A prediction interval in random-effects meta-analysis defines the range within which the true effect size in a future, similar study is expected to fall, with a specified probability (usually 95%). It accounts not just for sampling uncertainty in the pooled estimate but also for the genuine variability in true effects across settings, populations, and implementations.
Confidence intervals answer: "Where does the mean true effect lie?" Prediction intervals answer: "Where will the next true effect lie?" For anyone applying a meta-analysis finding to a new clinical or policy context, the prediction interval is the more relevant quantity.
Try our free make a forest plot online to compute and display prediction intervals alongside your pooled effect and confidence interval.
Why Confidence Intervals Alone Mislead Readers
The problem with reporting only a pooled effect and its confidence interval in the presence of heterogeneity is that the confidence interval describes only the precision of the average effect across your included studies. It shrinks as you add more studies, regardless of whether the true effects in those studies are converging or diverging.
Consider a pooled risk ratio of 1.35 with a 95% confidence interval of 1.18 to 1.55, p less than 0.001. But if tau-squared is 0.08 and the prediction interval runs from 0.82 to 2.21, the picture is entirely different. In some settings the intervention nearly halves risk; in others it appears harmful. The confidence interval would lead a clinician to apply the intervention universally. The prediction interval correctly signals that the effect is not reliably positive across contexts.
This is precisely the scenario that prompted major journals and the Cochrane Collaboration to recommend reporting prediction intervals whenever I-squared exceeds 0%.
The Mathematics Behind Prediction Intervals
Prediction intervals use the t-distribution with k minus 2 degrees of freedom, where k is the number of studies. The formula is:
PI = pooled estimate +/- t(k-2, 0.975) * sqrt(tau-squared + SE-squared)
The t-distribution accounts for the additional uncertainty introduced by estimating tau-squared from a limited number of studies. When k is small, the t-distribution has heavy tails, and prediction intervals are appropriately wide.
For k equals 5 studies, the t-critical value at alpha 0.05 two-tailed with 3 degrees of freedom is 3.18, compared to 1.96 for the normal distribution. This means prediction intervals from small meta-analyses are substantially wider than a naive normal-approximation calculation would suggest.
Our compute effect size can help you compute the input effect sizes and standard errors needed before constructing prediction intervals.
Interpreting Prediction Intervals in Practice
When the prediction interval excludes the null: The pooled effect is not only statistically significant on average but also expected to be significant in a new study. This is the strongest form of evidence from a random-effects synthesis.
When the prediction interval crosses the null despite a significant pooled effect: The average effect is positive and distinguishable from zero, but in some settings the true effect may be null or negative. The heterogeneity is large enough that you cannot predict with confidence that a new application will replicate the benefit. Subgroup analyses and meta-regression become the scientific priority.
When the prediction interval crosses the null and the pooled effect is also non-significant: The evidence simply does not support a consistent effect.
Pair your prediction interval interpretation with our free sensitivity analysis to check whether removing any single study collapses the heterogeneity and clarifies the prediction interval.
