Likelihood approaches for proportional likelihood ratio model with right-censored data

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Traditional semiparametric transformation models (e.g., Cox regression, proportional odds) for right-censored survival data have limitations.
• These limitations include potential assumption violations and difficulties in interpreting regression coefficients.
• Existing methods may lack flexibility and direct clinical applicability for complex survival data.

Purpose of the Study:

• To extend the proportional likelihood ratio model for flexible modeling of survival outcomes and covariates.
• To provide a practical alternative to semiparametric transformation models with improved interpretability.
• To develop robust estimation and inference methods for regression parameters under various censoring scenarios.

Main Methods:

• Extension of the proportional likelihood ratio model, connecting it to generalized linear and density ratio models.
• Development of two likelihood approaches: a conditional likelihood using uncensored data and a full likelihood approach.
• Utilizing pairwise pseudo-likelihood maximization and profile likelihood for parameter estimation and inference.

Main Results:

• The proposed proportional likelihood ratio model demonstrates enhanced flexibility and direct clinical interpretability.
• Simulation studies confirm the finite-sample properties of the developed estimators.
• Comparison of the two likelihood approaches highlights their relative efficiencies in handling censored survival data.

Conclusions:

• The extended proportional likelihood ratio model offers a practical and flexible alternative for survival data analysis.
• The developed likelihood approaches provide reliable methods for estimation and inference, even with dependent censoring.
• The method is illustrated with bone marrow transplantation data, showing its utility in handling non-proportional hazards.