### 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 meta analyses 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: Main assumptions, establishing variables and relation between them Computation: Running the model (series of random simulations) Establishing prior distributions of the variables (can be non informative) Inputing conditions, i.e. values obtained in observations Obtaining results of meta-analysis in required form

### Frequentist vs Bayesian approach

philosophy Bayesian approach First: assumptions and construction then: inputing results of studies Frequentialist methods Construction based on the results of studies flexibility

YES

computation Makov Chain Monte Carlo simulations software specialistic, e.g. WinBUGS

NO

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 MCMC simulations results of studies

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

!

results of randomized studies MCMC simulations

Results of Meta-analysis

### Example

T. Huynh et. al., 2009, Comparison of Primary Percutaneous

Coronary Intervention and Fibrinolytic Therapy in ST-Segment Elevation Myocardial Infarction.

Total in RCTs (24) Total in Observational studies(30)

Primary PCI

4068 57124

Fibrinolytic Therapy

4072 123753 What should we do with data from non-randomized studies?

### Assessing clinical significance

main assumptions of the model establihing the level of clinical significant result (e.g. RR > 1.2) non-informative prior distributions MCMC simulations results of studies

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 non-informative prior distributions results of studies

establihing the structure of comparisons !

MCMC simulations

Results of Meta-analysis

### 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

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 meta- analysis 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 ST Segment-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.