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Network meta-analysis is used to simultaneously compare multiple treatments in a single analysis. However, network meta-analyses may exhibit inconsistency, where direct and different forms of indirect evidence are not in agreement with each other, even after allowing for between-study heterogeneity. Models for network meta-analysis with random inconsistency effects have the dual aim of allowing for inconsistencies and estimating average treatment effects across the whole network. To date, two classical estimation methods for fitting this type of model have been developed: a method of moments that extends DerSimonian and Laird's univariate method and maximum likelihood estimation. However, the Paule and Mandel estimator is another recommended classical estimation method for univariate meta-analysis. In this paper, we extend the Paule and Mandel method so that it can be used to fit models for network meta-analysis with random inconsistency effects. We apply all three estimation methods to a variety of examples that have been used previously and we also examine a challenging new dataset that is highly heterogenous. We perform a simulation study based on this new example. We find that the proposed Paule and Mandel method performs satisfactorily and generally better than the previously proposed method of moments because it provides more accurate inferences. Furthermore, the Paule and Mandel method possesses some advantages over likelihood-based methods because it is both semiparametric and requires no convergence diagnostics. Although restricted maximum likelihood estimation remains the gold standard, the proposed methodology is a fully viable alternative to this and other estimation methods., (© 2017 The Authors. Research Synthesis Methods Published by John Wiley & Sons Ltd.)

One of the reasons for the popularity of meta-analysis is the notion that these analyses will possess more power to detect effects than individual studies. This is inevitably the case under a fixed-effect model. However, the inclusion of the between-study variance in the random-effects model, and the need to estimate this parameter, can have unfortunate implications for this power. We develop methods for assessing the power of random-effects meta-analyses, and the average power of the individual studies that contribute to meta-analyses, so that these powers can be compared. In addition to deriving new analytical results and methods, we apply our methods to 1991 meta-analyses taken from the Cochrane Database of Systematic Reviews to retrospectively calculate their powers. We find that, in practice, 5 or more studies are needed to reasonably consistently achieve powers from random-effects meta-analyses that are greater than the studies that contribute to them. Not only is statistical inference under the random-effects model challenging when there are very few studies but also less worthwhile in such cases. The assumption that meta-analysis will result in an increase in power is challenged by our findings., (Copyright © 2017 The Authors. Research Synthesis Methods Published by John Wiley & Sons Ltd.)

When combining results across related studies, a multivariate meta-analysis allows the joint synthesis of correlated effect estimates from multiple outcomes. Joint synthesis can improve efficiency over separate univariate syntheses, may reduce selective outcome reporting biases, and enables joint inferences across the outcomes. A common issue is that within-study correlations needed to fit the multivariate model are unknown from published reports. However, provision of individual participant data (IPD) allows them to be calculated directly. Here, we illustrate how to use IPD to estimate within-study correlations, using a joint linear regression for multiple continuous outcomes and bootstrapping methods for binary, survival and mixed outcomes. In a meta-analysis of 10 hypertension trials, we then show how these methods enable multivariate meta-analysis to address novel clinical questions about continuous, survival and binary outcomes; treatment-covariate interactions; adjusted risk/prognostic factor effects; longitudinal data; prognostic and multiparameter models; and multiple treatment comparisons. Both frequentist and Bayesian approaches are applied, with example software code provided to derive within-study correlations and to fit the models., (© 2014 The Authors. Research Synthesis Methods published by John Wiley & Sons, Ltd.)

Meta-analysis of time-to-event data has proved difficult in the past because consistent summary statistics often cannot be extracted from published results. The use of individual patient data allows for the re-analysis of each study in a consistent fashion and thus makes meta-analysis of time-to-event data feasible. Time-to-event data can be analysed using proportional hazards models, but incorporating random effects into these models is not straightforward in standard software. This paper fits random-effects proportional hazards models by treating the random effects as missing data and applying the expectation-maximisation algorithm. This approach has been used before by using Markov chain Monte Carlo methods to perform the expectation step of the algorithm. In this paper, the expectation step is simplified, without sacrificing accuracy, by approximating the expected values of the random effects using simple shrinkage estimators. This provides a robust method for fitting random-effects models that can be implemented in standard statistical packages. Copyright © 2012 John Wiley & Sons, Ltd., (Copyright © 2012 John Wiley & Sons, Ltd.)

Background: Methods need to be further developed to include non-randomised studies (NRS) in systematic reviews of the effects of health care interventions. NRS are often required to answer questions about harms and interventions for which evidence from randomised controlled trials (RCTs) is not available. Methods used to review randomised controlled trials may be inappropriate or insufficient for NRS., Aim and Methods: A workshop was convened to discuss relevant methodological issues. Participants were invited from important stakeholder constituencies, including methods and review groups of the Cochrane and Campbell Collaborations, the Cochrane Editorial Unit and organisations that commission reviews and make health policy decisions. The aim was to discuss methods for reviewing evidence when including NRS and to formulate methodological guidance for review authors., Workshop Format: The workshop was structured around four sessions on topics considered in advance to be most critical: (i) study designs and bias; (ii) confounding and meta-analysis; (iii) selective reporting; and (iv) applicability. These sessions were scheduled between introductory and concluding sessions., Summary: This is the first of six papers and provides an overview. Subsequent papers describe the discussions and conclusions from the four main sessions (papers 2 to 5) and summarise the proposed guidance into lists of issues for review authors to consider (paper 6). Copyright © 2013 John Wiley & Sons, Ltd., (Copyright © 2013 John Wiley & Sons, Ltd.)

