Semiparametric Bayesian analysis of censored linear regression with errors-in-covariates

Area of Science:

• Biostatistics
• Survival Analysis
• Bayesian Statistics

Background:

• Accelerated Failure Time (AFT) models are alternatives to Cox models for time-to-event data.
• Analyzing right-censored data with predictor measurement error presents significant statistical challenges.
• Existing methods often require distributional assumptions or struggle with complex error structures.

Purpose of the Study:

• To develop a robust statistical method for fitting AFT models to right-censored time-to-event data with predictor measurement error.
• To address the complexities arising from both censoring and unobserved predictor variability.
• To provide a flexible framework for estimating model parameters and survival probabilities.

Main Methods:

• A non-parametric Bayesian approach is proposed.
• Mixtures of Dirichlet process priors are used to model event time, unobserved true predictor, and measurement error distributions.
• The method allows for flexible, assumption-free modeling of these components.

Main Results:

• The proposed Bayesian method effectively handles right-censored data with predictor measurement error.
• Simulation studies demonstrate the operating characteristics and accuracy of the approach.
• The method successfully estimates AFT model parameters and survival probabilities.

Conclusions:

• The non-parametric Bayesian method offers a powerful tool for analyzing complex time-to-event data with measurement error.
• This approach enhances the reliability of survival analysis in the presence of data imperfections.
• The method is illustrated using a real-world AIDS clinical trial dataset.