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

We develop a Bayesian variable selection method for logistic regression models that can simultaneously accommodate qualitative covariates and interaction terms under various heredity constraints. We use expectation-maximization variable selection (EMVS) with a deterministic annealing variant as the platform for our method, due to its proven flexibility and efficiency. We propose a variance adjustment of the priors for the coefficients of qualitative covariates, which controls false-positive rates, and a flexible parameterization for interaction terms, which accommodates user-specified heredity constraints. This method can handle all pairwise interaction terms as well as a subset of specific interactions. Using simulation, we show that this method selects associated covariates better than the grouped LASSO and the LASSO with heredity constraints in various exploratory research scenarios encountered in epidemiological studies. We apply our method to identify genetic and non-genetic risk factors associated with smoking experimentation in a cohort of Mexican-heritage adolescents.

本研究针对逻辑回归模型（logistic regression models）开发了一种贝叶斯变量选择（Bayesian variable selection）方法，该方法可在各类层级约束下同时兼容定性协变量与交互项。本方法以经证实兼具灵活性与高效性的确定性退火变体期望最大化变量选择（Expectation-Maximization Variable Selection, EMVS）作为基础框架。我们针对定性协变量的系数提出了先验方差调整策略，以控制假阳性率；同时为交互项设计了灵活的参数化方案，可适配用户指定的层级约束。该方法可处理所有两两交互项以及特定交互项的子集。通过模拟实验验证，在流行病学研究中常见的各类探索性研究场景下，本方法的关联协变量选择效果优于分组套索（Grouped LASSO）与带层级约束的套索回归（Least Absolute Shrinkage and Selection Operator, LASSO）。我们将该方法应用于墨西哥裔青少年队列，以识别与吸烟尝试相关的遗传及非遗传危险因素。