Bayesian Variable Selection With l 1 $$ {l}_1 $$ -Ball for Spatially Partly Interval-Censored Data.

Area of Science:

• Biostatistics
• Spatial Statistics
• Survival Analysis

Background:

• Partly interval-censored data present challenges in survival analysis.
• Incorporating spatial effects can improve model accuracy.
• Existing methods may lack efficiency in variable selection and parameter estimation.

Purpose of the Study:

• To develop a novel Bayesian proportional hazards model for partly interval-censored data with spatial effects.
• To enable efficient variable selection and parameter estimation.
• To compare different spatial structures (adjacency and distance) for model applicability.

Main Methods:

• Utilized a differentiable l1-ball prior via projection-based methods.
• Developed an efficient Bayesian algorithm using latent variables and stochastic gradient Langevin dynamics.
• Applied Bayesian model selection criteria (log pseudo-marginal likelihood and deviance information criterion).

Main Results:

• Simulations confirmed the method's effectiveness in variable selection and parameter estimation across various scenarios.
• The approach successfully identified significant variables related to permanent tooth emergence.
• The method accurately determined the most suitable spatial structure for the real-world data.

Conclusions:

• The proposed Bayesian method offers an efficient and robust approach for analyzing partly interval-censored survival data with spatial components.
• It provides valuable insights into variable selection and spatial structure identification.
• The method demonstrates practical utility in epidemiological and public health research, exemplified by its application to dental development data.