Bayesian model selection and averaging in additive and proportional hazards models.

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Cox proportional hazards regression is standard for time-to-event data.
• Uncertainty exists regarding whether predictor effects are multiplicative or additive.
• Existing methods may violate non-negative hazard constraints.

Purpose of the Study:

• To develop an additive-multiplicative hazards model accommodating uncertainty in predictor effects.
• To provide a framework for selecting between additive, multiplicative, or combined effects.
• To ensure non-negative hazard rates in survival analysis.

Main Methods:

• Introduced a model selection prior on coefficients within an additive-multiplicative hazards model.
• Incorporated sub-models for no association, additive effects only, and proportional effects only.
• Utilized Poisson latent variable augmentation for conditional conjugacy.
• Employed an efficient Gibbs sampling algorithm for posterior computation.

Main Results:

• The proposed prior allows for flexible model selection, including pure additive or multiplicative effects.
• The constrained additive component ensures non-negative hazard rates.
• The Gibbs sampling algorithm provides an efficient computational approach.

Conclusions:

• The additive-multiplicative hazards model offers a robust alternative to standard Cox regression.
• This methodology enhances the analysis of time-to-event data by handling model uncertainty.
• The approach is validated through simulation studies and application to the Framingham Heart Study data.