Using the EM algorithm for Bayesian variable selection in logistic regression models with related covariates.

Area of Science:

• Biostatistics
• Epidemiology
• Genetics

Background:

• Logistic regression models are crucial for analyzing binary outcomes in epidemiological studies.
• Variable selection is challenging, especially with qualitative covariates and interaction terms.
• Existing methods like LASSO may not adequately handle heredity constraints or complex covariate types.

Purpose of the Study:

• To develop a flexible Bayesian variable selection method for logistic regression.
• To accommodate qualitative covariates and interaction terms under heredity constraints.
• To improve the identification of risk factors in epidemiological research.

Main Methods:

• Developed a Bayesian variable selection method using expectation-maximization variable selection (EMVS) with deterministic annealing.
• Incorporated a variance adjustment for priors of qualitative covariate coefficients to control false positives.
• Implemented a flexible parameterization for interaction terms to manage user-specified heredity constraints.

Main Results:

• The proposed method demonstrated superior covariate selection performance compared to grouped LASSO and LASSO with heredity constraints in simulations.
• The method successfully identified genetic and non-genetic risk factors for smoking experimentation.
• False-positive rates were effectively controlled for qualitative covariates.

Conclusions:

• The novel Bayesian variable selection method offers enhanced flexibility and accuracy for logistic regression models.
• This approach is particularly beneficial for complex epidemiological studies involving qualitative data and interactions.
• The method provides a robust tool for identifying risk factors in population health research.