Random effect meta-analysis in a nutshell

Owen Yang

Dear ChatGPT, what is random effect meta-analysis?

Meta-analysis is a statistical method that combines results from multiple studies to provide an overall estimate of the effect of an intervention. Random effects meta-analysis is a commonly used technique in medical statistics that allows for variability between studies by assuming that the effect size varies across studies. In this article, we will explain what random effects meta-analysis is, how it works, and why it is important in medical research.

Meta-analysis combines results from multiple studies by calculating a weighted average of the effect sizes observed in each study. The weights are determined by the precision of the effect estimate in each study, with more weight given to studies with larger sample sizes or smaller variance. However, this assumes that all studies share the same true effect size, which may not be the case due to differences in study design, population characteristics, or other factors.

Random effects meta-analysis addresses this issue by assuming that the effect sizes in each study are drawn from a normal distribution with a mean equal to the true effect size and a variance equal to the between-study variance. This means that the effect sizes in each study may differ from the true effect size due to random error, but also due to systematic differences between studies. The between-study variance represents the variability in effect sizes that is not explained by sampling error or measurement error within studies.

The random effects model estimates both the overall effect size and the between-study variance, allowing for more accurate inference about the true effect size. The overall effect size is calculated as the weighted average of the study-specific effect sizes, with the weights accounting for both within-study and between-study variability. The between-study variance is estimated from the heterogeneity in effect sizes across studies, and is used to calculate the standard error of the overall effect size estimate.

The random effects model also provides a measure of heterogeneity, which is the amount of variation in effect sizes that is due to differences between studies rather than random error within studies. The most commonly used measure of heterogeneity is the I-squared statistic, which ranges from 0% to 100% and represents the percentage of total variation in effect sizes that is due to heterogeneity. A high value of I-squared indicates substantial heterogeneity, while a low value suggests that the studies are relatively homogeneous.

Random effects meta-analysis is important in medical research because it allows for more accurate estimation of the true effect size and its variability, while accounting for heterogeneity between studies. This can lead to more reliable conclusions about the effectiveness of interventions, and can help identify sources of heterogeneity that may need further investigation. Random effects meta-analysis is commonly used in systematic reviews and meta-analyses of clinical trials, observational studies, and diagnostic accuracy studies.

There are several assumptions and limitations of random effects meta-analysis that should be considered when interpreting the results. One important assumption is that the between-study variance is constant across all subgroups of studies, which may not be true if there are systematic differences between subgroups. Another limitation is that random effects meta-analysis assumes that the true effect size follows a normal distribution, which may not be the case for some outcomes or interventions. Finally, random effects meta-analysis is sensitive to the choice of prior distribution for the between-study variance, which can affect the estimation of the overall effect size and heterogeneity.

In conclusion, random effects meta-analysis is a statistical method that allows for variability between studies by assuming that the effect size varies across studies. It estimates both the overall effect size and the between-study variance, and provides a measure of heterogeneity to assess the variability in effect sizes between studies. Random effects meta-analysis is important in medical research because it allows for more accurate estimation of the true effect size and its variability, while accounting for heterogeneity between studies. However, it also has assumptions and limitations that should be considered when interpreting the results.