Semiparametric Efficient Estimation for a Class of Generalized Proportional Odds Cure Models

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Mixture cure models are essential for analyzing data with a proportion of individuals who never experience the event of interest.
• Existing methods for mixture cure models face computational challenges, particularly in the maximization step of expectation-maximization algorithms.
• The generalized proportional odds model offers a flexible framework for modeling survival data with distinct long-term and short-term effects.

Purpose of the Study:

• To develop and evaluate novel algorithms for fitting mixture cure models using generalized proportional odds models.
• To address the computational difficulties encountered in the M-step of standard expectation-maximization algorithms.
• To assess the performance of the proposed algorithms through simulation studies and a real-world case study.

Main Methods:

• Proposed a mixture cure model incorporating a generalized proportional odds model for the uncured group.
• Developed two novel algorithms to overcome M-step computational challenges: a majorize-minimize (MM) algorithm and a proportional hazards frailty model formulation.
• Employed nonparametric maximum likelihood estimation, proven to be consistent and semiparametric efficient.

Main Results:

• The majorize-minimize (MM) algorithm demonstrated superior computational stability and efficiency compared to existing methods.
• Both proposed algorithms successfully addressed the computational hurdles in the M-step of the expectation-maximization algorithm.
• The MM algorithm proved to be a robust and efficient method for fitting mixture cure models.

Conclusions:

• The proposed majorize-minimize algorithm offers a stable and efficient solution for fitting mixture cure models with generalized proportional odds.
• The developed methods provide valuable tools for survival data analysis, particularly in scenarios with a cured fraction.
• The leukemia data case study validates the practical applicability and effectiveness of the proposed statistical procedures.