Copyright © 2021 pubrica. All rights reserved 1

Which is Appropriate to use Fixed-Effect or Random Effect Statistical Model

while Conducting Meta-Analyses

Dr. Nancy Agnes, Head,

Technical Operations, Pubrica

sales@pubrica.com

Keywords:

Meta analysis, fixed effect model, random

effect model, statistical model, statistical

analysis, sources of heterogeneity, null

hypothesis

I. 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. 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.

II. 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. 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.

III. FIXED AND RANDOM EFFECT

MODELS

In the fixed-effect model, it is assumed that

there is one real effect that underpins all of

the 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). 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

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included in the meta-analysis and that

synthesizing the data is appropriate. 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).

IV. THE COMPARISON

Both of these widely used meta-analysis

models 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. 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)).

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)).

V. 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. 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)).

Fig. 1: Comparison of fixed and random effect

statistical models

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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.

REFERENCES

1. Borenstein, M., Hedges, L., & Rothstein, H. (2007).

Meta-analysis: Fixed effect vs. random effects. Meta-

analysis. Com.

2. Borenstein, M., Hedges, L. V., Higgins, J. P., &

Rothstein, H. R. (2021). Introduction to meta-analysis.

John Wiley & Sons.

3. Lin, E., Tong, T., Chen, Y., & Wang, Y. (2020).

Fixed-effects model: the most convincing model for

meta-analysis with few studies. arXiv preprint

arXiv:2002.04211.

4. Schober, P., & Vetter, T. R. (2020). Meta-Analysis in

Clinical Research. Anesthesia and analgesia, 131(4),

1090–1091.

5. Spinelii, L. M., & Pandis, N. (2020). The importance

of careful selection between fixed-effect and random-

effects models. American journal of orthodontics and

dentofacial orthopedics, 157(3), 432-433. *(a)

6. Spineli, L. M., & Pandis, N. (2020). Fixed-effect

versus random-effects model in meta-regression

analysis. American journal of orthodontics and

dentofacial orthopedics, 158(5), 770-772. *(b)

7. Wang, X. M., Zhang, X. R., Li, Z. H., Zhong, W. F.,

Yang, P., & Mao, C. (2021). A brief introduction of

meta-analyses in clinical practice and research. The

journal of gene medicine, e3312. Advance online

publication.