Hierarchical network meta-analysis models for synthesis of evidence from randomised and non-randomised studies.

BACKGROUND: With the increased interest in the inclusion of non-randomised data in network meta-analyses (NMAs) of randomised controlled trials (RCTs), analysts need to consider the implications of the differences in study designs as such data can be prone to increased bias due to the lack of randomisation and unmeasured confounding. This study aims to explore and extend a number of NMA models that account for the differences in the study designs, assessing their impact on the effect estimates and uncertainty. METHODS: Bayesian random-effects meta-analytic models, including naïve pooling and hierarchical models differentiating between the study designs, were extended to allow for the treatment class effect and accounting for bias, with further extensions allowing for bias terms to vary depending on the treatment class. Models were applied to an illustrative example in type 2 diabetes; using data from a systematic review of RCTs and non-randomised studies of two classes of glucose-lowering medications: sodium-glucose co-transporter 2 inhibitors and glucagon-like peptide-1 receptor agonists. RESULTS: Across all methods, the estimated mean differences in glycated haemoglobin after 24 and 52 weeks remained similar with the inclusion of observational data. The uncertainty around these estimates reduced when conducting naïve pooling, compared to NMA of RCT data alone, and remained similar when applying hierarchical model allowing for class effect. However, the uncertainty around these effect estimates increased when fitting hierarchical models allowing for the differences in study design. The impact on uncertainty varied between treatments when applying the bias adjustment models. Hierarchical models and bias adjustment models all provided a better fit in comparison to the naïve-pooling method. CONCLUSIONS: Hierarchical and bias adjustment NMA models accounting for study design may be more appropriate when conducting a NMA of RCTs and observational studies. The degree of uncertainty around the effectiveness estimates varied depending on the method but use of hierarchical models accounting for the study design resulted in increased uncertainty. Inclusion of non-randomised data may, however, result in inferences that are more generalisable and the models accounting for the differences in the study design allow for more detailed and appropriate modelling of complex data, preventing overly optimistic conclusions.

Use of copula to model within-study association in bivariate meta-analysis of binomial data at the aggregate level: A Bayesian approach and application to surrogate endpoint evaluation.

Bivariate meta-analysis provides a useful framework for combining information across related studies and has been utilized to combine evidence from clinical studies to evaluate treatment efficacy on two outcomes. It has also been used to investigate surrogacy patterns between treatment effects on the surrogate endpoint and the final outcome. Surrogate endpoints play an important role in drug development when they can be used to measure treatment effect early compared to the final outcome and to predict clinical benefit or harm. The standard bivariate meta-analytic approach models the observed treatment effects on the surrogate and the final outcome outcomes jointly, at both the within-study and between-studies levels, using a bivariate normal distribution. For binomial data, a normal approximation on log odds ratio scale can be used. However, this method may lead to biased results when the proportions of events are close to one or zero, affecting the validation of surrogate endpoints. In this article, we explore modeling the two outcomes on the original binomial scale. First, we present a method that uses independent binomial likelihoods to model the within-study variability avoiding to approximate the observed treatment effects. However, the method ignores the within-study association. To overcome this issue, we propose a method using a bivariate copula with binomial marginals, which allows the model to account for the within-study association. We applied the methods to an illustrative example in chronic myeloid leukemia to investigate the surrogate relationship between complete cytogenetic response and event-free-survival.

Bayesian network meta-analysis methods for combining individual participant data and aggregate data from single arm trials and randomised controlled trials.

