USING PROFILE LIKELIHOOD FOR SEMIPARAMETRIC MODEL SELECTION WITH APPLICATION TO PROPORTIONAL HAZARDS MIXED MODELS

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Semiparametric models are widely used but selecting between nested and non-nested models with nuisance parameters is challenging.
• The proportional hazards mixed effects model (PHMM) is a complex model incorporating random effects, requiring robust selection criteria.
• Existing methods for model selection often struggle with nuisance parameters and boundary cases.

Purpose of the Study:

• To develop a unified framework for selecting nested and non-nested semiparametric models, particularly those with nuisance parameters.
• To extend the utility of likelihood ratio statistics and Akaike information for complex models like the PHMM.
• To compare computational algorithms for likelihood estimation in the context of the PHMM.

Main Methods:

• Utilized profile likelihood to define likelihood ratio statistics and Akaike information for semiparametric models.
• Employed asymptotic quadratic expansion of the log profile likelihood to derive null distributions and unbiased estimators.
• Applied Laplace approximation, reciprocal importance sampling, and bridge sampling for profile likelihood computation under PHMM.

Main Results:

• Derived the asymptotic null distribution of the likelihood ratio statistic, accounting for boundary cases.
• Developed an unbiased Akaike information criterion for estimating Akaike information.
• Compared the performance of three computational algorithms for profile likelihood estimation under various data structures.

Conclusions:

• The proposed profile likelihood approach provides a robust method for semiparametric model selection, even with nuisance parameters.
• The methods are applicable to complex models such as the proportional hazards mixed effects model (PHMM).
• The study demonstrated the practical application of these methods using a multi-center lung cancer clinical trial dataset.