Fully Bayesian Logistic Regression with Hyper-Lasso Priors for High-dimensional Feature Selection

High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands of genes that are active (expressed) in certain tissue cells. To this end, we wish to fit regression and classification models with a large number of features (also called variables, predictors). In the past decade, penalized likelihood methods for fitting regression models based on hyper-LASSO penalization have received increasing attention in the literature. However, fully Bayesian methods that use Markov chain Monte Carlo (MCMC) are still in lack of development in the literature. In this paper we introduce an MCMC (fully Bayesian) method for learning severely multi-modal posteriors of logistic regression models based on hyper-LASSO priors (non-convex penalties). Our MCMC algorithm uses Hamiltonian Monte Carlo in a restricted Gibbs sampling framework; we call our method Bayesian logistic regression with hyper-LASSO (BLRHL) priors. We have used simulation studies and real data analysis to demonstrate the superior performance of hyper-LASSO priors, and to investigate the issues of choosing heaviness and scale of hyper-LASSO priors.Comment: 33 pages. arXiv admin note: substantial text overlap with arXiv:1308.469

Modified Logistic Regression Models Using Gene Coexpression and Clinical Features to Predict Prostate Cancer Progression

Predicting disease progression is one of the most challenging problems in prostate cancer research. Adding gene expression data to prediction models that are based on clinical features has been proposed to improve accuracy. In the current study, we applied a logistic regression (LR) model combining clinical features and gene co-expression data to improve the accuracy of the prediction of prostate cancer progression. The top-scoring pair (TSP) method was used to select genes for the model. The proposed models not only preserved the basic properties of the TSP algorithm but also incorporated the clinical features into the prognostic models. Based on the statistical inference with the iterative cross validation, we demonstrated that prediction LR models that included genes selected by the TSP method provided better predictions of prostate cancer progression than those using clinical variables only and/or those that included genes selected by the one-gene-at-a-time approach. Thus, we conclude that TSP selection is a useful tool for feature (and/or gene) selection to use in prognostic models and our model also provides an alternative for predicting prostate cancer progression

Network-Based Biomarker Discovery : Development of Prognostic Biomarkers for Personalized Medicine by Integrating Data and Prior Knowledge

Advances in genome science and technology offer a deeper understanding of biology while at the same time improving the practice of medicine. The expression profiling of some diseases, such as cancer, allows for identifying marker genes, which could be able to diagnose a disease or predict future disease outcomes. Marker genes (biomarkers) are selected by scoring how well their expression levels can discriminate between different classes of disease or between groups of patients with different clinical outcome (e.g. therapy response, survival time, etc.). A current challenge is to identify new markers that are directly related to the underlying disease mechanism

Machine learning and computational methods to identify molecular and clinical markers for complex diseases – case studies in cancer and obesity

In biomedical research, applied machine learning and bioinformatics are the essential disciplines heavily involved in translating data-driven findings into medical practice. This task is especially accomplished by developing computational tools and algorithms assisting in detection and clarification of underlying causes of the diseases. The continuous advancements in high-throughput technologies coupled with the recently promoted data sharing policies have contributed to presence of a massive wealth of data with remarkable potential to improve human health care. In concordance with this massive boost in data production, innovative data analysis tools and methods are required to meet the growing demand. The data analyzed by bioinformaticians and computational biology experts can be broadly divided into molecular and conventional clinical data categories. The aim of this thesis was to develop novel statistical and machine learning tools and to incorporate the existing state-of-the-art methods to analyze bio-clinical data with medical applications. The findings of the studies demonstrate the impact of computational approaches in clinical decision making by improving patients risk stratification and prediction of disease outcomes. This thesis is comprised of five studies explaining method development for 1) genomic data, 2) conventional clinical data and 3) integration of genomic and clinical data. With genomic data, the main focus is detection of differentially expressed genes as the most common task in transcriptome profiling projects. In addition to reviewing available differential expression tools, a data-adaptive statistical method called Reproducibility Optimized Test Statistic (ROTS) is proposed for detecting differential expression in RNA-sequencing studies. In order to prove the efficacy of ROTS in real biomedical applications, the method is used to identify prognostic markers in clear cell renal cell carcinoma (ccRCC). In addition to previously known markers, novel genes with potential prognostic and therapeutic role in ccRCC are detected. For conventional clinical data, ensemble based predictive models are developed to provide clinical decision support in treatment of patients with metastatic castration resistant prostate cancer (mCRPC). The proposed predictive models cover treatment and survival stratification tasks for both trial-based and realworld patient cohorts. Finally, genomic and conventional clinical data are integrated to demonstrate the importance of inclusion of genomic data in predictive ability of clinical models. Again, utilizing ensemble-based learners, a novel model is proposed to predict adulthood obesity using both genetic and social-environmental factors. Overall, the ultimate objective of this work is to demonstrate the importance of clinical bioinformatics and machine learning for bio-clinical marker discovery in complex disease with high heterogeneity. In case of cancer, the interpretability of clinical models strongly depends on predictive markers with high reproducibility supported by validation data. The discovery of these markers would increase chance of early detection and improve prognosis assessment and treatment choice

