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Updated: Apr 18, 2026

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Hypothesis Tests of Direct and Indirect Effects Under Various Semicompeting Risks Models.

Jih-Chang Yu1, Yen-Tsung Huang2

  • 1Department of Statistics, National Taipei University, Taiwan.

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|April 17, 2026
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Summary
This summary is machine-generated.

This study introduces causal methods to analyze direct (DE) and indirect effects (IE) in semicompeting risks, using Clayton copula, gamma frailty, and multistate models. Results show the Clayton copula model offers high power but risks bias, while gamma frailty is robust and multistate models balance efficiency and robustness.

Keywords:
copula modelfrailty modelmediation modelmultistate modelsemicompeting risks

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Area of Science:

  • Biostatistics
  • Causal Inference
  • Survival Analysis

Background:

  • Semicompeting risks involve two time-to-event outcomes, with potential censoring of intermediate events by primary events.
  • These risks can be modeled using mediation frameworks, allowing study of direct effects (DE) and indirect effects (IE).

Purpose of the Study:

  • To propose unified causal testing procedures for evaluating direct and indirect effects in semicompeting risks.
  • To establish testing rules and analyze the correspondence between effects and parameters across three classic models.

Main Methods:

  • Formulating semicompeting risks as a mediation model.
  • Applying causal inference approaches for testing direct and indirect effects.
  • Utilizing U-statistic for Clayton copula and nonparametric maximum likelihood estimation for gamma frailty and multistate models.

Main Results:

  • The Clayton copula model provides the highest statistical power when assumptions hold but is sensitive to misspecification.
  • The gamma frailty model demonstrates robustness at the cost of efficiency.
  • The multistate model offers a balance between efficiency and robustness.

Conclusions:

  • The study provides a unified framework for analyzing direct and indirect effects in semicompeting risks.
  • Application to a hepatitis study indicates that hepatitis B and C increase liver cancer risk via liver cirrhosis.
  • The choice of model impacts statistical power, robustness, and efficiency in semicompeting risks analysis.