Bayesian variable selection for parametric survival model with applications to cancer omics data

Bayesian linear mixed model with multiple random effects for prediction analysis on high-dimensional multi-omics data

MOTIVATION

Accurate disease risk prediction is an essential step in the modern quest for precision medicine. While high-dimensional multi-omics data have provided unprecedented data resources for prediction studies, their high-dimensionality and complex inter/intra-relationships have posed significant analytical challenges.

RESULTS

We proposed a two-step Bayesian linear mixed model framework (TBLMM) for risk prediction analysis on multi-omics data. TBLMM models the predictive effects from multi-omics data using a hybrid of the sparsity regression and linear mixed model with multiple random effects. It can resemble the shape of the true effect size distributions and accounts for non-linear, including interaction effects, among multi-omics data via kernel fusion. It infers its parameters via a computationally efficient variational Bayes algorithm. Through extensive simulation studies and the prediction analyses on the positron emission tomography imaging outcomes using data obtained from the Alzheimer's Disease Neuroimaging Initiative, we have demonstrated that TBLMM can consistently outperform the existing method in predicting the risk of complex traits.

AVAILABILITY AND IMPLEMENTATION

The corresponding R package is available on GitHub (https://github.com/YaluWen/TBLMM).

Bayesian penalized Buckley-James method for high dimensional bivariate censored regression models

For high dimensional gene expression data, one important goal is to identify a small number of genes that are associated with progression of the disease or survival of the patients. In this paper, we consider the problem of variable selection for multivariate survival data. We propose an estimation procedure for high dimensional accelerated failure time (AFT) models with bivariate censored data. The method extends the Buckley-James method by minimizing a penalized [Formula: see text] loss function with a penalty function induced from a bivariate spike-and-slab prior specification. In the proposed algorithm, censored observations are imputed using the Kaplan-Meier estimator, which avoids a parametric assumption on the error terms. Our empirical studies demonstrate that the proposed method provides better performance compared to the alternative procedures designed for univariate survival data regardless of whether the true events are correlated or not, and conceptualizes a formal way of handling bivariate survival data for AFT models. Findings from the analysis of a myeloma clinical trial using the proposed method are also presented.

Integration of immune and hypoxia gene signatures improves the prediction of radiosensitivity in breast cancer

Immunity and hypoxia are two important factors that affect the response of cancer patients to radiotherapy. At the same time, considering the limited predictive value of a single predictive model and the uncertainty of grouping patients near the cutoff value, we developed and validated a combined model based on immune- and hypoxia-related gene expression profiles to predict the radiosensitivity of breast cancer patients. This study was based on breast cancer data from The Cancer Genome Atlas (TCGA). Spike-and-slab Lasso regression analysis was performed to select three immune-related genes and develop a radiosensitivity model. Lasso Cox regression modeling selected 11 hypoxia-related genes for development of radiosensitivity model. Three independent datasets (Molecular Taxonomy of Breast Cancer International Consortium [METABRIC], E-TABM-158, GSE103746) were used to validate the predictive value of radiosensitivity signatures. In the TCGA dataset, the 10-year survival probabilities of the immune radioresistant (IRR) and hypoxia radioresistant (HRR) groups were 0.189 (0.037, 0.973) and 0.477 (0.293, 0.776), respectively. The 10-year survival probabilities of the immune radiosensitive (IRS) and hypoxia radiosensitive (HRS) groups were 0.778 (0.676, 0.895) and 0.824 (0.723, 0.939), respectively. Based on these two gene signatures, we further constructed a combined model and divided all patients into three groups (IRS/HRS, mixed, IRR/HRR). We identified the IRS/HRS patients most likely to benefit from radiotherapy; the 10-year survival probability was 0.886 (0.806, 0.976). The 10-year survival probability of the IRR/HRR group was 0. In conclusion, a combined model integrating immune- and hypoxia-related gene signatures could effectively predict the radiosensitivity of breast cancer and more accurately identify radiosensitive and radioresistant patients than a single model.

