Assessing the fit of parametric cure models

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Survival data analysis often includes subjects who are cured and no longer at risk.
• Cure-mixture models address this by separately modeling cure status and failure risk in non-cured individuals.
• Existing diagnostic tools, like Schoenfeld residuals, are not suitable for cure-mixture models.

Purpose of the Study:

• To develop a novel diagnostic tool for assessing the goodness-of-fit of cure-mixture models.
• To create a pseudo-residual method applicable to the non-cured fraction of survival data.
• To extend residual analysis beyond the proportional hazards assumption.

Main Methods:

• Proposed a pseudo-residual, analogous to Schoenfeld residuals, for cure-mixture models.
• Derived the asymptotic distribution of the proposed residuals.
• Evaluated the method's performance through simulations across various parametric models.
• Applied the pseudo-residuals to real-world data from a smoking cessation trial.

Main Results:

• The proposed pseudo-residual effectively assesses survival regression fit within the non-cured population.
• The method is applicable to both proportional hazards (PH) and non-PH models.
• Simulations demonstrated the robustness and utility of the new diagnostic tool.

Conclusions:

• The developed pseudo-residual offers a valuable diagnostic for cure-mixture models, addressing a critical gap in survival data analysis.
• This approach enhances the reliability of statistical models dealing with cured subjects.
• The method provides a flexible tool for evaluating survival models in diverse settings.