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- Harvard University Biostatistics Working Paper Series (9)
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Articles 1 - 30 of 58
Full-Text Articles in Microarrays
Gene Set Testing By Distance Correlation, Sho-Hsien Su
Gene Set Testing By Distance Correlation, Sho-Hsien Su
Graduate Theses and Dissertations
Pathways are the functional building blocks of complex diseases such as cancers. Pathway-level studies may provide insights on some important biological processes. Gene set test is an important tool to study the differential expression of a gene set between two groups, e.g., cancer vs normal. The differential expression of a gene set could be due to the difference in mean, variability, or both. However, most existing gene set tests only target the mean difference but overlook other types of differential expression. In this thesis, we propose to use the recently developed distance correlation for gene set testing. To assess the …
Statistical Approaches Of Gene Set Analysis With Quantitative Trait Loci For High-Throughput Genomic Studies., Samarendra Das
Statistical Approaches Of Gene Set Analysis With Quantitative Trait Loci For High-Throughput Genomic Studies., Samarendra Das
Electronic Theses and Dissertations
Recently, gene set analysis has become the first choice for gaining insights into the underlying complex biology of diseases through high-throughput genomic studies, such as Microarrays, bulk RNA-Sequencing, single cell RNA-Sequencing, etc. It also reduces the complexity of statistical analysis and enhances the explanatory power of the obtained results. Further, the statistical structure and steps common to these approaches have not yet been comprehensively discussed, which limits their utility. Hence, a comprehensive overview of the available gene set analysis approaches used for different high-throughput genomic studies is provided. The analysis of gene sets is usually carried out based on …
Gene Expression Profiling In Salmonella Choleraesuis-Infected Porcine Lung Using A Long Oligonucleotide Microarray, Shu-Hong Zhao, Daniel Kuhar, Joan K. Lunney, Harry Dawson, Catherine Guidry, Jolita J. Uthe, Shawn M. D. Bearson, Justin Recknor, Dan Nettleton, Christopher K. Tuggle
Gene Expression Profiling In Salmonella Choleraesuis-Infected Porcine Lung Using A Long Oligonucleotide Microarray, Shu-Hong Zhao, Daniel Kuhar, Joan K. Lunney, Harry Dawson, Catherine Guidry, Jolita J. Uthe, Shawn M. D. Bearson, Justin Recknor, Dan Nettleton, Christopher K. Tuggle
Dan Nettleton
Understanding the transcriptional response to pathogenic bacterial infection within food animals is of fundamental and applied interest. To determine the transcriptional response to Salmonella enterica serovar Choleraesuis (SC) infection, a 13,297-oligonucleotide swine array was used to analyze RNA from control, 24-h postinoculation (hpi), and 48-hpi porcine lung tissue from pigs infected with SC. In total, 57 genes showed differential expression (p < 0.001; false discovery rate = 12%). Quantitative real-time PCR (qRT-PCR) of 61 genes was used to confirm the microarray results and to identify pathways responding to infection. Of the 33 genes identified by microarray analysis as differentially expressed, 23 were confirmed by qRT-PCR results. A novel finding was that two transglutaminase family genes (TGM1 and TGM3) showed dramatic increases in expression postinoculation; combined with several other apoptotic genes, they indicated the induction of apoptotic pathways during SC infection. A predominant T helper 1-type immune response occurred during infection, with interferon …
Scanning Microarrays At Multiple Intensities Enhances Discovery Of Differentially Expressed Genes, David S. Skibbe, Xiujuan Wang, Xuefeng Zhao, Lisa A. Borsuk, Dan Nettleton, Patrick S. Schnable
Scanning Microarrays At Multiple Intensities Enhances Discovery Of Differentially Expressed Genes, David S. Skibbe, Xiujuan Wang, Xuefeng Zhao, Lisa A. Borsuk, Dan Nettleton, Patrick S. Schnable
Dan Nettleton
Motivation: Scanning parameters are often overlooked when optimizing microarray experiments. A scanning approach that extends the dynamic data range by acquiring multiple scans of different intensities has been developed.
