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Tests for disease often produce a continuous measure, such as the concentration of some biomarker in a blood sample. In clinical practice, a threshold C is selected such that results, say, greater than C are declared positive and those less than C negative. Measures of test accuracy such as sensitivity and specificity depend crucially on C, and the optimal value of this threshold is usually a key question for clinical practice. Standard methods for meta-analysis of test accuracy (i) do not provide summary estimates of accuracy at each threshold, precluding selection of the optimal threshold, and furthermore, (ii) do not make use of all available data. We describe a multinomial meta-analysis model that can take any number of pairs of sensitivity and specificity from each study and explicitly quantifies how accuracy depends on C. Our model assumes that some prespecified or Box-Cox transformation of test results in the diseased and disease-free populations has a logistic distribution. The Box-Cox transformation parameter can be estimated from the data, allowing for a flexible range of underlying distributions. We parameterise in terms of the means and scale parameters of the two logistic distributions. In addition to credible intervals for the pooled sensitivity and specificity across all thresholds, we produce prediction intervals, allowing for between-study heterogeneity in all parameters. We demonstrate the model using two case study meta-analyses, examining the accuracy of tests for acute heart failure and preeclampsia. We show how the model can be extended to explore reasons for heterogeneity using study-level covariates., (© 2019 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

Published studies of the duration of asymptomatic Chlamydia trachomatis infection in women have produced diverse estimates, and most reviewers have not attempted an evidence synthesis. We review the designs of duration studies, distinguishing between the incident cases presenting soon after infection in clinic-based studies and prevalent cases ascertained in population screening studies. We combine evidence from all studies under fixed-effect (single clearance rate), random-effect (study-specific clearance rate), and mixture-of-exponentials models, in which there are either two or three classes of infection that clear at different rates. We can identify classes as 'passive' infection and fast-clearing and slow-clearing infections. We estimate models by Bayesian MCMC and compared them using posterior mean residual deviance and the deviance information criterion. The single fixed-effect clearance rate model fitted very poorly. The random-effect model was adequate but inferior to the two-class and three-class mixture of exponentials. According to the two-class model, the proportion in the first class was 23% (95% CI: 16-31%), and the mean duration of C. trachomatis infection is 1.36 years (95% CI: 1.13-1.63 years). With the three-rate model, duration was similar, but identification of the proportions in each class (19%, 31%, and 49%) was poor. Although the random-effect model was descriptively adequate, the extreme degree of between-study variation in the clearance rate it predicted lacked biological plausibility. Differences in study recruitment and sampling mechanisms, acting through a mixture-of-exponentials model, better explains the apparent heterogeneity in duration., (Copyright © 2012 John Wiley & Sons, Ltd.)

Willan and Eckermann describe a method for dealing with heterogeneity in value of information (VOI) calculations for prioritising and designing new research. Their article raises three fundamental (inter-related) issues for VOI methods: (1) how to make sense of the concept of uncertainty in a cost-effectiveness analysis (CEA) model, (2) the interpretation of heterogeneity in CEA, and (3) the relationship between data from a new study and the CEA model when there is heterogeneity. We discuss these three issues using an illustrative example meta-analysis of magnesium for myocardial infarction. Careful consideration of the relationship between existing (and future) evidence and the CEA model is required to provide practical VOI methods that can help research funders prioritise new research in the face of heterogeneity., (Copyright © 2011 John Wiley & Sons, Ltd.)

Heterogeneity and small-study effects are major concerns for the validity of meta-analysis. Although random effects meta-analysis provides a partial solution to heterogeneity, neither takes into account the presence of small-study effects, although they can rarely be ruled out with certainty. In this paper, we facilitate a better understanding of the properties of a recently described regression-based approach to deriving a meta-analysis estimator robust to small-study effects and unexplainable heterogeneity. The weightings of studies in the meta-analysis are derived algebraically for the regression model and compared with the weightings allocated to studies by fixed and random effects models. These weightings are compared in case studies with and without small-study effects. The presence of small-study effects causes pooled estimates from fixed and random effects meta-analyses to differ, potentially markedly, as a result of the different weights allocated to individual studies. Because random effects meta-analysis gives more weight to smaller studies, it becomes more vulnerable to the small-study effects. The regression approach gives heavier weight to the larger studies than either the fixed or random effects models, leading to its dominance in the estimated pooled effect. The weighting properties of the proposed regression-derived meta-analysis estimator are presented and compared with those of the standard meta-analytic estimators. We propose that there is much to recommend the routine use of this model as a reliable way to derive a pooled meta-analysis estimate that is robust to potential small-study effects, while still accommodating heterogeneity, even though uncertainty will often be considerably larger than for standard estimators., (Copyright © 2012 John Wiley & Sons, Ltd.)

