Non-Parametric Mediation Analysis of Non-Markov Illness-Death Model

Area of Science:

• Biostatistics
• Epidemiology
• Causal Inference

Background:

• Illness-death models are crucial for understanding disease progression.
• Existing models often rely on the restrictive Markov assumption, limiting causal interpretation.
• A gap exists in causal analysis that accounts for the timing of intermediate events.

Purpose of the Study:

• To propose a novel definition of counterfactual hazard that relaxes the Markov assumption.
• To develop methods for estimating direct and indirect causal effects in illness-death models.
• To apply the new methodology to real-world data, such as a hepatitis study.

Main Methods:

• Defined a new counterfactual hazard incorporating the intermediate event's history.
• Derived an identification formula involving an integral of the intermediate event's probability density function.
• Developed non-parametric kernel estimators for direct and indirect effects and analyzed their asymptotic properties.

Main Results:

• The proposed method successfully relaxes the Markov assumption.
• Numerical simulations demonstrated the estimators' finite-sample performance.
• Analysis of a hepatitis study revealed no mediation of hepatitis C's effect on mortality by septicemia within the first 15 years.

Conclusions:

• The novel counterfactual hazard definition and estimation methods provide a more flexible approach to illness-death modeling.
• The findings from the hepatitis study highlight the importance of considering event timing in causal inference.
• This work advances causal inference in the presence of intermediate events, particularly when the Markov assumption is violated.