BACKGROUND: Multi-omics integration may provide additional information about the development of tumors and improve the performance of predictive models. The key challenge lies in integrating several omics sources, especially to capture their biological relationships. Previous studies proposed a structural equation model framework to combine two data platforms for predicting survival; however, several limitations remain. RESULTS: In this study, we introduce an extended Bayesian survival model combined with a structural equation model for adaptation to broader applications. The No U-turn Sampling (NUTS) algorithm was utilized to efficiently sample the posterior distribution of model parameters. Through a series of simulation studies, our model showed excellent goodness-of-fit and predictive performance. To validate the efficiency of our model, we utilized a gastric cancer dataset with three omics types (mRNA, microRNA, and methylation) obtained from The Cancer Genome Atlas. After bioinformatic processing, we included six mRNA, microRNA, and methylation loci datasets into the framework and discovered that our model exhibited greater predictive performance compared to non-integrated and Integrative Bayesian Analysis of Genomics (iBAG) models. CONCLUSIONS: In conclusion, our extended Bayesian structural equation model for multi-omics survival analysis provides a robust framework that significantly enhances predictive accuracy by effectively capturing complex biological relationships across diverse omics data sources, demonstrating clear advantages over both non-integrated approaches and existing integrative methods like iBAG.

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.

BACKGROUND: Group structures among genes encoded in functional relationships or biological pathways are valuable and unique features in large-scale molecular data for survival analysis. However, most of previous approaches for molecular data analysis ignore such group structures. It is desirable to develop powerful analytic methods for incorporating valuable pathway information for predicting disease survival outcomes and detecting associated genes. RESULTS: We here propose a Bayesian hierarchical Cox survival model, called the group spike-and-slab lasso Cox (gsslasso Cox), for predicting disease survival outcomes and detecting associated genes by incorporating group structures of biological pathways. Our hierarchical model employs a novel prior on the coefficients of genes, i.e., the group spike-and-slab double-exponential distribution, to integrate group structures and to adaptively shrink the effects of genes. We have developed a fast and stable deterministic algorithm to fit the proposed models. We performed extensive simulation studies to assess the model fitting properties and the prognostic performance of the proposed method, and also applied our method to analyze three cancer data sets. CONCLUSIONS: Both the theoretical and empirical studies show that the proposed method can induce weaker shrinkage on predictors in an active pathway, thereby incorporating the biological similarity of genes within a same pathway into the hierarchical modeling. Compared with several existing methods, the proposed method can more accurately estimate gene effects and can better predict survival outcomes. For the three cancer data sets, the results show that the proposed method generates more powerful models for survival prediction and detecting associated genes. The method has been implemented in a freely available R package BhGLM at https://github.com/nyiuab/BhGLM .

Motivation: Large-scale molecular data have been increasingly used as an important resource for prognostic prediction of diseases and detection of associated genes. However, standard approaches for omics data analysis ignore the group structure among genes encoded in functional relationships or pathway information. Results: We propose new Bayesian hierarchical generalized linear models, called group spike-and-slab lasso GLMs, for predicting disease outcomes and detecting associated genes by incorporating large-scale molecular data and group structures. The proposed model employs a mixture double-exponential prior for coefficients that induces self-adaptive shrinkage amount on different coefficients. The group information is incorporated into the model by setting group-specific parameters. We have developed a fast and stable deterministic algorithm to fit the proposed hierarchal GLMs, which can perform variable selection within groups. We assess the performance of the proposed method on several simulated scenarios, by varying the overlap among groups, group size, number of non-null groups, and the correlation within group. Compared with existing methods, the proposed method provides not only more accurate estimates of the parameters but also better prediction. We further demonstrate the application of the proposed procedure on three cancer datasets by utilizing pathway structures of genes. Our results show that the proposed method generates powerful models for predicting disease outcomes and detecting associated genes. Availability and implementation: The methods have been implemented in a freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/). Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Large-scale molecular profiling data have offered extraordinary opportunities to improve survival prediction of cancers and other diseases and to detect disease associated genes. However, there are considerable challenges in analyzing large-scale molecular data. RESULTS: We propose new Bayesian hierarchical Cox proportional hazards models, called the spike-and-slab lasso Cox, for predicting survival outcomes and detecting associated genes. We also develop an efficient algorithm to fit the proposed models by incorporating Expectation-Maximization steps into the extremely fast cyclic coordinate descent algorithm. The performance of the proposed method is assessed via extensive simulations and compared with the lasso Cox regression. We demonstrate the proposed procedure on two cancer datasets with censored survival outcomes and thousands of molecular features. Our analyses suggest that the proposed procedure can generate powerful prognostic models for predicting cancer survival and can detect associated genes. AVAILABILITY AND IMPLEMENTATION: The methods have been implemented in a freely available R package BhGLM ( http://www.ssg.uab.edu/bhglm/ ). CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.