Results: Data from each of three scan intensities (low, medium, high) were analyzed separately using multiple scan and linear regression approaches to identify and compare the sets of genes that exhibit statistically significant differential expression. In the multiple scan approach only one-third of the differentially expressed genes were shared among the three intensities, and each scan intensity identified unique sets of differentially expressed genes. The set of differentially expressed genes from …
Unified Methods For Feature Selection In Large-Scale Genomic Studies With Censored Survival Outcomes, Lauren Spirko-Burns, Karthik Devarajan
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 …
A Novel Pathway-Based Distance Score Enhances Assessment Of Disease Heterogeneity In Gene Expression, Yunqing Liu, Xiting Yan
A Novel Pathway-Based Distance Score Enhances Assessment Of Disease Heterogeneity In Gene Expression, Yunqing Liu, Xiting Yan
Yale Day of Data
Distance-based unsupervised clustering of gene expression data is commonly used to identify heterogeneity in biologic samples. However, high noise levels in gene expression data and the relatively high correlation between genes are often encountered, so traditional distances such as Euclidean distance may not be effective at discriminating the biological differences between samples. In this study, we developed a novel computational method to assess the biological differences based on pathways by assuming that ontologically defined biological pathways in biologically similar samples have similar behavior. Application of this distance score results in more accurate, robust, and biologically meaningful clustering results in both …
Computational Modelling Of Human Transcriptional Regulation By An Information Theory-Based Approach, Ruipeng Lu
Computational Modelling Of Human Transcriptional Regulation By An Information Theory-Based Approach, Ruipeng Lu
Electronic Thesis and Dissertation Repository
ChIP-seq experiments can identify the genome-wide binding site motifs of a transcription factor (TF) and determine its sequence specificity. Multiple algorithms were developed to derive TF binding site (TFBS) motifs from ChIP-seq data, including the entropy minimization-based Bipad that can derive both contiguous and bipartite motifs. Prior studies applying these algorithms to ChIP-seq data only analyzed a small number of top peaks with the highest signal strengths, biasing their resultant position weight matrices (PWMs) towards consensus-like, strong binding sites; nor did they derive bipartite motifs, disabling the accurate modelling of binding behavior of dimeric TFs.
This thesis presents a novel …
Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang
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 …
Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, Amalia Magaret
Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, Amalia Magaret
UW Biostatistics Working Paper Series
We have frequently implemented crossover studies to evaluate new therapeutic interventions for genital herpes simplex virus infection. The outcome measured to assess the efficacy of interventions on herpes disease severity is the viral shedding rate, defined as the frequency of detection of HSV on the genital skin and mucosa. We performed a simulation study to ascertain whether our standard model, which we have used previously, was appropriately considering all the necessary features of the shedding data to provide correct inference. We simulated shedding data under our standard, validated assumptions and assessed the ability of 5 different models to reproduce the …
Graph-Based Regularization In Machine Learning: Discovering Driver Modules In Biological Networks, Xi Gao
Graph-Based Regularization In Machine Learning: Discovering Driver Modules In Biological Networks, Xi Gao
Theses and Dissertations
Curiosity of human nature drives us to explore the origins of what makes each of us different. From ancient legends and mythology, Mendel's law, Punnett square to modern genetic research, we carry on this old but eternal question. Thanks to technological revolution, today's scientists try to answer this question using easily measurable gene expression and other profiling data. However, the exploration can easily get lost in the data of growing volume, dimension, noise and complexity. This dissertation is aimed at developing new machine learning methods that take data from different classes as input, augment them with knowledge of feature relationships, …
Methods For Integrative Analysis Of Genomic Data, Paul Manser
Methods For Integrative Analysis Of Genomic Data, Paul Manser
Theses and Dissertations
In recent years, the development of new genomic technologies has allowed for the investigation of many regulatory epigenetic marks besides expression levels, on a genome-wide scale. As the price for these technologies continues to decrease, study sizes will not only increase, but several different assays are beginning to be used for the same samples. It is therefore desirable to develop statistical methods to integrate multiple data types that can handle the increased computational burden of incorporating large data sets. Furthermore, it is important to develop sound quality control and normalization methods as technical errors can compound when integrating multiple genomic …
Global Quantitative Assessment Of The Colorectal Polyp Burden In Familial Adenomatous Polyposis Using A Web-Based Tool, Patrick M. Lynch, Jeffrey S. Morris, William A. Ross, Miguel A. Rodriguez-Bigas, Juan Posadas, Rossa Khalaf, Diane M. Weber, Valerie O. Sepeda, Bernard Levin, Imad Shureiqi
Global Quantitative Assessment Of The Colorectal Polyp Burden In Familial Adenomatous Polyposis Using A Web-Based Tool, Patrick M. Lynch, Jeffrey S. Morris, William A. Ross, Miguel A. Rodriguez-Bigas, Juan Posadas, Rossa Khalaf, Diane M. Weber, Valerie O. Sepeda, Bernard Levin, Imad Shureiqi
Jeffrey S. Morris
Background: Accurate measures of the total polyp burden in familial adenomatous polyposis (FAP) are lacking. Current assessment tools include polyp quantitation in limited-field photographs and qualitative total colorectal polyp burden by video.
