Confidence estimation based on data from independent studies

Area of Science:

• Statistics
• Biostatistics
• Meta-analysis

Background:

• Synthesizing evidence from multiple independent studies is crucial for robust statistical inference.
• Existing methods for constructing confidence intervals from combined data may have limitations in coverage probability and precision.
• Developing versatile methods applicable to diverse data distributions is essential for meta-analysis.

Purpose of the Study:

• To propose a general method for constructing confidence intervals by inverting combined tests for data from several independent studies.
• To evaluate the performance of confidence intervals derived from Fisher's test, weighted inverse normal test, inverse chi-square test, and inverse Cauchy test.
• To compare these novel confidence intervals with existing approximate methods regarding coverage probability and precision.

Main Methods:

• A general framework for confidence interval construction by inverting combined tests is presented.
• The method is applied to various scenarios, including common means of normal, lognormal, and gamma populations, and common correlation coefficients and coefficients of variation.
• Performance evaluation involves comparing coverage probability and precision against established approximate confidence intervals.

Main Results:

• The proposed method provides a unified approach to confidence interval estimation across different statistical models.
• Confidence intervals derived from combined tests demonstrate competitive or superior performance in terms of coverage and precision compared to existing methods.
• The study provides R functions for practical implementation and illustrates the methods with real-world examples.

Conclusions:

• Inverting combined tests offers a powerful and generalizable strategy for constructing confidence intervals in meta-analysis.
• The proposed method enhances the reliability of statistical inference when pooling data from multiple independent sources.
• The availability of R functions facilitates the application of these advanced statistical techniques in research.