Mixed treatment comparison (MTC) meta-analyses estimate relative treatment effects from networks of evidence while preserving randomisation. We extend the MTC framework to allow for repeated measurements of a continuous endpoint that varies over time. We used, as a case study, a systematic review and meta-analysis of intraocular pressure (IOP) measurements from randomised controlled trials evaluating topical ocular hypotensives in primary open-angle glaucoma or ocular hypertension because IOP varies over the day and over the treatment course, and repeated measurements are frequently reported. We adopted models for conducting MTC in WinBUGS (The BUGS Project, Cambridge, UK) to allow for repeated IOP measurements and to impute missing standard deviations of the raw data using the predictive distribution from observations with standard deviations. A flexible model with an unconstrained baseline for IOP variations over time and time-invariant random treatment effects fitted the data well. We also adopted repeated measures models to allow for class effects; assuming treatment effects to be exchangeable within classes slightly improved model fit but could bias estimated treatment effects if exchangeability assumptions were not valid. We enabled all timepoints to be included in the analysis, allowing for repeated measures to increase precision around treatment effects and avoid bias associated with selecting timepoints for meta-analysis.The methods we developed for modelling repeated measures and allowing for missing data may be adapted for use in other MTC meta-analyses., (Copyright © 2011 John Wiley & Sons, Ltd.)

Standard approaches to analysis of randomized controlled trials (RCTs) using Markov models make it difficult to generalize treatment effects to new patient groups and synthesize evidence across trials. This paper demonstrates how pair-wise and mixed treatment comparison meta-analysis can be applied to event history data for disease progression reported by RCTs. The data, in the form of aggregated discrete time transitions, have a multi-nomial likelihood. In order for evidence synthesis to be performed a structured approach to modelling the differences in the effects of the different treatments must be taken. A multi-state continuous-time Markov model similar to others used in published economic evaluations of asthma treatments is developed, with transition rates related to the likelihood via Kolmogorov's forward equations. The formulation in terms of rates allows a flexible characterization of summary treatment effects. These ideas are applied to an illustrative data set consisting of a set of five trials comparing eight different treatments for asthma. A range of models is developed in which the relative treatment effects act on forward, backward transitions, or both, and models are compared using the DIC. Bayesian inferential techniques are used and the parameters are estimated using MCMC simulation in WinBUGS. An intuitively appealing mechanism of action involving a single parameter acting on all backward transitions was identified for the relative effects of the treatments, which allowed the estimation of a pooled treatment effect, allowing us to rank the different treatment options within each connected evidence network to ascertain which were the most clinically effective., (Copyright © 2010 John Wiley & Sons, Ltd.)

We propose a hierarchical model for the analysis of data from several randomized trials where some outcomes are missing. The degree of departure from a missing-at-random assumption in each arm of each trial is expressed by an informative missing odds ratio (IMOR). We require a realistic prior for the IMORs, including an assessment of the prior correlation between IMORs in different arms and in different trials. The model is fitted by Monte Carlo Markov Chain techniques. By applying the method in three different data sets, we show that it is possible to appropriately capture the extra uncertainty due to missing data, and we discuss in what circumstances it is possible to learn about the IMOR.

This paper outlines the current 'state of play' regarding the use of evidence in decision modelling and highlights both practical issues and methodological challenges related to identifying, combining and reporting evidence to inform decision model parameters and structure. Based on discussions at two MRC HSRC-funded workshops consisting of 37 experts from a range of disciplines (i.e. decision-makers, health economists, information specialists, operations researchers and statisticians), it aims to derive a multi-disciplinary standpoint on the appropriate use of evidence in economic decision models and, where applicable, offer some suggestions for good modelling practice. Gaps in the established methodology knowledge base are identified for future research., (Copyright (c) 2007 John Wiley & Sons, Ltd.)