Conditional Akaike information under generalized linear and proportional hazards mixed models.

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Clustered data analysis often requires cluster-specific inference, frequently modeled using random effects.
• Conditional Akaike information provides a criterion for linear mixed models but requires extension for other mixed models.
• Existing methods for model selection in mixed models are limited, especially for generalized linear and proportional hazards models.

Purpose of the Study:

• To extend conditional Akaike information for model selection in generalized linear and proportional hazards mixed models.
• To develop and evaluate analytic and bootstrap-based criteria for cluster-specific inference.
• To address challenges with nuisance parameters using a profile conditional Akaike information approach.

Main Methods:

• Extension of conditional Akaike information to generalized linear and proportional hazards mixed models.
• Development of analytic criteria using asymptotic approximations for non-normal mixed models.
• Implementation and evaluation of bootstrap methods for model selection in finite samples.
• Proposal of a profile conditional Akaike information to handle nuisance parameters.

Main Results:

• Simulations demonstrate that bootstrap and analytic criteria exhibit comparable performance.
• Bootstrap methods show advantages in finite samples, particularly with larger cluster sizes.
• The proposed criteria effectively select models for cluster-specific inference in applied datasets.

Conclusions:

• The developed criteria provide robust methods for model selection in clustered data with a focus on cluster-specific inference.
• Both analytic and bootstrap approaches are valuable, with bootstrap offering benefits in specific scenarios.
• The methods are successfully applied to real-world cancer datasets, highlighting their practical utility.