Analysis of clustered failure time data with cure fraction using copula

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Clustered survival data with a cure fraction is a complex area of statistical research.
• Existing methods may not fully capture the intricate associations within clusters.

Purpose of the Study:

• To develop a semiparametric mixture cure model for clustered survival data.
• To assess the association between susceptibility and failure times within clusters using Archimedean copula models.

Main Methods:

• A semiparametric mixture cure model with logistic regression for cure fraction and semiparametric regression for failure time.
• Utilized Archimedean copula (AC) models to quantify associations.
• Employed a composite likelihood function and a two-stage estimation procedure.
• A cluster-based Jackknife method for variance estimation.
• Akaike information criterion for model selection.

Main Results:

• The proposed two-stage estimation procedure effectively estimates marginal and association parameters.
• The Jackknife variance estimation provides reliable measures of uncertainty.
• Simulation studies demonstrate the validity of the developed methods.
• Real-world data analysis showcases the practical applicability.

Conclusions:

• The developed semiparametric mixture cure model with Archimedean copulas provides a flexible framework for analyzing clustered survival data with cure fractions.
• The composite likelihood approach and two-stage estimation are efficient and robust.
• The method is valuable for understanding complex dependencies in health and biological studies.