BACKGROUND: Increasingly in network meta-analysis (NMA), there is a need to incorporate non-randomised evidence to estimate relative treatment effects, and in particular in cases with limited randomised evidence, sometimes resulting in disconnected networks of treatments. When combining different sources of data, complex NMA methods are required to address issues associated with participant selection bias, incorporating single-arm trials (SATs), and synthesising a mixture of individual participant data (IPD) and aggregate data (AD). We develop NMA methods which synthesise data from SATs and randomised controlled trials (RCTs), using a mixture of IPD and AD, for a dichotomous outcome. METHODS: We propose methods under both contrast-based (CB) and arm-based (AB) parametrisations, and extend the methods to allow for both within- and across-trial adjustments for covariate effects. To illustrate the methods, we use an applied example investigating the effectiveness of biologic disease-modifying anti-rheumatic drugs for rheumatoid arthritis (RA). We applied the methods to a dataset obtained from a literature review consisting of 14 RCTs and an artificial dataset consisting of IPD from two SATs and AD from 12 RCTs, where the artificial dataset was created by removing the control arms from the only two trials assessing tocilizumab in the original dataset. RESULTS: Without adjustment for covariates, the CB method with independent baseline response parameters (CBunadjInd) underestimated the effectiveness of tocilizumab when applied to the artificial dataset compared to the original dataset, albeit with significant overlap in posterior distributions for treatment effect parameters. The CB method with exchangeable baseline response parameters produced effectiveness estimates in agreement with CBunadjInd, when the predicted baseline response estimates were similar to the observed baseline response. After adjustment for RA duration, there was a reduction in across-trial heterogeneity in baseline response but little change in treatment effect estimates. CONCLUSIONS: Our findings suggest incorporating SATs in NMA may be useful in some situations where a treatment is disconnected from a network of comparator treatments, due to a lack of comparative evidence, to estimate relative treatment effects. The reliability of effect estimates based on data from SATs may depend on adjustment for covariate effects, although further research is required to understand this in more detail.

Using threshold analysis to assess the robustness of public health intervention recommendations from network meta-analyses: application to accident prevention in households with children under five.

BACKGROUND: In the appraisal of clinical interventions, complex evidence synthesis methods, such as network meta-analysis (NMA), are commonly used to investigate the effectiveness of multiple interventions in a single analysis. The results from a NMA can inform clinical guidelines directly or be used as inputs into a decision-analytic model assessing the cost-effectiveness of the interventions. However, there is hesitancy in using complex evidence synthesis methods when evaluating public health interventions. This is due to significant heterogeneity across studies investigating such interventions and concerns about their quality. Threshold analysis has been developed to help assess and quantify the robustness of recommendations made based on results obtained from NMAs to potential limitations of the data. Developed in the context of clinical guidelines, the method may prove useful also in the context of public health interventions. In this paper, we illustrate the use of the method in public health, investigating the effectiveness of interventions aiming to increase the uptake of accident prevention behaviours in homes with children aged 0-5. METHODS: Two published random effects NMAs were replicated and carried out to assess the effectiveness of several interventions for increasing the uptake of accident prevention behaviours, focusing on the safe storage of other household products and stair gates outcomes. Threshold analysis was then applied to the NMAs to assess the robustness of the intervention recommendations made based on the results from the NMAs. RESULTS: The results of the NMAs indicated that complex intervention, including Education, Free/low-cost equipment, Fitting equipment and Home safety inspection, was the most effective intervention at promoting accident prevention behaviours for both outcomes. However, the threshold analyses highlighted that the intervention recommendation was robust for the stair gate outcome, but not robust for the safe storage of other household items outcome. CONCLUSIONS: In our case study, threshold analysis allowed us to demonstrate that there was some discrepancy in the intervention recommendation for promoting accident prevention behaviours as the recommendation was robust for one outcome but not the other. Therefore, caution should be taken when considering such interventions in practice for the prevention of poisonings in homes with children aged 0-5. However, there can be some confidence in the use of this intervention in practice to promote the possession of stair gates to prevent falls in homes with children under 5. We have illustrated the potential benefit of threshold analysis in the context of public health and, therefore, encourage the use of the method in practice as a sensitivity analysis for NMA of public health interventions.

Double-counting of populations in evidence synthesis in public health: a call for awareness and future methodological development.

