<p>This paper addresses three-category and multi-category diagnostic problems, emphasizing the importance of identifying pseudo-categories before multi-dimensional ROC analysis. When the distributions of diagnostic variable for adjacent categories are undiagnosable, they should be combined into one category, removing nuisance parameters. First, this work introduces a test method called Nonparametric Test by Bootstrap AUC (NTBA), rooted in bootstrap technique and nonparametric AUC estimation theory. This method helps determine whether two adjacent categories can be fused and is applicable in multi-category problems. For three-category medical diagnostics, the hypothesis test is formulated by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$H_{0} :P\left( {X < Y} \right) = 0.5{ }VS{ }H_{1} :P\left( {X < Y} \right) \ne 0.5.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo>:</mo> <mi>P</mi> <mfenced close=")" open="("> <mrow> <mi>X</mi> <mo><</mo> <mi>Y</mi> </mrow> </mfenced> <mo>=</mo> <mn>0.5</mn> <mrow /> <mi>V</mi> <mi>S</mi> <mrow /> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>:</mo> <mi>P</mi> <mfenced close=")" open="("> <mrow> <mi>X</mi> <mo><</mo> <mi>Y</mi> </mrow> </mfenced> <mo>≠</mo> <mn>0.5</mn> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> If <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$H_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> is not rejected, merging them to two categories is justified. Second, three existing tests have been introduced and compared for the above <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$H_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> to assess which can achieve optimal size and power similar to NTBA. Simulation experiments compare the performance of NTBA with three popular tests under various distribution conditions. Finally, the Wilcoxon–Mann–Whitney test, despite lacking the theoretical foundation of AUC, can achieve results comparable to those of NTBA. This discovery opens new applications for WMW in the fusion of categories for multi-way ROC analysis. Additionally, two medical datasets are utilized to evaluate the feasibility of fusing two categories using four different hypothesis testing methods.</p>

Comparison of Different Statistical Tests on the Fusion of Categories for Multi-way ROC Analysis

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发表日期：

2026年4月24日

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Lei Huang,
Rui Zhou

摘要

This paper addresses three-category and multi-category diagnostic problems, emphasizing the importance of identifying pseudo-categories before multi-dimensional ROC analysis. When the distributions of diagnostic variable for adjacent categories are undiagnosable, they should be combined into one category, removing nuisance parameters. First, this work introduces a test method called Nonparametric Test by Bootstrap AUC (NTBA), rooted in bootstrap technique and nonparametric AUC estimation theory. This method helps determine whether two adjacent categories can be fused and is applicable in multi-category problems. For three-category medical diagnostics, the hypothesis test is formulated by $H_{0} :P\left( {X < Y} \right) = 0.5{ }VS{ }H_{1} :P\left( {X < Y} \right) \ne 0.5.$ $H_{0} : P (X < Y) = 0.5 V S H_{1} : P (X < Y) \neq 0.5 .$ If $H_{0}$ $H_{0}$ is not rejected, merging them to two categories is justified. Second, three existing tests have been introduced and compared for the above $H_{0}$ $H_{0}$ to assess which can achieve optimal size and power similar to NTBA. Simulation experiments compare the performance of NTBA with three popular tests under various distribution conditions. Finally, the Wilcoxon–Mann–Whitney test, despite lacking the theoretical foundation of AUC, can achieve results comparable to those of NTBA. This discovery opens new applications for WMW in the fusion of categories for multi-way ROC analysis. Additionally, two medical datasets are utilized to evaluate the feasibility of fusing two categories using four different hypothesis testing methods.