Bounds on the covariate-time transformation for competing-risks survival analysis

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• The latent-time framework in competing risks analysis suffers from non-identifiability of the joint distribution.
• Checking assumptions about covariate effects is challenging as general models may lose identifiability.
• Existing methods struggle to validate specific covariate effect assumptions in competing risks.

Purpose of the Study:

• To develop a general framework for modeling covariate effects in competing risks.
• To establish a method for checking assumptions about covariate effects in latent-time models.
• To provide a model-checking tool using derived bounds on covariate-time transformations.

Main Methods:

• Proposed a general framework assuming covariate-invariant copula dependency structure of latent times.
• Introduced covariate-time transformations as the core of the modeling framework.
• Derived bounds on these transformations using only crude incidence functions.

Main Results:

• The main result provides bounds on covariate-time transformations, offering a model-checking tool.
• These bounds are derived without strong assumptions on the form of covariate effects.
• Demonstrated the utility of the bounds by checking the assumption of independent competing risks.

Conclusions:

• The proposed framework and derived bounds enhance identifiability and model checking in competing risks analysis.
• This approach provides a more robust method for validating assumptions about covariate effects.
• The findings are crucial for reliable statistical inference in scenarios with competing risks and covariates.