What Is a Meta-Analysis? How to Read a Pooled Result

Each study supplies an estimate, such as a risk ratio or mean difference, together with uncertainty. A meta-analysis combines suitable estimates using a specified method. It is not a simple average of every number in the papers. More precise studies often receive greater weight, although the exact weighting depends on the method and model.

The pooled result summarizes the evidence entered into that analysis under its assumptions. It is not automatically the effect that will occur in every setting. A narrow interval cannot repair a misrecorded outcome, a biased study or an unsuitable combination of research questions. Those issues must be considered before and after the calculation.

A systematic review defines the question, finds and selects evidence, appraises studies and synthesizes findings. Meta-analysis is one possible synthesis method within that process. Pooling a convenient collection of studies does not make the collection systematic, and a carefully conducted review may conclude that pooling would not be useful.

When a headline says “a meta-analysis of twenty studies,” ask how the studies were found, why they were eligible and whether several publications describe the same participants. The number alone does not establish adequate coverage. The systematic-review explainer describes that broader evidence trail.

First define the question and the quantity you want to estimate. Populations, interventions or exposures, comparators, outcomes and follow-up times must be sufficiently compatible for the planned combination to mean something. Studies need not be identical, but the differences require a scientific rationale.

Then check independence and data availability. Multiple reports of the same participants, repeated time points and shared control groups can create correlated estimates. Treating them as independent may make uncertainty appear too small. A point estimate may also be unusable for a particular calculation without a suitable measure of uncertainty or information from which to derive it.

The fictional situations below all concern a planned 12-week outcome. They illustrate decisions about entering that synthesis, not tests of a particular product. Missing data or an incompatible time point can exclude a result from this calculation without excluding an otherwise eligible study from the entire review.

A risk ratio compares event probabilities. An odds ratio compares odds: the probability divided by one minus that probability. The two are not interchangeable, especially when events are common. A mean difference uses the original measurement unit, whereas a standardized mean difference expresses the difference relative to variability. Cochrane’s effect-measure chapter explains these choices.

For a ratio measure, 1 is the no-difference value; for a difference measure, it is usually 0. A ratio below 1 is not inherently beneficial. Check whether the event is desirable or harmful, which group is the numerator and how the outcome is defined. A relative effect also needs a relevant baseline risk to express its absolute impact.

Ratio measures are commonly analyzed on a logarithmic scale. Since log(1) = 0, a symmetric interval around a log estimate becomes asymmetric when exponentiated back to the ratio scale. That is expected, not a plotting error. The example below uses log risk ratios to make the calculation transparent; no real event or intervention is assigned.

For fuller calculations and conversions beyond this example, see the guide to Cohen’s d, Hedges’ g, odds ratios and risk ratios. Keep the measure, comparison direction, units and follow-up attached to each estimate when using those methods.

The following dataset is entirely synthetic. It contains three independent study estimates with log risk ratios of 0.10, 0.20 and 0.30; each has a standard error of 0.10. We use a common-effect inverse-variance calculation and a normal-approximation 95% confidence interval to illustrate the method. The equal standard errors make the weights equal; this is not an example of unequal weighting or evidence about a real intervention.

Each variance is 0.10² = 0.01, so each inverse-variance weight is 100. The total weight is 300, and the weighted mean is (100 × 0.10 + 100 × 0.20 + 100 × 0.30) / 300 = 0.20. The pooled standard error is √(1 / 300) = 0.057735. Using 1.96 standard errors gives a log-scale interval of approximately 0.08684 to 0.31316.

Exponentiating gives a pooled risk ratio of 1.221 and a 95% confidence interval of 1.091 to 1.368. Each study supplies one third of the weight; displayed percentages are rounded. The same calculations yield the study intervals in the table. Because no real event or comparator has been assigned, the example has no benefit-versus-harm direction. A ratio above 1 simply denotes a larger event probability in the numerator group in this constructed comparison.

In the forest plot, a marker locates each study estimate and its horizontal line shows the confidence interval. The vertical reference line at 1 denotes no ratio difference. The pooled diamond centers on 1.221 and spans 1.091–1.368. A narrow diamond describes precision under this model; it does not evaluate bias, missing evidence or applicability. The accessible table carries the same numerical information as the figure.

A common-effect model, often called a fixed-effect model in this setting, treats the studies as estimating one underlying effect for the analysis. A random-effects model allows underlying effects to vary and summarizes their distribution. Choose the model for the scientific question and plausible differences, not solely because a heterogeneity test crosses a threshold. Cochrane’s meta-analysis chapter explains the assumptions and methods.

Clinical and methodological heterogeneity concern differences in participants, settings, designs and measurements. Statistical heterogeneity describes variation in estimates beyond sampling error under the model. I² summarizes relative inconsistency; it is neither the percentage of poor-quality studies nor the effect size. Its estimate can be uncertain, especially with few studies. The between-study variance, τ², describes another aspect of that variation.

A random-effects model does not repair an inappropriate combination or remove bias. Results depend on the variance estimator and interval method, particularly with few studies. A prediction interval describes the spread of underlying effects in comparable settings under additional assumptions. It is different from the confidence interval around the pooled mean and is not a guarantee for a particular new study.

Use prespecified subgroup or sensitivity analyses to examine meaningful differences where justified, and identify exploratory changes. If the next task is checking that software implements those choices correctly, the meta-analysis tools guide covers the inputs, code and records needed for reproducible analysis.

Bias in included studies can flow into the pooled estimate. Missing outcomes, selective reporting and flaws in study conduct are not corrected by inverse-variance weights. Use design-appropriate appraisal and interpret how it affects the particular result; see Cochrane’s bias guidance.

Missing evidence is another concern. If studies or results are less likely to be available because of their findings, the observed set may give a distorted picture. Funnel plots and statistical tests require careful interpretation; asymmetry is not proof of publication bias, and a reassuring-looking plot does not establish that nothing is missing. Cochrane’s missing-results chapter discusses the problem and assessment methods.

Finally, distinguish a confidence interval excluding the null from an important or certain result. Statistical significance does not specify practical importance, applicability or the certainty of the evidence. Read the effect size and interval alongside study limitations, inconsistency, indirectness and other relevant considerations. Cochrane’s certainty guidance provides a framework where applicable.

• Interpret the result only after its source data and study identities have been checked.

• Read sensitivity analyses and missing-data decisions alongside the main estimate.

• Distinguish insufficient evidence from evidence that an important effect is absent.

• Carry material limitations into the conclusion, not just a technical appendix.

When a pooled estimate would not answer the question, use an explicit alternative. Structured tables or plots without pooling can keep study results visible; other questions may need qualitative synthesis or a different method. Explain how studies were grouped and findings compared rather than counting significant results. Cochrane’s guidance on other synthesis methods provides methodological options, and the evidence-synthesis workflow guide helps connect the chosen approach to a toolchain.

Whichever method you use, retain the inputs and reasons needed to revisit the analysis. The PRISMA reporting guide explains how to connect the methods and findings to the report. Choosing and verifying analysis software is a separate next step; it does not resolve whether the question supports pooling.