A semiparametric copula method for Cox models with covariate measurement error.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Measurement error in covariates is a common problem in survival analysis, potentially biasing results.
• Traditional methods often assume specific error distributions (e.g., linear additive, Gaussian), limiting applicability.
• Validating exposure measurements is crucial for accurate risk assessment.

Purpose of the Study:

• To develop a flexible statistical framework for handling measurement error in Cox proportional hazards models.
• To accommodate general distributional forms of measurement error without restrictive assumptions.
• To enable the use of internal or external validation data within the Cox model framework.

Main Methods:

• A copula-based approach was developed to model the association between true exposure and its surrogate.
• This method allows for flexible modeling of covariate distributions and measurement error structures.
• Large sample properties were theoretically derived, and finite sample performance was assessed via simulations.

Main Results:

• The proposed copula-based method effectively handles measurement error in Cox models.
• The approach is applicable to both internal and external validation study designs.
• Simulation studies confirmed the reliability and performance of the developed methods.

Conclusions:

• The copula-based approach provides a robust and flexible solution for measurement error problems in Cox regression.
• This methodology enhances the accuracy of estimating exposure-disease relationships in observational studies.
• The approach was successfully applied to real-world data on physical activity and breast cancer mortality.