Measures of explained variation under the mixture cure model for survival data

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Explained variation is crucial for understanding model fit in statistical analysis.
• Existing measures are well-established for linear and survival models.
• Mixture cure models present unique challenges for quantifying explained variation.

Purpose of the Study:

• To propose novel measures for explained variation specifically tailored for mixture cure models.
• To evaluate the statistical properties and utility of these new measures.
• To provide practical tools for assessing model performance in mixture cure settings.

Main Methods:

• Development of two distinct approaches for explained variation: one using Kullback-Leibler information gain, another using residual sum of squares.
• Theoretical assessment of the proposed measures against desired properties of explained variation.
• Empirical validation through a comprehensive simulation study.
• Application to real-world datasets to demonstrate practical utility.

Main Results:

• The proposed measures effectively quantify explained variation within mixture cure models.
• Both Kullback-Leibler and residual sum of squares approaches demonstrate desirable statistical properties.
• Simulation results confirm the reliability and performance of the new measures.
• Real data analyses showcase the practical applicability and interpretability of the explained variation measures.

Conclusions:

• The developed methods provide robust and interpretable measures of explained variation for mixture cure models.
• These measures enhance the assessment of model fit and predictive performance in survival analysis with cure fractions.
• The findings contribute to a deeper understanding of explained variation in advanced statistical modeling contexts.