BACKGROUND: There is a growing interest in the inclusion of real-world and observational studies in evidence synthesis such as meta-analysis and network meta-analysis in public health. While this approach offers great epidemiological opportunities, use of such studies often introduce a significant issue of double-counting of participants and databases in a single analysis. Therefore, this study aims to introduce and illustrate the nuances of double-counting of individuals in evidence synthesis including real-world and observational data with a focus on public health. METHODS: The issues associated with double-counting of individuals in evidence synthesis are highlighted with a number of case studies. Further, double-counting of information in varying scenarios is discussed with potential solutions highlighted. RESULTS: Use of studies of real-world data and/or established cohort studies, for example studies evaluating the effectiveness of therapies using health record data, often introduce a significant issue of double-counting of individuals and databases. This refers to the inclusion of the same individuals multiple times in a single analysis. Double-counting can occur in a number of manners, such as, when multiple studies utilise the same database, when there is overlapping timeframes of analysis or common treatment arms across studies. Some common practices to address this include synthesis of data only from peer-reviewed studies, utilising the study that provides the greatest information (e.g. largest, newest, greater outcomes reported) or analysing outcomes at different time points. CONCLUSIONS: While common practices currently used can mitigate some of the impact of double-counting of participants in evidence synthesis including real-world and observational studies, there is a clear need for methodological and guideline development to address this increasingly significant issue.

Incorporating single-arm studies in meta-analysis of randomised controlled trials: a simulation study.

BACKGROUND: Use of real world data (RWD) from non-randomised studies (e.g. single-arm studies) is increasingly being explored to overcome issues associated with data from randomised controlled trials (RCTs). We aimed to compare methods for pairwise meta-analysis of RCTs and single-arm studies using aggregate data, via a simulation study and application to an illustrative example. METHODS: We considered contrast-based methods proposed by Begg & Pilote (1991) and arm-based methods by Zhang et al (2019). We performed a simulation study with scenarios varying (i) the proportion of RCTs and single-arm studies in the synthesis (ii) the magnitude of bias, and (iii) between-study heterogeneity. We also applied methods to data from a published health technology assessment (HTA), including three RCTs and 11 single-arm studies. RESULTS: Our simulation study showed that the hierarchical power and commensurate prior methods by Zhang et al provided a consistent reduction in uncertainty, whilst maintaining over-coverage and small error in scenarios where there was limited RCT data, bias and differences in between-study heterogeneity between the two sets of data. The contrast-based methods provided a reduction in uncertainty, but performed worse in terms of coverage and error, unless there was no marked difference in heterogeneity between the two sets of data. CONCLUSIONS: The hierarchical power and commensurate prior methods provide the most robust approach to synthesising aggregate data from RCTs and single-arm studies, balancing the need to account for bias and differences in between-study heterogeneity, whilst reducing uncertainty in estimates. This work was restricted to considering a pairwise meta-analysis using aggregate data.

Methods for the inclusion of real-world evidence in network meta-analysis.

BACKGROUND: Network Meta-Analysis (NMA) is a key component of submissions to reimbursement agencies world-wide, especially when there is limited direct head-to-head evidence for multiple technologies from randomised controlled trials (RCTs). Many NMAs include only data from RCTs. However, real-world evidence (RWE) is also becoming widely recognised as a valuable source of clinical data. This study aims to investigate methods for the inclusion of RWE in NMA and its impact on the level of uncertainty around the effectiveness estimates, with particular interest in effectiveness of fingolimod. METHODS: A range of methods for inclusion of RWE in evidence synthesis were investigated by applying them to an illustrative example in relapsing remitting multiple sclerosis (RRMS). A literature search to identify RCTs and RWE evaluating treatments in RRMS was conducted. To assess the impact of inclusion of RWE on the effectiveness estimates, Bayesian hierarchical and adapted power prior models were applied. The effect of the inclusion of RWE was investigated by varying the degree of down weighting of this part of evidence by the use of a power prior. RESULTS: Whilst the inclusion of the RWE led to an increase in the level of uncertainty surrounding effect estimates in this example, this depended on the method of inclusion adopted for the RWE. 'Power prior' NMA model resulted in stable effect estimates for fingolimod yet increasing the width of the credible intervals with increasing weight given to RWE data. The hierarchical NMA models were effective in allowing for heterogeneity between study designs, however, this also increased the level of uncertainty. CONCLUSION: The 'power prior' method for the inclusion of RWE in NMAs indicates that the degree to which RWE is taken into account can have a significant impact on the overall level of uncertainty. The hierarchical modelling approach further allowed for accommodating differences between study types. Consequently, further work investigating both empirical evidence for biases associated with individual RWE studies and methods of elicitation from experts on the extent of such biases is warranted.

