Power and sample size for testing homogeneity of relative risks in prospective studies

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Methods

Background:

• Assessing homogeneity of relative risks is crucial before combining data from multiple studies.
• The score method provides a framework for testing this homogeneity.
• Existing methods may lack sufficient power or clear sample-size guidance.

Purpose of the Study:

• To derive and present power and sample-size formulas for the homogeneity score test.
• To provide researchers with tools for study design and model validation in meta-analysis and epidemiological studies.
• To formally establish the equivalence between the homogeneity score test and the Pearson chi-square test.

Main Methods:

• Development of power and sample-size formulas based on the score method for testing homogeneity of relative risks.
• Formal mathematical derivation demonstrating the equivalence of the homogeneity score test to the Pearson chi-square test.
• Application of these formulas to practical scenarios in study design and meta-analysis.

Main Results:

• Formulas for calculating statistical power and required sample size for the homogeneity score test are presented.
• The homogeneity score test is shown to be formally equivalent to the Pearson chi-square test.
• The utility of these results in assessing the validity of a common relative risk model is highlighted.

Conclusions:

• The presented formulas offer valuable guidance for researchers designing studies involving relative risk meta-analysis.
• These tools facilitate the assessment of assumptions underlying pooled analyses, such as the common relative risk model.
• The findings enhance the statistical rigor in epidemiological research by providing methods to detect and account for heterogeneity in relative risks.