  For the inference of random-effects models in meta-analysis, the prediction
interval was proposed as a summary measure of the treatment effects that
explains the heterogeneity in the target population. While the
Higgins-Thompson-Spiegelhalter (HTS) plug-in-type prediction interval has been
widely used, in which the heterogeneity parameter is replaced with its point
estimate, its validity depends on a large sample approximation. Most
meta-analyses, however, include less than 20 studies. It has been revealed that
the validity of the HTS method is not assured under realistic situations, but
no solution to this problem has been proposed in literature. Therefore, in this
article, we describe our proposed prediction interval. Instead of using the
plug-in scheme, we developed a bootstrap approach using an exact confidence
distribution to account for the uncertainty in estimation of the heterogeneity
parameter. Compared to the HTS method, the proposed method provides an accurate
prediction interval that adequately explains the heterogeneity of treatment
effects and the statistical error. Simulation studies demonstrated that the HTS
method had poor coverage performance; by contrast, the coverage probabilities
for the proposed method satisfactorily retained the nominal level. Applications
to three published random-effects meta-analyses are presented.
