A Study of R² Measure under the Accelerated Failure Time Models

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• The accelerated failure time (AFT) model is a valuable alternative to proportional hazards models for analyzing right-censored data.
• AFT models are linear on the (log-transformed) outcome and suitable for non-time-to-event censored outcomes like laboratory measurements.
• Quantifying explained variation (R-squared) is crucial for assessing model fit in AFT models.

Purpose of the Study:

• To define a general and computable R-squared measure for the AFT model with right-censored data.
• To investigate the behavior of this R-squared measure under various censoring scenarios and error distributions.
• To assess the robustness of the R-squared measure when the parametric error distribution is misspecified.

Main Methods:

• Development of a general definition for the R-squared measure applicable to AFT models with right-censored data.
• Monte Carlo simulations to study the R-squared measure's performance under different censoring patterns and error distributions.
• Robustness analysis of the R-squared measure when the assumed parametric error distribution is incorrect.

Main Results:

• A computable R-squared measure for AFT models with right-censored data was successfully defined.
• Simulation results demonstrated the measure's behavior across different censoring conditions and error distributions.
• The log-normal distribution emerged as a robust choice for the parametric AFT model when R-squared is of interest.

Conclusions:

• The proposed R-squared measure provides a reliable way to assess explained variation in AFT models for censored data.
• The log-normal distribution is recommended for practical implementation of parametric AFT models focusing on R-squared.
• The methodology was successfully applied to a real-world dataset on alcohol consumption during pregnancy.