Weibull regression for lifetimes measured with error

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Lifetime data analysis often involves measurement error, which can bias standard statistical models.
• Weibull regression models are frequently used for analyzing time-to-event data.

Purpose of the Study:

• To develop and evaluate adjusted estimators for Weibull regression models when measured lifetimes are subject to error.
• To compare the bias properties of adjusted and standard estimators.

Main Methods:

• Modeling true lifetimes using a Weibull regression model.
• Incorporating measurement error models to simulate observed lifetimes.
• Theoretical bias analysis using small measurement error asymptotics.
• Simulation studies to compare estimator performance.

Main Results:

• Standard estimators for regression coefficients (except intercept) demonstrate robustness to bias.
• The proposed adjusted estimator successfully eliminates bias in the shape parameter estimation.
• Simulation results confirm theoretical findings on bias properties.

Conclusions:

• Adjusted estimators are crucial for accurate parameter estimation in Weibull regression with measurement error.
• The bias-robustness of standard coefficients is confirmed, but the shape parameter requires adjustment.
• This work provides a method to improve the reliability of survival analysis in the presence of measurement errors.