Prediction interval in random-effects meta-analysis

A prediction interval is defined as the interval within which the effect size of a new study would fall if this study was selected at random from the same population of the studies already included in the meta-analysis. Therefore, a prediction interval reflects the uncertainty we expect in the summary effect if a new study is included in the meta-analysis. Prediction intervals shall be reported routinely alongside the summary effect size and 95% confidence interval (CI) thereof. Depending on the extent of heterogeneity, prediction intervals are wider than the 95% CI of the summary effect size. Note that in a meta-analysis with few studies (eg, fewer than 5 studies), the prediction interval may be particularly imprecise, resulting from an imprecise estimation of the summary effect size and heterogeneity parameter.

Having estimated the population mean effect size M , its variance V M , and the variation of the true effects (ie, heterogeneity) T 2 , we can calculate the lower and upper limits of (1− a )% prediction interval using the following formulas, respectively:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='LLpred=M−ta,k−2·T2+VM’>𝐿𝐿𝑝𝑟𝑒𝑑=𝑀𝑡𝑎,𝑘2·𝑇2+𝑉𝑀LLpred=M−ta,k−2·T2+VM
LLpred=M−ta,k−2·T2+VM
<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='ULpred=M+ta,k−2·T2+VM’>𝑈𝐿𝑝𝑟𝑒𝑑=𝑀+𝑡𝑎,𝑘2·𝑇2+𝑉𝑀ULpred=M+ta,k−2·T2+VM
ULpred=M+ta,k−2·T2+VM