Bayesian hierarchical meta-analytic methods for modeling surrogate relationships that vary across treatment classes using aggregate data.

Surrogate endpoints play an important role in drug development when they can be used to measure treatment effect early compared to the final clinical outcome and to predict clinical benefit or harm. Such endpoints are assessed for their predictive value of clinical benefit by investigating the surrogate relationship between treatment effects on the surrogate and final outcomes using meta-analytic methods. When surrogate relationships vary across treatment classes, such validation may fail due to limited data within each treatment class. In this paper, two alternative Bayesian meta-analytic methods are introduced which allow for borrowing of information from other treatment classes when exploring the surrogacy in a particular class. The first approach extends a standard model for the evaluation of surrogate endpoints to a hierarchical meta-analysis model assuming full exchangeability of surrogate relationships across all the treatment classes, thus facilitating borrowing of information across the classes. The second method is able to relax this assumption by allowing for partial exchangeability of surrogate relationships across treatment classes to avoid excessive borrowing of information from distinctly different classes. We carried out a simulation study to assess the proposed methods in nine data scenarios and compared them with subgroup analysis using the standard model within each treatment class. We also applied the methods to an illustrative example in colorectal cancer which led to obtaining the parameters describing the surrogate relationships with higher precision.

Multivariate network meta-analysis incorporating class effects.

BACKGROUND: Network meta-analysis synthesises data from a number of clinical trials in order to assess the comparative efficacy of multiple healthcare interventions in similar patient populations. In situations where clinical trial data are heterogeneously reported i.e. data are missing for one or more outcomes of interest, synthesising such data can lead to disconnected networks of evidence, increased uncertainty, and potentially biased estimates which can have severe implications for decision-making. To overcome this issue, strength can be borrowed between outcomes of interest in multivariate network meta-analyses. Furthermore, in situations where there are relatively few trials informing each treatment comparison, there is a potential issue with the sparsity of data in the treatment networks, which can lead to substantial parameter uncertainty. A multivariate network meta-analysis approach can be further extended to borrow strength between interventions of the same class using hierarchical models. METHODS: We extend the trivariate network meta-analysis model to incorporate the exchangeability between treatment effects belonging to the same class of intervention to increase precision in treatment effect estimates. We further incorporate a missing data framework to estimate uncertainty in trials that did not report measures of variability in order to maximise the use of all available information for healthcare decision-making. The methods are applied to a motivating dataset in overactive bladder syndrome. The outcomes of interest were mean change from baseline in incontinence, voiding and urgency episodes. All models were fitted using Bayesian Markov Chain Monte Carlo (MCMC) methods in WinBUGS. RESULTS: All models (univariate, multivariate, and multivariate models incorporating class effects) produced similar point estimates for all treatment effects. Incorporating class effects in multivariate models often increased precision in treatment effect estimates. CONCLUSIONS: Multivariate network meta-analysis incorporating class effects allowed for the comparison of all interventions across all outcome measures to ameliorate the potential impact of outcome reporting bias, and further borrowed strength between interventions belonging to the same class of treatment to increase the precision in treatment effect estimates for healthcare policy and decision-making.

Bivariate network meta-analysis for surrogate endpoint evaluation.

