Evaluating the time-dependent predictive accuracy for event-to-time outcome with a cure fraction

Area of Science:

• Biostatistics
• Survival Analysis
• Medical Informatics

Background:

• Cure models are essential for populations with long-term survivors, such as early-stage cancer patients.
• Prognostic risk scores predict disease and cure status, but their performance is challenging to quantify with censoring.
• Time-dependent receiver operating characteristic (ROC) curves dynamically assess prediction performance.

Purpose of the Study:

• To develop a robust semi-parametric estimator for time-dependent ROC curves in mixture cure models.
• To quantify and estimate the predictive performance of prognostic risk scores in the presence of a cure fraction.
• To derive the time-dependent area under the ROC curve (AUC) for a global assessment of discriminatory capacity.

Main Methods:

• Utilized sieve maximum likelihood (ML) estimation under a mixture cure model framework.
• Incorporated a Bernstein-based smoothing method to enhance estimation efficiency.
• Proposed a time-dependent ROC curve estimator to address unknown cure and disease statuses in censored data.

Main Results:

• The proposed semi-parametric estimator provides an efficient way to assess predictive accuracy in cure models.
• The time-dependent AUC effectively summarizes the global discriminatory power of risk scores.
• Simulations demonstrated the finite sample performance of the developed methods.

Conclusions:

• The novel method accurately assesses predictive performance for survival outcomes in populations with cure fractions.
• This approach offers valuable tools for medical practitioners evaluating prognostic risk scores in cancer studies.
• The methods were illustrated using real-world data from melanoma and stomach cancer studies.