Bayesian approach to meta-analysis. What can you gain? Mateusz Nikodem CASPolska Association 19-th Cochrane Colloquium, Madrid, Oct 2011 Outline • On variety of statistical methods • Differences between Bayesian and classical (frequentist) approach • Most useful applications of Bayesian approach eBayesMet (Nov 2009 - Oct 2011) Partners: • CASPolska Association - leader • Queen Mary University of London • AMC Amsterdam • EMMERCE EEIG Main tasks: • Systematic Reviews on statistical methods of metaanalyses • Analysis of credibility of statistical methods • Creating e-learning tool and with a guide, helping in choosing optimal method for conducting meta-analises. Variety of methods Plenty of statistical methods (Mantel-Haenszel, Peto, Inverse Variance, DerSimonian Laird, 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) Bayesian method is NOT one particular formula or algorithm. It is rather wide statistician approach. Frequentist approach Classical methods are, usually based on algorithms using explicit formulas. main assumptions of the model results of studies (usually RCTs) Transformations of input data Results of Meta-analysis Bayesian approach Bayesian approach - wide range of flexible methods based on the theory of conditional probability. How does it work? Construction: Computation: Main assumptions, establishing variables and relation between them Establishing prior distributions of the variables (can be noninformative) Inputing conditions, i.e. values obtained in observations Running the model (series of random simulations) Obtaining results of meta-analysis in required form Frequentist vs Bayesian approach Bayesian approach Frequentialist methods philosophy First: assumptions and construction then: inputing results of studies Construction based on the results of studies flexibility YES NO computation Makov Chain Monte Carlo simulations software specialistic, e.g. WinBUGS formulas no special requirements 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. Typical meta-analysis in Bayesian approach main assumptions of the model non-informative prior distributions results of studies MCMC simulations Results of Meta-analysis More application of Bayesian approach Including extra (prior) information Assessing clinical significance of results Combining direct and indirect evidence, analyzing multiple treatments Including extra (prior) information main assumptions of the model establihing prior distributions basing on: Extra data e.g. results of non-randomized trials, historical observations, etc. Setting the level of conviction to this data ! MCMC simulations Results of Meta-analysis results of randomized studies Example T. Huynh et. al., 2009, Comparison of Primary Percutaneous Coronary Intervention and Fibrinolytic Therapy in ST-SegmentElevation Myocardial Infarction. Primary PCI Fibrinolytic Therapy Total in RCTs (24) 4068 4072 Total in Observational studies(30) 57124 123753 What should we do with data from non-randomized studies? Assessing clinical significance main assumptions of the model non-informative prior distributions results of studies establihing the level of clinical significant result (e.g. RR > 1.2) MCMC simulations Results of Meta-analysis ! Answering the question: How probable is that the result is clinically significant? Possible to obtain due to knowledge of whole distribution Multiple Treatments Comparison main assumptions of the model establihing the structure of comparisons non-informative prior distributions ! MCMC simulations Results of Meta-analysis results of studies Example Woo et. al, 2010, Tenofovir and Entecavir Are the Most Effective Antiviral Agents for Chronic Hepatitis B • 10 traetments to compare • 20 RCTs (comapring different pairs of treatments) to include MTC For each treatment the following is obtained: • estimated event rate • probability that the treatment is most effective • order in the group (ranking) References 1. 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. 2. A.J. Sutton, K.R. Abrams, Bayesian methods in metaanalysis and evidence synthesis, Statistical Methods in Medical Research 2001; 10: 277-303. 3. 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]. References 4. G. Woodworth „Biostatistics, a Bayesian Intruduction”, WILEY, (2004), 5. D. J. Spiegelhalter, N. G. Best Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-efectiveness modelling, Stat Med. 22(23): 3687-3709, (2003), 6. 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. References 7. T. Huynh et. al. „Comparison of Primary Percutaneous Coronary Intervention and Fibrinolytic Therapy in STSegment-Elevation Myocardial Infarction Bayesian Hierarchical Meta-Analyses of Randomized Controlled Trials and Observational Studies”, Circulation 2009, 119, 3101-3109 8. G. Woo et.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.