Weighted Z-Test

Weighted Z-Test combines p-values from multiple studies using a weighted inverse normal (Z) method to produce a single combined test statistic for meta-analysis and is implemented as a MATLAB script.

Key Features:

• Weighted combination: Transforms individual p-values to z-scores via the inverse normal method and combines them using weights, commonly the square roots of study sample sizes.
• Adaptability to study size: Incorporates weighting to adjust for heterogeneous study sizes, mitigating power loss seen with unweighted methods such as Fisher's method.
• Handling of one-sided T-tests: Addresses limitations of Fisher's method when combining results from one-sided T-tests by operating on inverse normal-transformed p-values.
• Comparative power: Can achieve comparable or improved statistical power relative to Lancaster's variation or Fisher's method when appropriate weighting is applied.
• Refinable weighting: Allows incorporation of additional information beyond sample sizes to refine weights and potentially improve combined-test power.

Scientific Applications:

• Genetics: Combining p-values from multiple genetic association studies to produce a single meta-analytic test statistic.
• Epidemiology: Pooling significance results across epidemiological studies with varying sample sizes.
• Clinical research: Aggregating p-values from clinical trials or studies to assess overall evidence of effect.
• Meta-analysis of heterogeneous studies: Producing combined significance measures when constituent studies differ in size or available weighting information.

Methodology:

Transform p-values to z-scores using the inverse normal method, weight each z-score by a predefined scheme (commonly the square root of sample size), and aggregate the weighted z-scores to produce a single combined test statistic.