Model diagnostics for censored regression via randomized survival probabilities.

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Traditional regression diagnostics rely on residuals with known distributions.
• Censored regression lacks analogous residuals for model assessment.
• Assessing goodness-of-fit and identifying model misspecification in censored data is challenging.

Purpose of the Study:

• To propose and validate a novel residual diagnostic tool for censored regression models.
• To introduce normalized randomized survival probabilities (NRSP) for model diagnostics.
• To evaluate the performance of NRSP residuals in detecting model misspecification, including incorrect distribution family and nonlinear covariate effects.

Main Methods:

• Proposed replacing censored survival probabilities with random numbers from a uniform distribution.
• Developed normalized randomized survival probabilities (NRSP) by transforming these values using the normal quantile function.
• Conducted simulation studies to assess statistical test performance for goodness-of-fit and nonlinearity detection.
• Applied NRSP residuals to a real-world breast cancer recurrence-free survival dataset.

Main Results:

• NRSP residuals provide a characterized reference distribution for censored regression diagnostics.
• Goodness-of-fit tests using NRSP residuals showed lower power compared to traditional methods.
• Nonlinearity tests based on NRSP residuals demonstrated significantly higher power in detecting nonlinear effects.
• NRSP residuals successfully identified a subtle nonlinear relationship in the breast cancer dataset missed by other methods.

Conclusions:

• Normalized randomized survival probabilities (NRSP) offer a valuable new approach for diagnosing censored regression models.
• NRSP residuals are particularly effective for detecting nonlinear effects in survival data.
• This method enhances model interpretability and accuracy in survival analysis applications.