Rank tests for survival analysis: a comparison by analogy with games

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Two-sample linear rank tests are vital for analyzing censored data in various scientific fields.
• Existing literature suggests mathematical similarities among these rank tests.
• A clear pedagogical approach is needed to elucidate these complex relationships.

Purpose of the Study:

• To demonstrate the interconnectedness of commonly used two-sample linear rank tests for censored data.
• To provide an intuitive understanding of the mathematical structures underlying these statistical tests.
• To introduce a novel pedagogical framework for teaching rank tests in survival analysis.

Main Methods:

• A conceptual videogame model involving two teams (boys and girls) with varying payment rules for consecutive losers was introduced.
• The total team winnings for the girls' team were analyzed under different payment rule scenarios.
• The outcomes were mathematically mapped to established rank statistics used for censored data.

Main Results:

• The videogame's payment rules directly correspond to the mathematical formulations of the Wilcoxon rank-sum test and the Savage (log-rank) test.
• Specific payment rules generate the standard Wilcoxon statistic and the Savage statistic when applied to censored data.
• Generalizations of these statistics under censoring conditions were derived through variations in the videogame's payment rules.

Conclusions:

• The videogame model effectively illustrates the underlying mathematical unity of several two-sample linear rank tests for censored data.
• This pedagogical approach simplifies the understanding of complex statistical concepts in survival analysis.
• The findings offer a new perspective for educators and researchers working with censored survival data.