Background: There is increasing interest from review authors about including non-randomized studies (NRS) in their systematic reviews of health care interventions. This series from the Ottawa Non-Randomized Studies Workshop consists of six papers identifying methodological issues when doing this., Aim: To format the guidance from the preceding papers on study design and bias, confounding and meta-analysis, selective reporting, and applicability/directness into checklists of issues for review authors to consider when including NRS in a systematic review., Checklists: Checklists were devised providing frameworks to describe/assess: (1) study designs based on study design features; (2) risk of residual confounding and when to consider meta-analysing data from NRS; (3) risk of selective reporting based on the Cochrane framework for detecting selective outcome reporting in trials but extended to selective reporting of analyses; and (4) directness of evidence contributed by a study to aid integration of NRS findings into summary of findings tables., Summary: The checklists described will allow review groups to operationalize the inclusion of NRS in systematic reviews in a more consistent way. The next major step is extending the existing Cochrane Risk of Bias tool so that it can assess the risk of bias to NRS included in a review. Copyright © 2013 John Wiley & Sons, Ltd., (Copyright © 2013 John Wiley & Sons, Ltd.)

Meta-analyses that simultaneously compare multiple treatments (usually referred to as network meta-analyses or mixed treatment comparisons) are becoming increasingly common. An important component of a network meta-analysis is an assessment of the extent to which different sources of evidence are compatible, both substantively and statistically. A simple indirect comparison may be confounded if the studies involving one of the treatments of interest are fundamentally different from the studies involving the other treatment of interest. Here, we discuss methods for addressing inconsistency of evidence from comparative studies of different treatments. We define and review basic concepts of heterogeneity and inconsistency, and attempt to introduce a distinction between 'loop inconsistency' and 'design inconsistency'. We then propose that the notion of design-by-treatment interaction provides a useful general framework for investigating inconsistency. In particular, using design-by-treatment interactions successfully addresses complications that arise from the presence of multi-arm trials in an evidence network. We show how the inconsistency model proposed by Lu and Ades is a restricted version of our full design-by-treatment interaction model and that there may be several distinct Lu-Ades models for any particular data set. We introduce novel graphical methods for depicting networks of evidence, clearly depicting multi-arm trials and illustrating where there is potential for inconsistency to arise. We apply various inconsistency models to data from trials of different comparisons among four smoking cessation interventions and show that models seeking to address loop inconsistency alone can run into problems. Copyright © 2012 John Wiley & Sons, Ltd., (Copyright © 2012 John Wiley & Sons, Ltd.)

Network meta-analysis (multiple treatments meta-analysis, mixed treatment comparisons) attempts to make the best use of a set of studies comparing more than two treatments. However, it is important to assess whether a body of evidence is consistent or inconsistent. Previous work on models for network meta-analysis that allow for heterogeneity between studies has either been restricted to two-arm trials or followed a Bayesian framework. We propose two new frequentist ways to estimate consistency and inconsistency models by expressing them as multivariate random-effects meta-regressions, which can be implemented in some standard software packages. We illustrate the approach using the mvmeta package in Stata. Copyright © 2012 John Wiley & Sons, Ltd., (Copyright © 2012 John Wiley & Sons, Ltd.)

Meta-analysis is widely used to synthesise results from randomised trials. When the relevant trials collected time-to-event data, individual participant data are commonly sought from all trials. Meta-analyses of time-to-event data are typically performed using variants of the log-rank test, but modern statistical software allows for the use of maximum likelihood methods such as Cox proportional hazards models or interval-censored logistic regression. In this paper, the different approaches to the analysis of time-to-event data are examined and compared with show that log-rank test approaches are in fact first-order approximations to the maximum likelihood methods and that some methods assume proportional hazards, whereas others assume proportional odds. A simulation study is performed to compare the different methods, which shows that log-rank test approaches give biased estimates when the underlying hazard ratio or odds ratio is far from unity. It also shows that proportional hazards methods give biased results when hazards are not proportional, and proportional odds methods give biased results when odds are not proportional. Maximum likelihood models should, therefore, be preferred to log-rank test based methods for the meta-analysis of time-to-event data and any such meta-analysis should investigate whether proportional hazards or proportional odds assumptions are valid. Copyright © 2011 John Wiley & Sons, Ltd., (Copyright © 2011 John Wiley & Sons, Ltd.)

Meta-analyses of individual patient data (IPD) provide a strong and authoritative basis for evidence synthesis. IPD are particularly useful when the outcome of interest is the time to an event. Methodological developments now enable the meta-analysis of time-to-event IPD using a single model, allowing treatment effect and across-trial heterogeneity parameters to be estimated simultaneously. This differs from the standard approaches used with aggregate data, and also predominantly with IPD. Facilitated by a simulation study, we investigate what these new 'one-stage' random-effects models offer over standard 'two-stage' approaches. We find that two-stage approaches represent a robust, reliable and easily implementable way to estimate treatment effects and account for heterogeneity. Nevertheless, one-stage models can be used to provide a deeper insight into the data. Software for fitting one-stage Cox models with random effects using Restricted Maximum Likelihood methodology is made available, and its use demonstrated on an IPD meta-analysis assessing post-operative radio therapy for patients with non-small cell lung cancer. Copyright © 2011 John Wiley & Sons, Ltd., (Copyright © 2011 John Wiley & Sons, Ltd.)