Statistical Models Commons^™

Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, Lauren Spirko-Burns, Karthik Devarajan

COBRA Preprint Series

One of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease's process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous data sets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional hazards …

Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang

COBRA Preprint Series

Non-negative matrix factorization (NMF) is a widely used machine learning algorithm for dimension reduction of large-scale data. It has found successful applications in a variety of fields such as computational biology, neuroscience, natural language processing, information retrieval, image processing and speech recognition. In bioinformatics, for example, it has been used to extract patterns and profiles from genomic and text-mining data as well as in protein sequence and structure analysis. While the scientific performance of NMF is very promising in dealing with high dimensional data sets and complex data structures, its computational cost is high and sometimes could be critical for …

A Unified Approach To Non-Negative Matrix Factorization And Probabilistic Latent Semantic Indexing, Karthik Devarajan, Guoli Wang, Nader Ebrahimi

COBRA Preprint Series

Non-negative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two matrices, W and H, each with nonnegative entries, V ~ WH. NMF has been shown to have a unique parts-based, sparse representation of the data. The nonnegativity constraints in NMF allow only additive combinations of the data which enables it to learn parts that have distinct physical representations in reality. In the last few years, NMF has been successfully applied in a variety of areas such as natural language processing, information retrieval, image processing, speech recognition …

A Bayesian Shared Component Model For Genetic Association Studies, Juan J. Abellan, Carlos Abellan, Juan R. Gonzalez

COBRA Preprint Series

We present a novel approach to address genome association studies between single nucleotide polymorphisms (SNPs) and disease. We propose a Bayesian shared component model to tease out the genotype information that is common to cases and controls from the one that is specific to cases only. This allows to detect the SNPs that show the strongest association with the disease. The model can be applied to case-control studies with more than one disease. In fact, we illustrate the use of this model with a dataset of 23,418 SNPs from a case-control study by The Welcome Trust Case Control Consortium (2007) …

Minimum Description Length And Empirical Bayes Methods Of Identifying Snps Associated With Disease, Ye Yang, David R. Bickel

COBRA Preprint Series

The goal of determining which of hundreds of thousands of SNPs are associated with disease poses one of the most challenging multiple testing problems. Using the empirical Bayes approach, the local false discovery rate (LFDR) estimated using popular semiparametric models has enjoyed success in simultaneous inference. However, the estimated LFDR can be biased because the semiparametric approach tends to overestimate the proportion of the non-associated single nucleotide polymorphisms (SNPs). One of the negative consequences is that, like conventional p-values, such LFDR estimates cannot quantify the amount of information in the data that favors the null hypothesis of no disease-association.

We …

The Strength Of Statistical Evidence For Composite Hypotheses With An Application To Multiple Comparisons, David R. Bickel

COBRA Preprint Series

The strength of the statistical evidence in a sample of data that favors one composite hypothesis over another may be quantified by the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function. Unlike the p-value and the Bayes factor, this measure of evidence is coherent in the sense that it cannot support a hypothesis over any hypothesis that it entails. Further, when comparing the hypothesis that the parameter lies outside a non-trivial interval to the hypotheses that it lies within the interval, the proposed measure of evidence almost always asymptotically favors the correct hypothesis …

New Statistical Paradigms Leading To Web-Based Tools For Clinical/Translational Science, Knut M. Wittkowski

COBRA Preprint Series

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics.

Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal …