Systematic review, meta-analysis and economic modelling of ...

DOI: 10.3310/hta17010 Health Technology Assessment 2013 Vol. 17 No. 11 0(( 1 ) )∑ ~IW ,R = 5AB 0The impact of this is mainly on the prior estimates of the between-study SDs, which are reduced from 1.5[95% credible interval (CrI) 0.4 to 33.1] to 0.5 (95% CrI 0.3 to 1.4) when R is increased from ‘2’ to ‘5’ inthe inverse Wishart distribution.Meta-analysis of prognostic test accuracy Data were available from studies in which patients wereclassified as either having an event or not having an event, depending on whether the index test waspositive, inconclusive or negative. Not all studies reported inconclusive tests separately; some reportedinconclusive results with the positives, others with the negatives and in others it was not clear whether ornot there were any inconclusive tests. Furthermore, some studies reported outcomes only for those with apositive or negative index test. We excluded studies that reported outcomes only for positive or negativeindex tests. If no inconclusive tests were reported, we included the data in the analyses by assuming thatthere were no inconclusive results.Relative risks (RRs) were calculated by comparing (1) positive compared with inconclusive and negativeand (2) positive and inconclusive compared with negative. The data were meta-analysed using a Bayesianrandom-effects model as follows. 34We let r ijrepresent the number of events in category j in study i and N ijrepresent the total number ofindividuals in category j in study i. We assumed that the data followed a Binomial distribution such that:r( )~ Binomial P,Nij ij ijwhere P ijrepresents the probability of an event category j in study I.We let:( ) ( )log P = µ + min δ − log( P ) I≠ij i i ij ( J 1)so that the µ iare study-specific baselines representing the log of the absolute risk of an event in thebaseline category and the second term is the log-RR in study i.We assumed a random-effects model in which the study-specific RRs are assumed to come from apopulation of effects that are normally distributed such that:2N( )δ ~ µ , τiWe completed the model by giving the uncertain parameters the following prior distributions:exp( )~ 0,1µ Uniform( )iδ ~ N( 0,1000)iτ ~ U ( 0,2 )The data were analysed using the freely available WinBUGS software. 33 Convergence was assessed usingthe Gelman–Rubin convergence statistic. 35 Convergence occurred after 50,000 iterations. There was someevidence of high autocorrelation between successive iterations of the Markov chains. We used a burn-in of50,000 and generated a further 60,000 iterations after thinning the chains every 10 iterations to estimatethe parameters.© Queen’s Printer and Controller of HMSO 2013. This work was produced by Goodacre et al. under the terms of a commissioning contract issued by the Secretary of Statefor Health. This issue may be freely reproduced for the purposes of private research and study and extracts (or indeed, the full report) may be included in professional journalsprovided that suitable acknowledgement is made and the reproduction is not associated with any form of advertising. Applications for commercial reproduction should beaddressed to: NIHR Journals Library, National Institute for Health Research, Evaluation, Trials and Studies Coordinating Centre, Alpha House, University of Southampton SciencePark, Southampton SO16 7NS, UK.15