En-PaFlower: An Ensemble Approach using PSO and Flower Pollination Algorithm for Cancer Diagnosis

Machine learning now is used across many sectors and provides consistently precise predictions. The machine learning system is able to learn effectively because the training dataset contains examples of previously completed tasks. After learning how to process the necessary data, researchers have proven that machine learning algorithms can carry out the whole work autonomously. In recent years, cancer has become a major cause of the worldwide increase in mortality. Therefore, early detection of cancer improves the chance of a complete recovery, and Machine Learning (ML) plays a significant role in this perspective. Cancer diagnostic and prognosis microarray dataset is available with the biopsy dataset. Because of its importance in making diagnoses and classifying cancer diseases, the microarray data represents a massive amount. It may be challenging to do an analysis on a large number of datasets, though. As a result, feature selection is crucial, and machine learning provides classification techniques. These algorithms choose the relevant features that help build a more precise categorization model. Accurately classifying diseases is facilitated as a result, which aids in disease prevention. This work aims to synthesize existing knowledge on cancer diagnosis using machine learning techniques into a compact report.  Current research work aims to propose an ensemble-based machine learning model En-PaFlower using Particle Swarm Optimization (PSO) as the feature selection algorithm, Flower Pollination algorithm (FPA) as the optimization algorithm with the majority voting algorithm. Finally, the performance of the proposed algorithm is evaluated over three different types of cancer disease datasets with accuracy, precision, recall, specificity, and F-1 Score etc as the evaluation parameters. The empirical analysis shows that the proposed methodology shows highest accuracy as 95.65%

A Multivariate Framework for Variable Selection and Identification of Biomarkers in High-Dimensional Omics Data

In this thesis, we address the identification of biomarkers in high-dimensional omics data. The identification of valid biomarkers is especially relevant for personalized medicine that depends on accurate prediction rules. Moreover, biomarkers elucidate the provenance of disease, or molecular changes related to disease. From a statistical point of view the identification of biomarkers is best cast as variable selection. In particular, we refer to variables as the molecular attributes under investigation, e.g. genes, genetic variation, or metabolites; and we refer to observations as the specific samples whose attributes we investigate, e.g. patients and controls. Variable selection in high-dimensional omics data is a complicated challenge due to the characteristic structure of omics data. For one, omics data is high-dimensional, comprising cellular information in unprecedented details. Moreover, there is an intricate correlation structure among the variables due to e.g internal cellular regulation, or external, latent factors. Variable selection for uncorrelated data is well established. In contrast, there is no consensus on how to approach variable selection under correlation. Here, we introduce a multivariate framework for variable selection that explicitly accounts for the correlation among markers. In particular, we present two novel quantities for variable importance: the correlation-adjusted t (CAT) score for classification, and the correlation-adjusted (marginal) correlation (CAR) score for regression. The CAT score is defined as the Mahalanobis-decorrelated t-score vector, and the CAR score as the Mahalanobis-decorrelated correlation between the predictor variables and the outcome. We derive the CAT and CAR score from a predictive point of view in linear discriminant analysis and regression; both quantities assess the weight of a decorrelated and standardized variable on the prediction rule. Furthermore, we discuss properties of both scores and relations to established quantities. Above all, the CAT score decomposes Hotelling’s T 2 and the CAR score the proportion of variance explained. Notably, the decomposition of total variance into explained and unexplained variance in the linear model can be rewritten in terms of CAR scores. To render our approach applicable on high-dimensional omics data we devise an efficient algorithm for shrinkage estimates of the CAT and CAR score. Subsequently, we conduct extensive simulation studies to investigate the performance of our novel approaches in ranking and prediction under correlation. Here, CAT and CAR scores consistently improve over marginal approaches in terms of more true positives selected and a lower model error. Finally, we illustrate the application of CAT and CAR score on real omics data. In particular, we analyze genomics, transcriptomics, and metabolomics data. We ascertain that CAT and CAR score are competitive or outperform state of the art techniques in terms of true positives detected and prediction error

Statistical Modeling for Cellular Heterogeneity Problems in Cancer Research: Deconvolution, Gaussian Graphical Models and Logistic Regression