Surrogate endpoints are very important in regulatory decision making in healthcare, in particular if they can be measured early compared to the long-term final clinical outcome and act as good predictors of clinical benefit. Bivariate meta-analysis methods can be used to evaluate surrogate endpoints and to predict the treatment effect on the final outcome from the treatment effect measured on a surrogate endpoint. However, candidate surrogate endpoints are often imperfect, and the level of association between the treatment effects on the surrogate and final outcomes may vary between treatments. This imposes a limitation on methods which do not differentiate between the treatments. We develop bivariate network meta-analysis (bvNMA) methods, which combine data on treatment effects on the surrogate and final outcomes, from trials investigating multiple treatment contrasts. The bvNMA methods estimate the effects on both outcomes for all treatment contrasts individually in a single analysis. At the same time, they allow us to model the trial-level surrogacy patterns within each treatment contrast and treatment-level surrogacy, thus enabling predictions of the treatment effect on the final outcome either for a new study in a new population or for a new treatment. Modelling assumptions about the between-studies heterogeneity and the network consistency, and their impact on predictions, are investigated using an illustrative example in advanced colorectal cancer and in a simulation study. When the strength of the surrogate relationships varies across treatment contrasts, bvNMA has the advantage of identifying treatment comparisons for which surrogacy holds, thus leading to better predictions.

A matrix-based method of moments for fitting multivariate network meta-analysis models with multiple outcomes and random inconsistency effects.

Random-effects meta-analyses are very commonly used in medical statistics. Recent methodological developments include multivariate (multiple outcomes) and network (multiple treatments) meta-analysis. Here, we provide a new model and corresponding estimation procedure for multivariate network meta-analysis, so that multiple outcomes and treatments can be included in a single analysis. Our new multivariate model is a direct extension of a univariate model for network meta-analysis that has recently been proposed. We allow two types of unknown variance parameters in our model, which represent between-study heterogeneity and inconsistency. Inconsistency arises when different forms of direct and indirect evidence are not in agreement, even having taken between-study heterogeneity into account. However, the consistency assumption is often assumed in practice and so we also explain how to fit a reduced model which makes this assumption. Our estimation method extends several other commonly used methods for meta-analysis, including the method proposed by DerSimonian and Laird (). We investigate the use of our proposed methods in the context of both a simulation study and a real example.

Bayesian meta-analytical methods to incorporate multiple surrogate endpoints in drug development process.

A number of meta-analytical methods have been proposed that aim to evaluate surrogate endpoints. Bivariate meta-analytical methods can be used to predict the treatment effect for the final outcome from the treatment effect estimate measured on the surrogate endpoint while taking into account the uncertainty around the effect estimate for the surrogate endpoint. In this paper, extensions to multivariate models are developed aiming to include multiple surrogate endpoints with the potential benefit of reducing the uncertainty when making predictions. In this Bayesian multivariate meta-analytic framework, the between-study variability is modelled in a formulation of a product of normal univariate distributions. This formulation is particularly convenient for including multiple surrogate endpoints and flexible for modelling the outcomes which can be surrogate endpoints to the final outcome and potentially to one another. Two models are proposed, first, using an unstructured between-study covariance matrix by assuming the treatment effects on all outcomes are correlated and second, using a structured between-study covariance matrix by assuming treatment effects on some of the outcomes are conditionally independent. While the two models are developed for the summary data on a study level, the individual-level association is taken into account by the use of the Prentice's criteria (obtained from individual patient data) to inform the within study correlations in the models. The modelling techniques are investigated using an example in relapsing remitting multiple sclerosis where the disability worsening is the final outcome, while relapse rate and MRI lesions are potential surrogates to the disability progression.

Use of Bayesian multivariate meta-analysis to estimate the HAQ for mapping onto the EQ-5D questionnaire in rheumatoid arthritis.

