BHAFT: Bayesian heredity-constrained accelerated failure time models for detecting gene-environment interactions in survival analysis.

In addition to considering the main effects, understanding gene-environment (G × E) interactions is imperative for determining the etiology of diseases and the factors that affect their prognosis. In the existing statistical framework for censored survival outcomes, there are several challenges in detecting G × E interactions, such as handling high-dimensional omics data, diverse environmental factors, and algorithmic complications in survival analysis. The effect heredity principle has widely been used in studies involving interaction identification because it incorporates the dependence of the main and interaction effects. However, Bayesian survival models that incorporate the assumption of this principle have not been developed. Therefore, we propose Bayesian heredity-constrained accelerated failure time (BHAFT) models for identifying main and interaction (M-I) effects with novel spike-and-slab or regularized horseshoe priors to incorporate the assumption of effect heredity principle. The R package rstan was used to fit the proposed models. Extensive simulations demonstrated that BHAFT models had outperformed other existing models in terms of signal identification, coefficient estimation, and prognosis prediction. Biologically plausible G × E interactions associated with the prognosis of lung adenocarcinoma were identified using our proposed model. Notably, BHAFT models incorporating the effect heredity principle could identify both main and interaction effects, which are highly useful in exploring G × E interactions in high-dimensional survival analysis. The code and data used in our paper are available at https://github.com/SunNa-bayesian/BHAFT.

Incorporating historical models with adaptive Bayesian updates.

This article considers Bayesian approaches for incorporating information from a historical model into a current analysis when the historical model includes only a subset of covariates currently of interest. The statistical challenge is 2-fold. First, the parameters in the nested historical model are not generally equal to their counterparts in the larger current model, neither in value nor interpretation. Second, because the historical information will not be equally informative for all parameters in the current analysis, additional regularization may be required beyond that provided by the historical information. We propose several novel extensions of the so-called power prior that adaptively combine a prior based upon the historical information with a variance-reducing prior that shrinks parameter values toward zero. The ideas are directly motivated by our work building mortality risk prediction models for pediatric patients receiving extracorporeal membrane oxygenation (ECMO). We have developed a model on a registry-based cohort of ECMO patients and now seek to expand this model with additional biometric measurements, not available in the registry, collected on a small auxiliary cohort. Our adaptive priors are able to use the information in the original model and identify novel mortality risk factors. We support this with a simulation study, which demonstrates the potential for efficiency gains in estimation under a variety of scenarios.