Bayesian random-effects meta-analysis model for normal data - Pubrica
                     WHAT IS THE 
BAYESIAN  RANDOM-
EFFECTS  META-
ANALYSIS MODEL  FOR 
NORMAL DATA
An Academic presentation by
Dr. Nancy Agnes, Head, Technical Operations, 
Pubrica  Group: www.pubrica.com
Email: [email protected]
Today's 
Discussion
Outline
Introduction
Bayesian Methods: The 
Principles
Meta-Analysis 
Concept In  Bayesian 
Method
Bayesian Meta-Analysis 
Profits &  Contraindications
Future Scope
Introductio
In healthcare studies, systematic reviews are valuable  
n sources of evidence.
These are regarded as having a high
 evidence because degree of  reduce
tehveayluation process, offer debtaiailsedd euvriindgencthee regarding  
the efficacy of an experiment, and often resolve  
uncertainty caused by contradictory findings from  
various researches asking the same issue.
Meta-analysis is an effective computational method for
obtaining  a single effect size by combining the 
outcomes  of multiple individual experiments. Asa
result, the best level of proof is known be a
to  systematic study with meta-analysis.
Contd.
..
The conventional meta-analysis approach does not  
take into account previous knowledge from outside 
 sources.
As a result, a new approach to meta-analysis is  
established, in which historical data is combined using 
 Bayesian principles.
"The clear comparative use of external data in the  
design, control, study, and understanding of health  
care evaluation," according to the Bayesian approach.
Contd...
The prior belief about the parameter, which should be  
external to data, is one of the criteria of Bayesian 
 meta-analysis.
The observed data were paired with prior experience  
to provide new information about the parameter of  
interest.
The focus of this article is to define how extensively  
Bayesian methods have been used in meta-analysis,  
benefits, and implementations.
Bayesian  
Standard statistical inference means that the Methods: 
 sample comes from a population with a The  
fixed  and undefined parameter.
Principles
The sample information is used to make the  
whole parameter inference.
On the other hand, the Bayesian method  
treats parameters as random variables with 
 a probability distribution that reflects our  
prior knowledge.
Contd...
The likelihood function is summarised in the current data.
The prior distribution and probability function was merged using Bayesian rules 
 to produce the posterior distribution function.
Meta-
Analysis  
There are four basic stages in a Bayesian meta- 
Concept In   analysis:
Bayesian  
(1) Choosing the Right Priorities
Method
The first step in Bayesian meta-analysis is to 
 summarise the proof that isn't based on  
observed facts.
This document reviews previous evidence  
and assumptions about intervention's  
relative benefits.
Contd...
Contd.
..
Non-randomized experiments, invitroor  
invivo trials,experimental studies,  or
personal views may be used as verification.
Since the parameters are  called 
unpredictable random  
variables,  distributions are applied to prior
them.
(2) Current Evidence
The probability function of the parameters  
would be composed of observable data or  
impact predictions gathered from various  
studies asking the same query.
Contd...
For both measurable and unobservable  
quantities, a complete probability model is  
constructed.
(3) Posterior
The external information is then combined  
with the current data to arrive at a current  
understanding of the intervention's impact.
As a result, the posterior distribution is  
derived by combining the prior distribution 
 and the probability function.
The revised proof is another name for the  
posterior.
Contd...
In addition, unlike conventional Meta-analysis, 
 all inferences should be based on the  
posterior distribution.
(4) Recapitulating
In Bayesian Meta-analysis, the final step is to  
summarise the posterior distribution.
The posterior distribution obtained is often of  
high dimension and complexity, necessitating  
computer-based packages (BUGS and  
WINBUGS) to execute the integrations.
Contd...
Simulation techniques like Markov Chain  
Monte Carlo are used to sample directly  
from the posterior distribution.
As a result, all summary figures, such as 
 mean, standard deviation, odds ratio, risk  
ratio, and so on, are calculated using those  
samples.
Instead of 95 percent confidence intervals,  
95 percent accurate intervals (2.5 percentile  
and 97.5 percentile of posterior distribution)  
were measured.
Contd...
In Bayesian meta-analysis, two methods are  
widely used, similar to conventional meta- 
 analysis: fixed-effect and random-effects  
models.
The only difference between Bayesian Meta- 
 analysis and conventional meta-analysis is  
that prior distributions for uncertain  
parameters are defined.
Bayesian Meta-  
In prior distribution, Bayesian meta-analysis  Analysis Profits & 
integrates all applicable historical data  
outside of the litigation.  
Contraindications
They account for all uncertainties, especially  
when determining a predictive distribution for  
the true effect in a new sample.
When there are a limited number of studies  
involved, or when studies have fewer case  
results, or when studies report only the  
summary estimation rather than its variance,  
Bayesian meta-analysis is sufficient.
Contd...
The posterior distribution is optimal for any decision-making situation, and the  
odds are more understandable than p values.
They also provide for the interpretation of the likelihood or consequence of action.
Prior probabilities can be used as a sensitivity analysis instrument to search for  
robustness andanalyses and calculate various theories.
The main drawback is that as the number of parameters increases with the 
 number of experiments, imposing vague priors on all parameters will lead to  
contradictory outcomes.
Contd...
Different prior distributions provide different outcomes.
Researchers must exercise caution when using informative priors since they may 
 significantly affect the posterior.
The software's implementation necessitates excellence.
Future Scope
Due to Bayesian's clear methodology for  
integrating external data, these  
approaches are commonly used in network 
 meta-analysis.
One renders both direct indirect 
and  observations dependent  
compaorantor anda ranks interventions.generic
However, although software makes much  
of the work simpler, it still necessitates  
many computational assistance and skills.
Contd...
In the field of clinical trial proof synthesis,  
Bayesian meta-analysis has gained  
attention.
Because public health interventions
are  geared to geographichaelltyerogeneous 
demographic,  multi-
interventions, context-specicfiocm, apnodn evnatrious  
effects, it did not gain traction in  
summarising them.
The use of conventional meta-analysis to  
combine the findings of such analyses has  
not been thoroughly studied.
Contd...
A recent effort was made to investigate the 
 complexities of public health approaches  
and create a meta-analysis for public  
health interventions that took complexity  
into account.
Any public health intervention's data is  
typically obtained from a mixture of  
retrospective and interventional trials.
Since there is no common mechanism for  
combining the findings of retrospective and 
 intervention trials, most systematic  
analyses are presented narratively.
Contd...
As a result, in complicated public health  
research, a reliable method of evidence  
synthesis is needed.
Finally, Bayesian meta-analysis-
specific  reporting criteria must be 
established.
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