BACKGROUND: In health technology assessment, decisions about reimbursement for new health technologies are largely based on effectiveness estimates. Sometimes, however, the target effectiveness estimates are not readily available. This may be because many alternative instruments measuring these outcomes are being used (and not all always reported) or an extended follow-up time of clinical trials is needed to evaluate long-term end points, leading to the limited data on the target clinical outcome. In the areas of highest priority in health care, decisions are required to be made on a short time scale. Therefore, alternative clinical outcomes, including surrogate end points, are increasingly being considered for use in evidence synthesis as part of economic evaluation. OBJECTIVE: To illustrate the potential effect of reduced uncertainty around the clinical outcome on the utility when estimating it from a multivariate meta-analysis. METHODS: Bayesian multivariate meta-analysis has been used to synthesize data on correlated outcomes in rheumatoid arthritis and to incorporate external data in the model in the form of informative prior distributions. Estimates of Health Assessment Questionnaire were then mapped onto the health-related quality-of-life measure EuroQol five-dimensional questionnaire, and the effect was compared with mapping the Health Assessment Questionnaire obtained from the univariate approach. RESULTS: The use of multivariate meta-analysis can lead to reduced uncertainty around the effectiveness parameter and ultimately uncertainty around the utility. CONCLUSIONS: By allowing all the relevant data to be incorporated in estimating clinical effectiveness outcomes, multivariate meta-analysis can improve the estimation of health utilities estimated through mapping methods. While reduced uncertainty may have an effect on decisions based on economic evaluation of new health technologies, the use of short-term surrogate end points can allow for early decisions. More research is needed to determine the circumstances under which uncertainty is reduced.

Network meta-analysis of multiple outcome measures accounting for borrowing of information across outcomes.

BACKGROUND: Network meta-analysis (NMA) enables simultaneous comparison of multiple treatments while preserving randomisation. When summarising evidence to inform an economic evaluation, it is important that the analysis accurately reflects the dependency structure within the data, as correlations between outcomes may have implication for estimating the net benefit associated with treatment. A multivariate NMA offers a framework for evaluating multiple treatments across multiple outcome measures while accounting for the correlation structure between outcomes. METHODS: The standard NMA model is extended to multiple outcome settings in two stages. In the first stage, information is borrowed across outcomes as well across studies through modelling the within-study and between-study correlation structure. In the second stage, we make use of the additional assumption that intervention effects are exchangeable between outcomes to predict effect estimates for all outcomes, including effect estimates on outcomes where evidence is either sparse or the treatment had not been considered by any one of the studies included in the analysis. We apply the methods to binary outcome data from a systematic review evaluating the effectiveness of nine home safety interventions on uptake of three poisoning prevention practices (safe storage of medicines, safe storage of other household products, and possession of poison centre control telephone number) in households with children. Analyses are conducted in WinBUGS using Markov Chain Monte Carlo (MCMC) simulations. RESULTS: Univariate and the first stage multivariate models produced broadly similar point estimates of intervention effects but the uncertainty around the multivariate estimates varied depending on the prior distribution specified for the between-study covariance structure. The second stage multivariate analyses produced more precise effect estimates while enabling intervention effects to be predicted for all outcomes, including intervention effects on outcomes not directly considered by the studies included in the analysis. CONCLUSIONS: Accounting for the dependency between outcomes in a multivariate meta-analysis may or may not improve the precision of effect estimates from a network meta-analysis compared to analysing each outcome separately.

Bayesian meta-analysis for evaluating treatment effectiveness in biomarker subgroups using trials of mixed patient populations.

During drug development, evidence can emerge to suggest a treatment is more effective in a specific patient subgroup. Whilst early trials may be conducted in biomarker-mixed populations, later trials are more likely to enroll biomarker-positive patients alone, thus leading to trials of the same treatment investigated in different populations. When conducting a meta-analysis, a conservative approach would be to combine only trials conducted in the biomarker-positive subgroup. However, this discards potentially useful information on treatment effects in the biomarker-positive subgroup concealed within observed treatment effects in biomarker-mixed populations. We extend standard random-effects meta-analysis to combine treatment effects obtained from trials with different populations to estimate pooled treatment effects in a biomarker subgroup of interest. The model assumes a systematic difference in treatment effects between biomarker-positive and biomarker-negative subgroups, which is estimated from trials which report either or both treatment effects. The systematic difference and proportion of biomarker-negative patients in biomarker-mixed studies are used to interpolate treatment effects in the biomarker-positive subgroup from observed treatment effects in the biomarker-mixed population. The developed methods are applied to an illustrative example in metastatic colorectal cancer and evaluated in a simulation study. In the example, the developed method improved precision of the pooled treatment effect estimate compared with standard random-effects meta-analysis of trials investigating only biomarker-positive patients. The simulation study confirmed that when the systematic difference in treatment effects between biomarker subgroups is not very large, the developed method can improve precision of estimation of pooled treatment effects while maintaining low bias.

