PliableBVS: A flexible Bayesian variable selection method for modeling interactions with mandatory modifying variables

2026-06-01

AI Summary

This study addresses the joint selection of main effects and mandatory interaction terms involving moderator variables in high-dimensional data by proposing a novel Bayesian variable selection method. Building upon the hierarchical constraints of the pliable lasso, the approach uniquely integrates a two-group spike-and-slab prior with a hierarchical structure, enabling probabilistic sparse modeling of both main effects and their conditional interactions. By combining Bayesian lasso–style continuous shrinkage with Markov chain Monte Carlo inference, the method ensures that an interaction term is included only when its corresponding main effect is present. Empirical evaluations demonstrate that the proposed method substantially outperforms pliable lasso on simulated data, achieving higher selection accuracy and fewer false positives. Applied to real-world data on preterm birth and preeclampsia, it successfully identifies biologically meaningful main and interaction effects.

Abstract

High-dimensional interaction models are useful for studying, for example, how a large set of variables of interest, such as gene expression or other omics features, interact with a smaller set of modifying variables, such as clinical covariates. In this context, the pliable lasso has recently been proposed as an efficient method for screening large numbers of potential interaction terms under an asymmetric weak hierarchical constraint. In this work, we extend this framework by introducing PliableBVS, a Bayesian variable selection approach that preserves the hierarchical structure of the pliable lasso while inducing sparsity through spike-and-slab priors. The proposed model combines the continuous shrinkage effect of Bayesian lasso with a hierarchical spike-and-slab prior formulation that has two layers of decision variables: one governing the inclusion of main effects and another controlling the inclusion of interaction effects which is conditional on the inclusion of the corresponding main effects. This structure enables simultaneous selection of high-dimensional main and interaction effects within a coherent probabilistic framework. In simulation studies the proposed method outperforms the original pliable lasso in identifying active main and interaction effects, reducing false discoveries, and improving prediction accuracy in most scenarios. Applications with data from a labor onset study and a preeclampsia study demonstrate that PliableBVS selects biologically meaningful features and interactions.

Problem

• high-dimensional interaction models
• Bayesian variable selection
• hierarchical structure
• spike-and-slab priors
• mandatory modifying variables

Innovation

• Bayesian variable selection
• spike-and-slab prior
• hierarchical interaction model
• pliable lasso
• high-dimensional inference