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

```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
• Queen Mary University of London
• AMC Amsterdam
• EMMERCE EEIG
• 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.
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