Likelihood-Based Inference for Semi-Parametric Transformation Cure Models with Interval Censored Data

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Survival data with a cure fraction requires specialized modeling techniques.
• Existing models like mixture and promotion time cure models have limitations.
• The Box-Cox transformation cure model (BCTM) offers a unified approach.

Purpose of the Study:

• To numerically investigate the statistical properties of the BCTM for interval-censored data.
• To develop and evaluate an expectation-maximization (EM) algorithm for parameter estimation in the BCTM.
• To assess the model's performance and estimation accuracy under various conditions.

Main Methods:

• Application of the Box-Cox transformation cure model (BCTM) to interval-censored survival data.
• Modeling time-to-event data using a proportional hazards structure with a non-parametric baseline hazard.
• Development of an expectation-maximization (EM) algorithm for maximum likelihood estimation of model parameters, including the Box-Cox transformation parameter (α).

Main Results:

• The developed EM algorithm effectively estimates BCTM parameters simultaneously, unlike traditional profile-likelihood methods.
• Simulation studies demonstrate the robustness and accuracy of the BCTM and the EM estimation method across various parameter settings.
• The model and method show good performance when applied to real-world data from a smoking cessation study.

Conclusions:

• The BCTM is a versatile and effective tool for modeling survival data with cure fractions, particularly for interval-censored data.
• The proposed EM algorithm provides a robust and accurate method for parameter estimation within the BCTM framework.
• The findings support the practical utility of the BCTM and EM algorithm in biostatistical research and applications.