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Background <p>Hierarchical Structural Component Model (HisCoM) are statistical tools developed for pathway analysis that enable the simultaneous evaluation of multiple pathways within a single model. Traditionally, HisCoM utilize permutation tests to assess the significance of pathways in relation to a phenotype of interest. While permutation tests are effective for generating exact distributions under the null hypothesis when the asymptotic distribution is unknown, they are computationally intensive, particularly for high-dimensional datasets, as they require significant time to compute <i>p</i>-values.</p> Objective <p>The aim of this study is to develop parametric testing procedures for HisCoM to determine pathway significance without relying on permutations. These parametric tests aim to improve statistical performance while significantly reducing computational burden.</p> Methods <p>The proposed parametric tests are built on asymptotic theory for high-dimensional frameworks with numerous biomarkers and pathways. Specifically, we introduce methods such as the standard <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\chi }^{2}\)</EquationSource> </InlineEquation> asymptotic test, non-centrality test, degrees of freedom (df) adjustment, saddle point approximation, and modified asymptotic tests with full df and one df.</p> Results <p>Simulation and real data results showed substantial reductions in computational time compared to permutation-based test. Through the simulation study, the modified <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\chi }^{2}\)</EquationSource> </InlineEquation> asymptotic test with full df shown to have higher power compare to the other methods. The real data analysis further supported its robustness and practical advantages.</p> Conclusion <p>This study presents computationally efficient parametric testing methods for HisCoM. Based on simulation results and real data analysis, the modified <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\chi }^{2}\)</EquationSource> </InlineEquation> asymptotic test with full df is recommended as the most reliable and effective approach for assessing pathway significance.</p>

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Parametric hypothesis testing for pathway based hierarchical structural component models

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • Md. Kamruzzaman,
  • Taesung Park

摘要

Background

Hierarchical Structural Component Model (HisCoM) are statistical tools developed for pathway analysis that enable the simultaneous evaluation of multiple pathways within a single model. Traditionally, HisCoM utilize permutation tests to assess the significance of pathways in relation to a phenotype of interest. While permutation tests are effective for generating exact distributions under the null hypothesis when the asymptotic distribution is unknown, they are computationally intensive, particularly for high-dimensional datasets, as they require significant time to compute p-values.

Objective

The aim of this study is to develop parametric testing procedures for HisCoM to determine pathway significance without relying on permutations. These parametric tests aim to improve statistical performance while significantly reducing computational burden.

Methods

The proposed parametric tests are built on asymptotic theory for high-dimensional frameworks with numerous biomarkers and pathways. Specifically, we introduce methods such as the standard \({\chi }^{2}\) asymptotic test, non-centrality test, degrees of freedom (df) adjustment, saddle point approximation, and modified asymptotic tests with full df and one df.

Results

Simulation and real data results showed substantial reductions in computational time compared to permutation-based test. Through the simulation study, the modified \({\chi }^{2}\) asymptotic test with full df shown to have higher power compare to the other methods. The real data analysis further supported its robustness and practical advantages.

Conclusion

This study presents computationally efficient parametric testing methods for HisCoM. Based on simulation results and real data analysis, the modified \({\chi }^{2}\) asymptotic test with full df is recommended as the most reliable and effective approach for assessing pathway significance.