Tumor tissue samples comprise a mixture of cancerous and surrounding normal cells. Investigating cellular heterogeneity in tumors is crucial to genomic analyses associated with cancer prognosis and treatment decisions, where the contamination of non-cancerous cells may substantially affect gene expression profiling in clinically derived malignant tumor samples. For this purpose, we first computationally purify tumor profiles, and then develop new statistical modeling techniques to incorporate tumor purity estimates for genetic correlation and prediction of clinical outcome in cancer research. In this thesis, we propose novel approaches to analyzing and modeling cellular heterogeneity problems using genomic data from three perspectives. First, we develop a computation tool, DeMixT, which applies a deconvolution algorithm to explicitly account for at most three cellular components associated with cancer. Compared with the experimental approach to isolate single cells, in silico dissection of tumor samples is faster and cheaper, but computational tools previously developed have limited ability to estimate cellular proportions and tumor-specific expression profiles, when neither is given with prior information. Our model al- lows inclusion of the infiltrating immune cells as a component as well as the tumor cells and stromal cells. We assume a linear mixture of gene expression profiles for each component satisfying a log2-normal distribution and propose an iterated conditional modes algorithm to estimate parameters. We also involve a novel two-stage estimation procedure for the three-component deconvolution. Our method is computationally feasible and yields accurate estimates through simulations and real data analyses. The estimated cellular proportions and purified expression profiles can pro- vide deeper insight for cancer biomarker studies. Second, we propose a novel edge regression model for undirected graphs, which incorporates subject-level covariates to estimate the conditional dependencies. Current work for constructing graphical models for multivariate data does not take into account the subject specific information, which can bias the conditional independence structure in heterogeneous data. Especially for tumor samples with inherent contamination from normal cells, ignoring the cellular heterogeneity and modeling the population-level genomic graphs may inhibit the discovery of the true tumor graph, which would be attenuated towards the normal graph. Our model allows undirected networks to vary with the exogenous covariates and is able to borrow strength from different related graphs for estimating more robust covariate-specific graphs. Bayesian shrinkage algorithms are presented to efficiently estimate and induce sparsity for generating subject-level graphs. We demonstrate the good performance of our method through simulation studies and apply our method to cytokine measurements from blood plasma samples from hepatocellular carcinoma (HCC) patients and normal controls. Third, we build a model with respect to logistic regression that includes tumor purity as a scaling factor to improve model robustness for the purpose of both estimation and prediction. Penalized logistic regression is used to identify variables (genes) and predict clinical status with binary outcomes that are associated with cancers in high-dimensional genomic data. We aim to reduce the uncertainty introduced by cellular heterogeneity through incorporating the measure of tumor purity to quantify the power of data for each sample. We provide strategies of choosing scaling parameters. Our model is finally shown to work well through a set of simulation studies. We believe that the statistical modeling, technical pipelines and computational results included in our work will serve as a first guide for the development of statistical methods accounting for cellular heterogeneity in cancer research

2022 SDSU Data Science Symposium Presentation Abstracts

This document contains abstracts for presentations and posters 2022 SDSU Data Science Symposium

Gene Expression based Survival Prediction for Cancer Patients: A Topic Modeling Approach

Cancer is one of the leading cause of death, worldwide. Many believe that genomic data will enable us to better predict the survival time of these patients, which will lead to better, more personalized treatment options and patient care. As standard survival prediction models have a hard time coping with the high-dimensionality of such gene expression (GE) data, many projects use some dimensionality reduction techniques to overcome this hurdle. We introduce a novel methodology, inspired by topic modeling from the natural language domain, to derive expressive features from the high-dimensional GE data. There, a document is represented as a mixture over a relatively small number of topics, where each topic corresponds to a distribution over the words; here, to accommodate the heterogeneity of a patient's cancer, we represent each patient (~document) as a mixture over cancer-topics, where each cancer-topic is a mixture over GE values (~words). This required some extensions to the standard LDA model eg: to accommodate the "real-valued" expression values - leading to our novel "discretized" Latent Dirichlet Allocation (dLDA) procedure. We initially focus on the METABRIC dataset, which describes breast cancer patients using the r=49,576 GE values, from microarrays. Our results show that our approach provides survival estimates that are more accurate than standard models, in terms of the standard Concordance measure. We then validate this approach by running it on the Pan-kidney (KIPAN) dataset, over r=15,529 GE values - here using the mRNAseq modality - and find that it again achieves excellent results. In both cases, we also show that the resulting model is calibrated, using the recent "D-calibrated" measure. These successes, in two different cancer types and expression modalities, demonstrates the generality, and the effectiveness, of this approach

2022 SDSU Data Science Symposium Presentation Abstracts

This document contains abstracts for presentations and posters 2022 SDSU Data Science Symposium