Meta‐analysis of quantile intervals from different studies with an application to a pulmonary tuberculosis data

After the completion of many studies, experimental results are reported in terms of distribution-free confidence intervals that may involve pairs of order statistics. This article considers a meta-analysis procedure to combine these confidence intervals from independent studies to estimate or construct a confidence interval for the true quantile of the population distribution. Data synthesis is made under both fixed-effect and random-effect meta-analysis models. We show that mean square error (MSE) of the combined quantile estimator is considerably smaller than that of the best individual quantile estimator. We also show that the coverage probability of the meta-analysis confidence interval is quite close to the nominal confidence level. The random-effect meta-analysis model yields a better coverage probability and smaller MSE than the fixed-effect meta-analysis model. The meta-analysis method is then used to synthesize medians of patient delays in pulmonary tuberculosis diagnosis in China to provide an illustration of the proposed methodology.