---
title: "Meta-analysis"
chunk: 2/7
source: "https://en.wikipedia.org/wiki/Meta-analysis"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:26:08.077779+00:00"
instance: "kb-cron"
---

=== Approaches ===
In general, two types of evidence can be distinguished when performing a meta-analysis: individual participant data (IPD), and aggregate data (AD). The aggregate data can be direct or indirect.
AD is more commonly available (e.g. from the literature) and typically represents summary estimates such as odds ratios or relative risks. This can be directly synthesized across conceptually similar studies using several approaches. On the other hand, indirect aggregate data measures the effect of two treatments that were each compared against a similar control group in a meta-analysis. For example, if treatment A and treatment B were directly compared vs placebo in separate meta-analyses, we can use these two pooled results to get an estimate of the effects of A vs B in an indirect comparison as effect A vs Placebo minus effect B vs Placebo.
IPD evidence represents raw data as collected by the study centers. This distinction has raised the need for different meta-analytic methods when evidence synthesis is desired, and has led to the development of one-stage and two-stage methods. In one-stage methods the IPD from all studies are modeled simultaneously whilst accounting for the clustering of participants within studies. Two-stage methods first compute summary statistics for AD from each study and then calculate overall statistics as a weighted average of the study statistics. By reducing IPD to AD, two-stage methods can also be applied when IPD is available; this makes them an appealing choice when performing a meta-analysis. Although it is conventionally believed that one-stage and two-stage methods yield similar results, recent studies have shown that they may occasionally lead to different conclusions.

=== Statistical models for aggregate data ===

==== Fixed effect model ====

The fixed effect model provides a weighted average of a series of study estimates. The inverse of the estimates' variance is commonly used as study weight, so that larger studies tend to contribute more than smaller studies to the weighted average. Consequently, when studies within a meta-analysis are dominated by a very large study, the findings from smaller studies are practically ignored. Most importantly, the fixed effects model assumes that all included studies investigate the same population, use the same variable and outcome definitions, etc. This assumption is typically unrealistic as research is often prone to several sources of heterogeneity.
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==== Random effects model ====
Most meta-analyses are based on sets of studies that are not exactly identical in their methods and/or the characteristics of the included samples. Differences in the methods and sample characteristics may introduce variability ("heterogeneity") among the true effects. One way to model the heterogeneity is to treat it as purely random. The weight that is applied in this process of weighted averaging with a random effects meta-analysis is achieved in two steps:

Step 1: Inverse variance weighting
Step 2: Un-weighting of this inverse variance weighting by applying a random effects variance component (REVC) that is simply derived from the extent of variability of the effect sizes of the underlying studies.
This means that the greater this variability in effect sizes (otherwise known as heterogeneity), the greater the un-weighting and this can reach a point when the random effects meta-analysis result becomes simply the un-weighted average effect size across the studies. At the other extreme, when all effect sizes are similar (or variability does not exceed sampling error), no REVC is applied and the random effects meta-analysis defaults to simply a fixed effect meta-analysis (only inverse variance weighting).
The extent of this reversal is solely dependent on two factors: