Penalized maximum likelihood inference under the mixture cure model in sparse data.

Area of Science:

• Biostatistics
• Survival Analysis
• Cancer Research

Background:

• Mixture cure (MC) models are preferred for analyzing long-term survival data with many survivors.
• Standard maximum likelihood (ML) estimation in MC models can be biased, particularly in samples with few observed events (recurrences).

Purpose of the Study:

• To extend Firth-type penalized likelihood (FT-PL) methods for bias reduction to Weibull-logistic MC models.
• To compare the performance of FT-PL with standard ML estimation in MC models using simulation studies.

Main Methods:

• The study extended FT-PL, using a Jeffreys invariant prior, to the Weibull-logistic MC model.
• Simulation studies were conducted based on a cohort study, comparing FT-PL estimates to ML estimates.
• Type 1 error (T1E) and statistical power were evaluated using likelihood ratio statistics.

Main Results:

• FT-PL estimates (FT-PLEs) demonstrated reduced bias and smaller mean squared error compared to ML estimates (MLEs) in samples with few events.
• FT-PL provided finite estimates in scenarios where MLEs were infinite.
• FT-PL consistently showed higher statistical power than ML under similar T1E rates when events were sparse.

Conclusions:

• FT-PL offers a robust approach for MC regression, providing finite estimates and improved bias-variance balance, outperforming other penalization methods.
• The FT-PL method is practical and effective for analyzing long-term recurrence-free survival data, as demonstrated in a breast cancer cohort study.