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

Area of Science:

• Statistics
• Biostatistics
• Medical Research Methodology

Background:

• Experimental results often rely on distribution-free confidence intervals derived from order statistics.
• Combining results from independent studies is crucial for robust statistical inference.

Purpose of the Study:

• To develop and evaluate a meta-analysis procedure for combining confidence intervals of population quantiles.
• To estimate or construct a confidence interval for the true population quantile using data from multiple studies.

Main Methods:

• Employed fixed-effect and random-effect meta-analysis models for data synthesis.
• Calculated mean square error (MSE) and coverage probability for the combined quantile estimator.
• Applied the method to synthesize medians of patient delays in pulmonary tuberculosis diagnosis.

Main Results:

• The meta-analysis quantile estimator demonstrated a considerably smaller MSE than individual estimators.
• Meta-analysis confidence intervals exhibited coverage probabilities close to the nominal confidence level.
• The random-effect model outperformed the fixed-effect model in terms of coverage probability and MSE.

Conclusions:

• Meta-analysis provides a powerful tool for combining distribution-free confidence intervals to estimate population quantiles.
• The proposed method enhances statistical precision and reliability in quantile estimation.
• The application to tuberculosis diagnosis highlights the practical utility of the meta-analysis approach.