Study specific prediction intervals for random-effects meta-analysis: A tutorial: Prediction intervals in...

Area of Science:

• Statistics
• Biostatistics
• Meta-analysis methodology

Background:

• Random-effects meta-analysis often prioritizes pooled effect estimates.
• Study-specific effect estimates are also crucial for detailed interpretation, commonly visualized in forest plots.
• Existing methods may not fully capture the nuances of individual study effects within a meta-analysis.

Purpose of the Study:

• To present the statistical theory and methodology for estimating study-specific true effects using empirical Bayes estimates (or Best Unbiased Linear Predictions) under the random-effects model.
• To introduce prediction intervals for quantifying the range of study-specific true effects.
• To illustrate the application of these methods using published meta-analyses and a simulation study.

Main Methods:

• Utilized empirical Bayes estimation, also known as Best Unbiased Linear Predictions, within the random-effects meta-analysis framework.
• Developed and applied prediction intervals to estimate the range of study-specific true effects.
• Conducted a simulation study to evaluate the performance of prediction intervals, particularly concerning coverage probability under varying between-study variance conditions.
• Illustrated the methodology with two real-world meta-analysis examples.

Main Results:

• Empirical Bayes estimates provide a robust method for estimating study-specific true effects in random-effects meta-analysis.
• Prediction intervals offer a plausible range for these study-specific effects.
• Simulation results indicated that prediction intervals may have substantially lower coverage probability than expected when the between-study variance is small but non-zero, a critical caveat for researchers.
• Demonstrated how these estimates and intervals can enhance forest plots for better visualization.

Conclusions:

• Empirical Bayes estimates and associated prediction intervals offer valuable insights into study-specific effects in meta-analysis.
• Researchers must be aware of the potential undercoverage of prediction intervals when the between-study variance is small.
• The proposed methodology, supported by clear theoretical underpinnings, has the potential to improve the interpretation and adoption of study-specific effect estimation in meta-analysis.