On a class of non-linear transformation cure rate models

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Traditional mixture (binary) cure rate models may not fully capture complex scenarios.
• The presence of zero-modified distributions (inflation or deflation) in competing cause models requires advanced statistical approaches.
• Existing transformation functions in cure rate modeling often lack realistic interpretations.

Purpose of the Study:

• To propose a generalized mixture cure rate model accommodating zero-modified distributions in competing cause scenarios.
• To provide a realistic interpretation for a specific class of proper transformation functions within cure rate modeling.
• To develop and evaluate parameter estimation and model discrimination methods for the proposed model.

Main Methods:

• Generalization of the mixture (binary) cure rate model.
• Incorporation of zero-modified distributions for the initial number of causes.
• Parameter estimation using the maximum likelihood method with a profile approach.
• Model discrimination via the likelihood ratio test.

Main Results:

• A novel generalized cure rate model is proposed, offering enhanced flexibility.
• The maximum likelihood and profile approach provide accurate parameter estimation.
• The likelihood ratio test effectively discriminates between models.
• Simulation studies confirm the accuracy of the proposed estimation and discrimination methods.

Conclusions:

• The proposed generalized cure rate model effectively handles competing risks with zero-modified distributions.
• The method provides realistic interpretations for transformation functions in cure rate modeling.
• The model and estimation techniques are validated through simulation and real-world data analysis (recidivism and cutaneous melanoma).