Which is appropriate to use fixed-effect or random effect statistical model while conducting meta-analyses - Pubrica
                     WHICH IS APPROPRIATE TO USE  
FIXED-EFFECT OR RANDOM 
EFFECT  STATISTICAL MODEL 
WHILE  CONDUCTING META-
ANALYSES
An Academic presentation by
Dr. Nancy Agnes, Head, Technical Operations, Pubrica 
 Group: www.pubrica.com
Email: [email protected]
Today's Discussion
Outline
Introduction
M eta-analyses - D ifferent 
Components  Fixed and Random 
Effect Models
The Comparison 
 Conclusion
Introduction
Meta-analysis is the statistical analysis of 
data  and an essential aspect of systematic 
reviews.
Here, the study is conducted based on  
mathematical models.
Meta-analyses are applicable for a number 
of  purposes, including synthesizing data on 
the  results of interventions and supporting 
evidence-  based policy and practice.
Contd...
A meta-analysis is a tool with multiple applications in various fields like 
medicine,  healthcare, pharmaceuticals, psychology, ecology, education, 
criminology and  business (Borenstein 2021).
The two most popular models used in conducting meta-analyses are fixed-
effect and  random-effect models.
This review focuses on and compares both these models based on recent 
studies.
Meta-analyses -  
Different Components
A meta-analysis is a statistical method for  
combining quantitative data from various 
studies  that address the same or similar 
research question  (Schober 2020).
A number of steps are involved in conducting 
a  meta-analysis.
Contd...
These include - question framing, formation of search strategy, the search 
of literature  database, selection of articles, data extraction, examination of 
quality of the articles,  test for heterogeneity, estimation of summary effect, 
evaluation of the sources of  heterogeneity, assessment of publication bias 
and finally, presentation of results  (Wang 2021).
Fixed-effect and random-effect methods help in
measuring the summary effect of a  meta-analysis. Both these 
approaches are very distinctive.
Fixed and  
Random  In the fixed-effect model, it is assumed that 
there is  one real effect that underpins all of the 
Effect Models studies in the  research, and that all 
variations in observed results  are due to 
sampling error in the fixed-effect model.
It is also known as the common-effect model.
In this model, all variables that could affect the 
effect  size is the same across all studies, and 
therefore the  true effect size is the same 
across all  studies(Borenstein 2021).
Contd...
The pooled or summary effect in a fixed-
effect  meta-analysis estimates this typical 
true effect size  (Schober 2020).
Two conditions must be satisfied in order for a 
fixed-  effect model to be applied.
To begin, one must be confident in the 
similarity of  all studies included in the 
meta-analysis and that  synthesizing the data 
is appropriate.
Contd...
Next, calculation of common-effect size is 
considered  that is only applicable to the meta-
analysis population  (Spineli 2020a).
Random effect models, on the other hand, 
presume  a different underlying effect for each 
sample and treat  this as a random source of 
variance (Wang 2021).
In this model, It is often assumed that true 
effects are  normally distributed, or they differ 
from study to study  (Borenstein 2021).
The  
Compariso Both of these widely used meta-analysis models 
n have their  own set of limitations.
When the heterogeneity of studies cannot be 
neglected, the  common-effect model can produce 
misleading results.
When the number of studies is small, the CI 
(confidence  interval) for the mean effect based 
on the random-effect  model can be too large to be 
helpful.
Contd...
Since a large portion of meta-analyses 
includes  numbers of studies with non-
negligible variability,  these limitations are 
significant roadblocks in  practice (Lin 2020).
Another point to note is, as we compare the  
weighting schemes of these two models, we 
can  observe that as we move from a fixed-
effect to a  random-effects model, larger 
studies tend to lose  influence, and smaller 
studies tend to gain influence  (Spineli 2020 
*(a)).
Contd...
Furthermore, the different assumptions for fixed-effect and random-effect 
models  indicate different meanings of the variance (resulting in 
distinguished computations of  the meta-analysis results due to varying 
weighting schemes) and the distinguished null  hypothesis of no linear 
correlation determinations.
The only source of error in a fixed-effect model is within-study variance and, 
the null  hypothesis states that the typical true effect size is unrelated to the 
covariate of interest.
Contrastingly in a random-effects model, both within-study and between-
study  variances are sources of error and, the null hypothesis states that the 
mean of the true  effect size is unrelated to the covariate of interest (Spineli 
2020 *(b)).
Conclusion
To conclude, a fixed-effect model can only be 
applied  if there are potential factors that 
indicate that the  studies involved are 
identical for all intents and  purposes 
(Borenstein 2007).
However, implementation of the fixed-effect 
model is  rarely possible in practice.
The effect size varies from study to study in 
real-  world synthesis.
Contd...
Contd...
It is due to a variety of factors like differences in participant mixes and 
intervention  implementation.
As a result, a random-effects model appears to be sufficient and efficient in 
most  meta-analyses (Spineli 2020 *(a)).
The question of which model matches the distribution of effect sizes and 
takes into  account the appropriate source(s) of error must be the sole 
consideration when  choosing a model (Borenstein 2021).
Finally, the best model to use depends highly on the type of study 
conducted and the  nature of the goals that it wants to achieve.
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