Extending Multiple Testing With Unknown Test Dependency via the CoCo Test: With Applications to Cancer Studies

Area of Science:

• Statistics
• Biostatistics
• Clinical Research Methodology

Background:

• Multiple testing is prevalent in research, posing challenges for controlling type I error rates (alpha-control).
• Existing methods for alpha-control are well-established for independent tests or known joint distributions.
• Verifying the positive dependency through stochastic ordering (PDS) condition is crucial for alpha-control with unknown dependencies, yet methods are lacking.

Purpose of the Study:

• To develop a novel nonparametric statistical test for validating the PDS condition in multiple testing scenarios.
• To enable reliable alpha-control irrespective of the dependency structure between test statistics.
• To provide a practical tool for researchers facing unknown dependencies in their data.

Main Methods:

• Development of the CoCo test, a nonparametric method utilizing ranked correlation coefficients (Spearman's rho and Kendall's tau).
• The CoCo test is designed to algebraically assess the PDS condition.
• Validation through simulation studies and application to real-world meta-analyses.

Main Results:

• The CoCo test effectively detects violations or confirmations of the PDS condition.
• Simulation studies demonstrated the test's reliability in assessing dependency structures.
• Application to meta-analyses showcased its practical utility in evaluating PDS.

Conclusions:

• The CoCo test offers a robust solution for validating the PDS condition in multiple testing.
• Researchers are encouraged to assess the PDS condition when dependencies are uncertain.
• The CoCo test provides methodological and technical advancements for statistical analysis.