Bayesian analysis for partly linear Cox model with measurement error and time-varying covariate effect.

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• The Cox proportional hazards model is standard for time-to-event analysis, assuming constant covariate effects.
• Existing methods for measurement error in Cox models often require specifying parametric forms for true covariate functions.
• Relaxing these assumptions is crucial for accurate survival analysis when data quality is imperfect.

Purpose of the Study:

• To develop a semiparametric partly linear Cox model addressing measurement error in covariates.
• To allow for an unspecified function of an error-contaminated covariate and a time-varying effect of an error-free covariate.
• To provide a flexible statistical framework for survival data with complex covariate relationships.

Main Methods:

• A Bayesian approach is employed to estimate model parameters.
• Unspecified functions are approximated using B-spline basis functions.
• Simulation studies are conducted to evaluate the method's finite sample performance.

Main Results:

• The proposed semiparametric model demonstrated favorable statistical performance in simulations.
• The method effectively handles measurement error in covariates within the Cox model framework.
• The approach allows for more flexible modeling of covariate effects compared to traditional methods.

Conclusions:

• The developed Bayesian semiparametric approach offers a robust alternative for survival analysis with measurement error.
• This method enhances the accuracy and flexibility of estimating covariate associations in time-to-event data.
• The approach is validated through simulations and an application to AIDS clinical trial data.