Chapter 25.1

### Models for Combining Data for Meta-Analysis

In a meta-analysis, results from 2 or more primary studies are combined statistically. The meta-analyst seeking a method to combine primary study results can do so by using either a fixed-effects model or a random-effects model.1

We explain the differences between the 2 models based on the underlying assumptions, statistical considerations, and how the choice of model affects the results (Table 25.1-1). Note, however, that this is a controversial area within the field of meta- analysis, and expert statisticians disagree even with the characterizations in Table 25.1-1. The approach we take is, however, largely consistent with that of the Cochrane Collaboration.

TABLE 25.1-1

Comparison of Fixed-Effects and Random-Effects Models

A fixed-effects model considers the set of studies included in the meta-analysis and assumes that there is a single true value underlying all of the study results.2 That is, the assumption is that if all studies that address the same question were infinitely large and completely free of bias, they would yield identical estimates of the effect. Thus, with the assumption that studies are free of risk of bias, the observed estimates of effect differ from one another only because of random error.3 This assumes that any differences in the patients enrolled, the way the intervention was administered, and the way the outcome was measured have no (or minimal) impact on the magnitude of effect. The error term for a fixed-effects model comes only from within-study variation (study variance); the model does not consider between-study variability in results (known as heterogeneity) (see Chapter 23, Understanding and Applying the Results of a Systematic Review and Meta-analysis). A fixed-effects model aims to estimate this common-truth effect and the uncertainty about it.

A random-effects model assumes that the studies included are a random sample of a population of studies that address the question posed in the meta-analysis.4 Because there are inevitably differences in the patients, interventions, and outcomes among studies that address a particular research question, each study estimates a different underlying true effect, and these effects will have a normal ...

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