Goodness-of-fit testing in the presence of cured data: IPCW approach

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Inference

Background:

• Goodness-of-fit testing is crucial for validating statistical models.
• Censored data and cured subjects present unique challenges in survival analysis.
• Existing methods may not adequately address populations with both susceptible and cured individuals.

Purpose of the Study:

• To develop and evaluate novel goodness-of-fit tests for randomly right-censored data in the presence of cured subjects.
• To adapt existing characterization-based tests using inverse probability of censoring weighting (IPCW) for improved performance.
• To assess the finite sample performance of the proposed tests against established competitors.

Main Methods:

• Modification of characterization-based goodness-of-fit tests using the inverse probability of censoring weighted U- or V-approach.
• Analysis of asymptotic properties of the proposed tests.
• Comparative power study involving recent CvM-based and other prominent tests, considering the presence of cured subjects.

Main Results:

• The proposed modified tests demonstrate good finite sample performance.
• The IPCW approach effectively handles censoring in the presence of cured subjects.
• The novel tests show competitive or superior power compared to existing methods in simulations.

Conclusions:

• The developed goodness-of-fit tests provide a robust tool for analyzing survival data with cured populations.
• The methodology is generalizable to other tests formulated using similar principles.
• The tests are effectively illustrated on a real-world dataset concerning leukemia relapse.