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Review and implementation of cure models based on first hitting times for Wiener processes
Jeremy Balka1, Anthony F Desmond, Paul D McNicholas
1Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada. jbalka@uoguelph.ca
Lifetime Data Analysis
|January 6, 2009
Summary
Process-based cure rate models using Wiener processes offer an improved alternative to standard mixture models. Modifications enhance the defective inverse Gaussian model, showing strong performance in real and simulated data analysis.
Area of Science:
- Statistics
- Survival Analysis
Background:
- Cure rate estimation is a key area in survival analysis.
- The standard mixture model is widely used, but process-based models are emerging.
- First passage time models for Wiener processes are being explored for cure rate estimation.
Purpose of the Study:
- To investigate Wiener process-based models for cure rate estimation.
- To address limitations of the defective inverse Gaussian model.
- To propose and evaluate modifications for improved model fit.
Main Methods:
- Focus on first passage time models for Wiener processes.
- Investigated the Wiener process with negative drift.
- Developed modifications: inverse Gaussian mixture, heterogeneity, and a second absorbing barrier.
- Utilized expectation-maximization (EM) algorithms for parameter estimation.
Main Results:
- The defective inverse Gaussian model showed a poor fit in some cases.
- Modified models demonstrated improved fit over the standard mixture model.
- Proposed process-based models performed well on real and simulated data.
- EM algorithms facilitated model implementation and parameter estimation.
Conclusions:
- Process-based models, particularly modified Wiener process models, are a valuable alternative to standard cure rate models.
- These models offer an improved fit for various datasets.
- EM algorithms provide an effective framework for implementing these advanced statistical models.
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