Firth adjusted score function for monotone likelihood in the mixture cure fraction model

Area of Science:

• Biomedical research
• Survival analysis
• Biostatistics

Background:

• Models with long-term survivors (immune or non-susceptible individuals) are crucial in biomedical research.
• Standard regression fitting is problematic with small sample sizes and high censoring rates due to monotone likelihood, leading to infinite estimates.
• Monotone likelihood occurs with categorical covariates that perfectly predict outcomes or are unassociated with failure.

Purpose of the Study:

• To address the rarely discussed topic of bias correction in mixture cure models.
• To propose an adjusted score function based on the Firth method to handle monotone likelihood.
• To evaluate the inference performance of penalized maximum likelihood estimates in cure models.

Main Methods:

• Adaptation of the Firth method, originally designed for bias reduction.
• Development of an adjusted score function using the Firth method.
• Extensive Monte Carlo simulation studies to assess performance.
• Application to a real-world dataset of melanoma patients.

Main Results:

• The proposed Firth method adaptation provides finite estimates, mitigating the monotone likelihood issue.
• Penalized maximum likelihood estimates demonstrate good inference performance in simulations.
• The method is successfully illustrated on a novel melanoma patient dataset with cured individuals and monotone likelihood.

Conclusions:

• The Firth method adaptation offers a viable solution for bias correction in mixture cure models affected by monotone likelihood.
• The penalized likelihood approach improves estimation stability and reliability in challenging survival data.
• This work contributes a valuable method for analyzing complex survival data with immune or non-susceptible subpopulations.