The Application of Bayesian Methods in Cancer Prognosis and Prediction

With the development of high-throughput biological techniques, high-dimensional omics data have emerged. These molecular data provide a solid foundation for precision medicine and prognostic prediction of cancer. Bayesian methods contribute to constructing prognostic models with complex relationships in omics and improving performance by introducing different prior distribution, which is suitable for modelling the high-dimensional data involved. Using different omics, several Bayesian hierarchical approaches have been proposed for variable selection and model construction. In particular, the Bayesian methods of multi-omics integration have also been consistently proposed in recent years. Compared with single-omics, multi-omics integration modelling will contribute to improving predictive performance, gaining insights into the underlying mechanisms of tumour occurrence and development, and the discovery of more reliable biomarkers. In this work, we present a review of current proposed Bayesian approaches in prognostic prediction modelling in cancer.

Genomic architecture and prediction of censored time-to-event phenotypes with a Bayesian genome-wide analysis

While recent advancements in computation and modelling have improved the analysis of complex traits, our understanding of the genetic basis of the time at symptom onset remains limited. Here, we develop a Bayesian approach (BayesW) that provides probabilistic inference of the genetic architecture of age-at-onset phenotypes in a sampling scheme that facilitates biobank-scale time-to-event analyses. We show in extensive simulation work the benefits BayesW provides in terms of number of discoveries, model performance and genomic prediction. In the UK Biobank, we find many thousands of common genomic regions underlying the age-at-onset of high blood pressure (HBP), cardiac disease (CAD), and type-2 diabetes (T2D), and for the genetic basis of onset reflecting the underlying genetic liability to disease. Age-at-menopause and age-at-menarche are also highly polygenic, but with higher variance contributed by low frequency variants. Genomic prediction into the Estonian Biobank data shows that BayesW gives higher prediction accuracy than other approaches.

Comparison of single and module-based methods for modeling gene regulatory networks

MOTIVATION

Gene regulatory networks describe the regulatory relationships among genes, and developing methods for reverse engineering these networks is an ongoing challenge in computational biology. The majority of the initially proposed methods for gene regulatory network discovery create a network of genes and then mine it in order to uncover previously unknown regulatory processes. More recent approaches have focused on inferring modules of co-regulated genes, linking these modules with regulatory genes and then mining them to discover new molecular biology.

RESULTS

In this work we analyze module-based network approaches to build gene regulatory networks, and compare their performance to single gene network approaches. In the process, we propose a novel approach to estimate gene regulatory networks drawing from the module-based methods. We show that generating modules of co-expressed genes which are predicted by a sparse set of regulators using a variational Bayes method, and then building a bipartite graph on the generated modules using sparse regression, yields more informative networks than previous single and module-based network approaches as measured by: (i) the rate of enriched gene sets, (ii) a network topology assessment, (iii) ChIP-Seq evidence and (iv) the KnowEnG Knowledge Network collection of previously characterized gene-gene interactions.

AVAILABILITY AND IMPLEMENTATION

The code is written in R and can be downloaded from https://github.com/mikelhernaez/linker.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Bayesian Inference of Lymph Node Ratio Estimation and Survival Prognosis for Breast Cancer Patients

OBJECTIVE

We evaluated the prognostic value of lymph node ratio (LNR) for the survival of breast cancer patients using Bayesian inference.

METHODS

Data on 5,279 women with infiltrating duct and lobular carcinoma breast cancer, diagnosed from 2006-2010, was obtained from the NCI SEER Cancer Registry. A prognostic modeling framework was proposed using Bayesian inference to estimate the impact of LNR in breast cancer survival. Based on the proposed model, we then developed a web application for estimating LNR and predicting overall survival.

RESULTS

The final survival model with LNR outperformed the other models considered (C-statistic 0.71). Compared to directly measured LNR, estimated LNR slightly increased the accuracy of the prognostic model. Model diagnostics and predictive performance confirmed the effectiveness of Bayesian modeling and the prognostic value of the LNR in predicting breast cancer survival.

CONCLUSION

The estimated LNR was found to have a significant predictive value for the overall survival of breast cancer patients.

SIGNIFICANCE

We used Bayesian inference to estimate LNR which was then used to predict overall survival. The models were developed from a large population-based cancer registry. We also built a user-friendly web application for individual patient survival prognosis. The diagnostic value of the LNR and the effectiveness of the proposed model were evaluated by comparisons with existing prediction models.