverse sources of evidence are increasingly employed in epidemiology as a means of exploiting all available information, perhaps from studies of differing designs. The application of the synthesis of evidence to real world problems generally leads to the formulation of probability models which are highly complex and for which there is a clear need for a well-defined iterative process of model criticism. This process should include an appraisal of model fit and the detection of inconsistent or conflicting evidence. The latter is especially relevant as, typically, multiple sources of data provide information on the same parameter. Detected conflicts need then to be resolved. We present a case-study of the detection and resolution of conflicting evidence, using as an illustration the estimation of the prevalence of human immunodeficiency virus (HIV) infection in England and Wales. We employ a Bayesian model to synthesize routine surveillance and survey data. The population aged 15–44 years is divided into mutually exclusive exposure groups. In each group g, we simultaneously estimate the proportion of the total population belonging to the group ( ρ≫), the proportion of individuals infected with HIV ( π≫) and the proportion of HIV positive individuals who are diagnosed ( δ≫). The total number of HIV infections, both diagnosed and undiagnosed, is then estimated as a function of the parameters ρ≫, π≫ and δ≫. Model fit is assessed by examining the posterior mean deviance. Identification of the data items to which the model exhibits a lack of fit leads to the detection of conflicting evidence, one example of which is a conflict between census data and survey data over the size of the female Sub-Saharan African born population. This conflict arises from a naive interpretation of the representativeness of the survey data and is resolved by using two approaches: exclusion of data and expansion of the model to accommodate the bias. [ABSTRACT FROM AUTHOR]

We investigate whether Bayesian decision theory, in the form of expected value of partial perfect information (EVPPI) analysis, is a realistic and practical approach to research prioritization. We develop a simple cost-effectiveness analysis of breast cancer screening as a typical case-study, motivated by data from a cluster randomized 2 × 2 factorial trial of interventions to increase uptake. An EVPPI analysis is developed which shows that, on the basis of the evidence that was available beforehand, the trial was cost effective, but that after incorporating the results of the trial it would still be cost effective to carry out research that further reduced decision uncertainty. We identify key conceptual and technical issues: the relationship between the target interventions and the previous evidence, the distinction between variation and uncertainty and methods for correlated parameters. EVPPI methods have clear advantages over current methods of research prioritization, but we suggest that some specific sensitivity analyses are required before they can be used confidently in practice. These have limitations, and there is a need to develop robust methods to optimize research portfolios. [ABSTRACT FROM AUTHOR]

Estimates of the number of prevalent human immunodeficiency virus infections are used in England and Wales to monitor development of the human immunodeficiency virus–acquired immune deficiency syndrome epidemic and for planning purposes. The population is split into risk groups, and estimates of risk group size and of risk group prevalence and diagnosis rates are combined to derive estimates of the number of undiagnosed infections and of the overall number of infected individuals. In traditional approaches, each risk group size, prevalence or diagnosis rate parameter must be informed by just one summary statistic. Yet a rich array of surveillance and other data is available, providing information on parameters and on functions of parameters, and raising the possibility of inconsistency between sources of evidence in some parts of the parameter space. We develop a Bayesian framework for synthesis of surveillance and other information, implemented through Markov chain Monte Carlo methods. The sources of data are found to be inconsistent under their accepted interpretation, but the inconsistencies can be resolved by introducing additional ‘bias adjustment’ parameters. The best-fitting model incorporates a hierarchical structure to spread information more evenly over the parameter space. We suggest that multiparameter evidence synthesis opens new avenues in epidemiology based on the coherent summary of available data, assessment of consistency and bias modelling. [ABSTRACT FROM AUTHOR]