Four alternative methodologies for simulated treatment comparison: How could the use of simulation be re-invigorated?

Simulated treatment comparison (STC) is an established method for performing population adjustment for the indirect comparison of two treatments, where individual patient data (IPD) are available for one trial but only aggregate level information is available for the other. The most commonly used method is what we call 'standard STC'. Here we fit an outcome model using data from the trial with IPD, and then substitute mean covariate values from the trial where only aggregate level data are available, to predict what the first of these trial's outcomes would have been if its population had been the same as the second. However, this type of STC methodology does not involve simulation and can result in bias when the link function used in the outcome model is non-linear. An alternative approach is to use the fitted outcome model to simulate patient profiles in the trial for which IPD are available, but in the other trial's population. This stochastic alternative presents additional challenges. We examine the history of STC and propose two new simulation-based methods that resolve many of the difficulties associated with the current stochastic approach. A virtue of the simulation-based STC methods is that the marginal estimands are then clearly targeted. We illustrate all methods using a numerical example and explore their use in a simulation study.

Multivariate meta-analysis of mixed outcomes: a Bayesian approach.

Multivariate random effects meta-analysis (MRMA) is an appropriate way for synthesizing data from studies reporting multiple correlated outcomes. In a Bayesian framework, it has great potential for integrating evidence from a variety of sources. In this paper, we propose a Bayesian model for MRMA of mixed outcomes, which extends previously developed bivariate models to the trivariate case and also allows for combination of multiple outcomes that are both continuous and binary. We have constructed informative prior distributions for the correlations by using external evidence. Prior distributions for the within-study correlations were constructed by employing external individual patent data and using a double bootstrap method to obtain the correlations between mixed outcomes. The between-study model of MRMA was parameterized in the form of a product of a series of univariate conditional normal distributions. This allowed us to place explicit prior distributions on the between-study correlations, which were constructed using external summary data. Traditionally, independent 'vague' prior distributions are placed on all parameters of the model. In contrast to this approach, we constructed prior distributions for the between-study model parameters in a way that takes into account the inter-relationship between them. This is a flexible method that can be extended to incorporate mixed outcomes other than continuous and binary and beyond the trivariate case. We have applied this model to a motivating example in rheumatoid arthritis with the aim of incorporating all available evidence in the synthesis and potentially reducing uncertainty around the estimate of interest.

Use of implicit and explicit bayesian methods in health technology assessment.

OBJECTIVES: The aim of this study was to examine the use of implicit and explicit Bayesian methods in health technology assessments and to identify whether this has changed over time. METHODS: A review of all health technology assessment (HTA) reports of secondary research published by the UK National Institute of Health Research (NIHR) between 1997 and 2011. Data were extracted on the use and implementation of Bayesian methods, whether defined as such by the original authors (i.e., explicit) or not (i.e., implicit). RESULTS: A total of 155 of 375 (41 percent) NIHR HTA reports, identified as relevant to this review, contained a Bayesian analysis. Of these, 128 (83 percent) contained an implicit Bayesian analysis, 3 (2 percent) an explicit Bayesian analysis and 24 (15 percent) both implicit and explicit Bayesian analyses. Of the twenty-seven reports that explicitly used Bayes theorem, only six included prior information in the form of (informative) prior distributions. Over time, the percentage of HTA reports that used Bayesian (implicit and/or explicit) methods increased from 0 percent in 1997 to nearly 80 percent in 2011. CONCLUSIONS: This review has shown that there has been an increase in the use of Bayesian methods in HTA, which is likely to be a result of the increase in freely available resources to implement the approach. Areas where Bayesian methods have the potential to advance healthcare evaluations in the future are considered in the discussion.