BHCox: Bayesian heredity-constrained Cox proportional hazards models for detecting gene-environment interactions.

Background: Gene-environment (G × E) interactions play a critical role in understanding the etiology of diseases and exploring the factors that affect disease prognosis. There are several challenges in detecting G × E interactions for censored survival outcomes, such as the high dimensionality, complexity of environmental effects, and specificity of survival analysis. The effect heredity, which incorporates the dependence of the main effects and interactions in the analysis, has been widely applied in the study of interaction detection. However, it has not yet been applied to Bayesian Cox proportional hazards models for detecting interactions for censored survival outcomes.

Results: In this study, we propose Bayesian heredity-constrained Cox proportional hazards (BHCox) models with novel spike-and-slab and regularized horseshoe priors that incorporate effect heredity to identify and estimate the main and interaction effects. The no-U-turn sampler (NUTS) algorithm, which has been implemented in the R package brms, was used to fit the proposed model. Extensive simulations were performed to evaluate and compare our proposed approaches with other alternative models. The simulation studies illustrated that BHCox models outperform other alternative models. We applied the proposed method to real data of non-small-cell lung cancer (NSCLC) and identified biologically plausible G × smoking interactions associated with the prognosis of patients with NSCLC.

Conclusions: In summary, BHCox can be used to detect the main effects and interactions and thus have significant implications for the discovery of high-dimensional interactions in censored survival outcome data.