Recently, health systems internationally have begun to use cost-effectiveness research as formal inputs into decisions about which interventions and programmes should be funded from collective resources. This process has raised some important methodological questions for this area of research. This paper considers one set of issues related to the synthesis of effectiveness evidence for use in decision-analytic cost-effectiveness (CE) models, namely the need for the synthesis of all sources of available evidence, although these may not 'fit neatly' into a CE model. Commonly encountered problems include the absence of head-to-head trial evidence comparing all options under comparison, the presence of multiple endpoints from trials and different follow-up periods. Full evidence synthesis for CE analysis also needs to consider treatment effects between patient subpopulations and the use of nonrandomised evidence. Bayesian statistical methods represent a valuable set of analytical tools to utilise indirect evidence and can make a powerful contribution to the decision-analytic approach to CE analysis. This paper provides a worked example and a general overview of these methods with particular emphasis on their use in economic evaluation. [ABSTRACT FROM AUTHOR]

Alongside the development of meta-analysis as a tool for summarizing research literature, there is renewed interest in broader forms of quantitative synthesis that are aimed at combining evidence from different study designs or evidence on multiple parameters. These have been proposed under various headings: the confidence profile method, cross-design synthesis, hierarchical models and generalized evidence synthesis. Models that are used in health technology assessment are also referred to as representing a synthesis of evidence in a mathematical structure. Here we review alternative approaches to statistical evidence synthesis, and their implications for epidemiology and medical decision-making. The methods include hierarchical models, models informed by evidence on different functions of several parameters and models incorporating both of these features. The need to check for consistency of evidence when using these powerful methods is emphasized. We develop a rationale for evidence synthesis that is based on Bayesian decision modelling and expected value of information theory, which stresses not only the need for a lack of bias in estimates of treatment effects but also a lack of bias in assessments of uncertainty. The increasing reliance of governmental bodies like the UK National Institute for Clinical Excellence on complex evidence synthesis in decision modelling is discussed. [ABSTRACT FROM AUTHOR]

We present a Bayesian evidence synthesis model combining data on seroprevalence, seroconversion and tests of recent infection, to produce estimates of current incidence of toxoplasmosis in the UK. The motivation for the study was the need for an estimate of current average incidence in the UK, with a realistic assessment of its uncertainty, to inform a decision model for a national screening programme to prevent congenital toxoplasmosis. The model has a hierarchical structure over geographic region, a random-walk model for temporal effects and a fixed age effect, with one or more types of data informing the regional estimates of incidence. Inference is obtained by using Markov chain Monte Carlo simulations. A key issue in the synthesis of evidence from multiple sources is model selection and the consistency of different types of evidence. Alternative models of incidence are compared by using the deviance information criterion, and we find that temporal effects are region specific. We assess the consistency of the various forms of evidence by using cross-validation where practical, and posterior and mixed prediction otherwise, and we discuss how these measures can be used to assess different aspects of consistency in a complex evidence structure. We discuss the contribution of the various forms of evidence to estimated current average incidence. [ABSTRACT FROM AUTHOR]

Monte Carlo simulation has become the accepted method for propagating parameter uncertainty through risk models. It is widely appreciated, however, that correlations between input variables must be taken into account if models are to deliver correct assessments of uncertainty in risk. Various two-stage methods have been proposed that first estimate a correlation structure and then generate Monte Carlo simulations, which incorporate this structure while leaving marginal distributions of parameters unchanged. Here we propose a one-stage alternative, in which the correlation structure is estimated from the data directly by Bayesian Markov Chain Monte Carlo methods. Samples from the posterior distribution of the outputs then correctly reflect the correlation between parameters, given the data and the model. Besides its computational simplicity, this approach utilizes the available evidence from a wide variety of structures, including incomplete data and correlated and uncorrelated repeat observations. The major advantage of a Bayesian approach is that, rather than assuming the correlation structure is fixed and known, it captures the joint uncertainty induced by the data in all parameters, including variances and covariances, and correctly propagates this through the decision or risk model. These features are illustrated with examples on emissions of dioxin congeners from solid waste incinerators. [ABSTRACT FROM AUTHOR]