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A two-way flexible generalized gamma transformation cure rate model.

Pei Wang1, Suvra Pal

  • 1Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA.

Statistics in Medicine
|March 9, 2022
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Summary

This study introduces a flexible cure rate model with two levels of adaptability, enhancing statistical analysis for survival data. The model improves accuracy in lifetime distribution and cure rate estimation, crucial for medical research.

Keywords:
Box-Cox transformationlong-term survivorsmodel mis-specificationpiecewise exponential approximationsensitivity analysis

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Cure rate models are essential for analyzing data where some individuals may never experience the event of interest.
  • Existing models often lack flexibility in characterizing both the cure proportion and the lifetime distribution of the uncured.
  • The Box-Cox transformation cure models and generalized gamma distributions are widely used but often applied separately.

Purpose of the Study:

  • To propose a novel two-way flexible cure rate model combining flexible cure models and lifetime distributions.
  • To develop methods for selecting the optimal cure model and lifetime distribution for a given dataset.
  • To assess the performance of the proposed model in terms of parameter estimation and hypothesis testing.

Main Methods:

  • Developed a generalized gamma Box-Cox transformation (GGBCT) model.
  • Employed maximum likelihood estimation for GGBCT model parameters.
  • Conducted simulation studies to evaluate the power of the likelihood ratio test for model selection.
  • Assessed bias and efficiency of cure rate estimators under model mis-specification.
  • Applied the model to breast cancer data.

Main Results:

  • The GGBCT model offers significant flexibility in choosing cure rate models and lifetime distributions.
  • Likelihood ratio tests effectively detect mis-specified models.
  • Model mis-specification can lead to biased and inefficient cure rate estimates.
  • The proposed model demonstrated a superior fit compared to existing methods in a breast cancer study.

Conclusions:

  • A two-way flexible cure rate model is crucial for accurate survival data analysis.
  • Proper selection of both the cure model and lifetime distribution is vital.
  • The proposed GGBCT model provides a robust framework for such analyses, outperforming existing approaches.