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Modified score function for monotone likelihood in the semiparametric mixture cure model.

Frederico M Almeida1, Enrico A Colosimo1, Vinícius D Mayrink1

  • 1Departamento de Estatística, ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil.

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|November 30, 2021
PubMed
Summary
This summary is machine-generated.

This study addresses monotone likelihood (ML) in cure fraction models, a common issue with small sample sizes and unbalanced data. The Firth correction method is adapted to provide finite estimates, improving survival analysis for immune populations.

Keywords:
Cox regressioncure rateem algorithmfirth methodmelanoma

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Modeling

Background:

  • Cure fraction models analyze lifetime data with immune individuals, jointly estimating cured and susceptible subject distributions.
  • Maximum likelihood estimation can yield non-finite coefficients (monotone likelihood) in small samples with censored data and unbalanced covariates.

Purpose of the Study:

  • To investigate the monotone likelihood (ML) issue in mixture cure models, a topic rarely discussed in existing literature.
  • To adapt the Firth correction for ML in semiparametric cure mixture models, enhancing estimation stability.

Main Methods:

  • Derivation of a modified score function using the Firth correction approach.
  • Monte Carlo simulations to evaluate finite sample properties of estimators under the Firth correction.
  • Application to a real-world melanoma dataset from a Brazilian university hospital.

Main Results:

  • The Firth correction effectively mitigates monotone likelihood issues in cure mixture models.
  • Simulation results show that covariate imbalance significantly impacts coefficient estimates.
  • The adapted method provides stable and finite estimates in semiparametric cure models.

Conclusions:

  • The Firth correction offers a robust solution for monotone likelihood in cure fraction models.
  • This research contributes novel insights into handling estimation challenges in survival analysis with cure fractions.
  • The findings are applicable to analyzing complex lifetime data, particularly in the presence of immune subpopulations.