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What is the Bayesian Random-Effects Meta-

Analysis Model for Normal Data

Dr. Nancy Agnes, Head, Technical Operations, Pubrica, sales@pubrica.com

I. INTRODUCTION

In healthcare studies, systematic reviews are valuable

sources of evidence. These are regarded as having a

high degree of evidence because they reduce bias

during the evaluation process, offer detailed evidence

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. As a

result, the best level of proof is known to be a

systematic study with meta-analysis.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. 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 [1].

The focus of this article is to define how extensively

Bayesian methods have been used in meta-analysis,

benefits, and implementations.

II. BAYESIAN METHODS: THE PRINCIPLES

Standard statistical inference means that the sample

comes from a population with a fixed and undefined

parameter. 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. 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

[2].

III. META-ANALYSIS CONCEPT IN BAYESIAN

METHOD

There are four basic stages in a Bayesian meta-

analysis [2]:

(1) Choosing the Right Priorities

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.

Non-randomized experiments, invitro or invivo trials,

experimental studies, or personal views may be used

as verification. Since the parameters are called

unpredictable random variables, prior distributions

are applied to 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.

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. 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.

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. In Bayesian

meta-analysis, two methods are widely used, similar

to conventional meta-analysis: fixed-effect and

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random-effects models. The only difference between

Bayesian Meta-analysis and conventional meta-

analysis is that prior distributions for uncertain

parameters are defined.

IV. BAYESIAN META-ANALYSIS PROFITS AND

CONTRAINDICATIONS

In prior distribution, Bayesian meta-analysis

integrates all applicable historical data outside of the

litigation. 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. The posterior

distribution is optimal for any decision-making

situation [3], 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 [4]

instrument to search for robustness andanalyses and

calculate various theories [5]. 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.

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.

V. FUTURE SCOPES

Due to Bayesian's clear methodology for integrating

external data, these approaches are commonly used in

network meta-analysis. One renders both direct and

indirect observations dependent on a generic

comparator and ranks interventions. However,

although software makes much of the work simpler, it

still necessitates many computational assistance and

skills.In the field of clinical trial proof synthesis,

Bayesian meta-analysis has gained attention. Because

public health interventions are geared to

geographically heterogeneous demographic, multi-

component interventions, context-specific, and

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various 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. 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. 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.

REFERENCE

[1] Lewis, Melissa Glenda and Nair, Sreekumaran

N (2015) Review of applications of Bayesian meta-

analysis in systematic reviews. Global Journal of

Medicine and Public Health, 4 (1). pp. 1-9. ISSN

2277-9604.

[2]

MatthaisE,GeorgeDS,JonathanAC(2002).Systematicr

eviews and Meta-‐analysis. In: Oxford textbook of

Public Health.4th

ed. New York: Oxford University

press.

[3]Młynarczyk, Dorota; Armero, Carmen; Gómez-

Rubio, Virgilio; Puig, Pedro. 2021. "Bayesian

Analysis of Population Health Data" Mathematics 9,

no. 5: 577. https://doi.org/10.3390/math9050577.

[4]Mojtaba GANJALI, Taban BAGHFALAKI,

Adeniyi Francis FAGBAMIGBE "A Bayesian

sensitivity analysis of the effect of different random

effects distributions on growth curve models,"

AfrikaStatistika, Afr. Stat. 15(3), 2387-2393, (July

2020)

[5]Paulewicz, B., Blaut, A. The bhsdtr package: a

general-purpose method of Bayesian inference for

signal detection theory models. Behav Res 52, 2122–

2141 (2020). https://doi.org/10.3758/s13428-020-

01370-y.

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