Bayesian approach to meta-analysis. What can you gain ?

1. Bayesian approach to meta-analysis. What can you gain? Mateusz Nikodem CASPolskaAssociation 19-th Cochrane Colloquium, Madrid, Oct 2011

2. Outline • On variety of statistical methods • Differences between Bayesian and classical (frequentist) approach • Most useful applications of Bayesian approach

3. eBayesMet (Nov 2009 - Oct 2011) • Partners: • CASPolskaAssociation - leader • Queen Mary University of London • AMC Amsterdam • EMMERCE EEIG • Maintasks: • SystematicReviews on statisticalmethods of meta-analyses • Analysis of credibility of statisticalmethods • Creating e-learning tool and with a guide, helpinginchoosingoptimalmethod for conductingmeta-analises.

5. Variety of methods • Plenty of statisticalmethods (Mantel-Haenszel, Peto, InverseVariance, DerSimonianLaird, Bűcher, etc.) are in use. • Among them there exist Bayesian methods • (rarely used in case of direct comparison, but frequently in case of indirect/network comparison) • Bayesianmethodis NOT one particularformulaoralgorithm. Itisratherwidestatisticianapproach.

6. Frequentist approach • Classicalmethodsare, usuallybased on algorithmsusingexplicitformulas. mainassumptionsofthe model results of studies (usuallyRCTs) Transformations of input data Results of Meta-analysis

7. Bayesian approach • Bayesianapproach - widerange of flexiblemethods • based on thetheory of conditionalprobability. • Howdoesitwork? Construction: Computation: Runningthe model (series of random simulations) Mainassumptions, establishingvariables and relationbetweenthem Obtainingresults of meta-analysisinrequired form Establishingpriordistributions of thevariables (can be non-informative) Inputingconditions, i.e. valuesobtainedinobservations

8. Frequentist vs Bayesian approach

9. Choosing optimal statistical method The adequate (most credible and precise) statistical method for meta-analysis should be chosen dependently on given data set (sample size, event rates, heterogeneity, etc.). In most cases there is some version of Bayesian model, which is (one of) optimal methods. On the other hand, usually in the simplest case of direct comparison of two treatments there is no substantial advantage of Bayesian approach.

10. Typical meta-analysis in Bayesian approach mainassumptionsofthe model non-informativepriordistributions results of studies MCMC simulations Results of Meta-analysis

11. More application of Bayesianapproach Including extra (prior) information Assessingclinicalsignificance of results Combiningdirect and indirectevidence, analyzingmultipletreatments

12. Including extra (prior) information mainassumptionsofthe model establihingpriordistributionsbasing on: results of randomizedstudies Extra data e.g. results of non-randomizedtrials, historicalobservations, etc. ! Settingthelevel of conviction to this data MCMC simulations Results of Meta-analysis

13. Example T. Huynh et. al., 2009, Comparison of Primary Percutaneous Coronary Intervention and Fibrinolytic Therapy in ST-Segment-Elevation Myocardial Infarction. What should we do with data from non-randomized studies?

14. Assessing clinical significance mainassumptionsofthe model non-informativepriordistributions results of studies establihingthelevel of clinicalsignificantresult (e.g. RR > 1.2) MCMC simulations Results of Meta-analysis Possible to obtaindue to knowledge of wholedistribution ! Answeringthequestion: Howprobableisthattheresultisclinicallysignificant?

15. Multiple Treatments Comparison mainassumptionsofthe model non-informativepriordistributions results of studies ! establihingthestructure of comparisons MCMC simulations Results of Meta-analysis

16. Example Woo et. al, 2010, Tenofovir and Entecavir Are the Most Effective Antiviral Agents forChronic Hepatitis B • 10 traetments to compare • 20 RCTs (comapringdifferentpairs of treatments) to include MTC • For eachtreatmentthefollowingisobtained: • estimatedeventrate • probabilitythatthetreatmentis most effective • order inthe group (ranking)

17. References • M. Bradburn, J.Deeks, J. Berlin,R.Localio„Much ado about nothing: a comparison of meta-analytical methods with rare events”, Statistics in medicine 2007;26:53-77. • A.J. Sutton, K.R. Abrams, Bayesian methods in meta-analysis and evidence synthesis, Statistical Methods in Medical Research 2001; 10: 277-303. • Higgins JPT, Green S (editors). Cochrane Handbook for Systematic Reviews of Interventions, Version 5.0.2, Chapters 9.4, 9.5,16.9 The Cochrane Collaboration, (2008) [updated 09.2009].

18. References • G. Woodworth „Biostatistics, a Bayesian Intruduction”, WILEY,(2004), • D. J. Spiegelhalter, N. G. Best Bayesian approaches to multiple sources of evidenceand uncertainty in complex cost-efectivenessmodelling, Stat Med. 22(23): 3687-3709, (2003), • M. Bradburn, J.Deeks, J. Berlin,R.Localio„Much ado about nothing: a comparison of meta-analytical methods with rare events”, Statistics in medicine 2007;26:53-77.

19. References • T. Huynh et. al. „Comparison of PrimaryPercutaneousCoronaryIntervention and FibrinolyticTherapyinST-Segment-ElevationMyocardialInfarctionBayesianHierarchicalMeta-Analyses of RandomizedControlledTrials and ObservationalStudies”, Circulation 2009, 119, 3101-3109 • G. Wooet.al. „Tenofovir and entecavir are the most effective antiviral agents for chronic hepatitis B: a systematic review and Bayesian meta-analyses.”, Gastroenterology. 2010, 139(4), 1218-29.