Objective: To develop global quantitative tools of the FAP colorectal adenoma burden.
Design: A single-arm, phase II trial.
Patients: Twenty-seven patients with FAP.
Intervention: Treatment with celecoxib for 6 months, with before-treatment and after-treatment videos posted to an intranet with an interactive site for scoring.
Main Outcome Measurements: Global adenoma counts and sizes (grouped into categories: less than 2 mm, 2-4 mm, and greater than 4 mm) were …
Bayesian Methods For Expression-Based Integration, Elizabeth M. Jennings, Jeffrey S. Morris, Raymond J. Carroll, Ganiraju C. Manyam, Veera Baladandayuthapani
Bayesian Methods For Expression-Based Integration, Elizabeth M. Jennings, Jeffrey S. Morris, Raymond J. Carroll, Ganiraju C. Manyam, Veera Baladandayuthapani
Jeffrey S. Morris
We propose methods to integrate data across several genomic platforms using a hierarchical Bayesian analysis framework that incorporates the biological relationships among the platforms to identify genes whose expression is related to clinical outcomes in cancer. This integrated approach combines information across all platforms, leading to increased statistical power in finding these predictive genes, and further provides mechanistic information about the manner in which the gene affects the outcome. We demonstrate the advantages of the shrinkage estimation used by this approach through a simulation, and finally, we apply our method to a Glioblastoma Multiforme dataset and identify several genes potentially …
Statistical Methods For Proteomic Biomarker Discovery Based On Feature Extraction Or Functional Modeling Approaches, Jeffrey S. Morris
Statistical Methods For Proteomic Biomarker Discovery Based On Feature Extraction Or Functional Modeling Approaches, Jeffrey S. Morris
Jeffrey S. Morris
In recent years, developments in molecular biotechnology have led to the increased promise of detecting and validating biomarkers, or molecular markers that relate to various biological or medical outcomes. Proteomics, the direct study of proteins in biological samples, plays an important role in the biomarker discovery process. These technologies produce complex, high dimensional functional and image data that present many analytical challenges that must be addressed properly for effective comparative proteomics studies that can yield potential biomarkers. Specific challenges include experimental design, preprocessing, feature extraction, and statistical analysis accounting for the inherent multiple testing issues. This paper reviews various computational …
Integrative Bayesian Analysis Of High-Dimensional Multi-Platform Genomics Data, Wenting Wang, Veerabhadran Baladandayuthapani, Jeffrey S. Morris, Bradley M. Broom, Ganiraju C. Manyam, Kim-Anh Do
Integrative Bayesian Analysis Of High-Dimensional Multi-Platform Genomics Data, Wenting Wang, Veerabhadran Baladandayuthapani, Jeffrey S. Morris, Bradley M. Broom, Ganiraju C. Manyam, Kim-Anh Do
Jeffrey S. Morris
Motivation: Analyzing data from multi-platform genomics experiments combined with patients’ clinical outcomes helps us understand the complex biological processes that characterize a disease, as well as how these processes relate to the development of the disease. Current integration approaches that treat the data are limited in that they do not consider the fundamental biological relationships that exist among the data from platforms.
Statistical Model: We propose an integrative Bayesian analysis of genomics data (iBAG) framework for identifying important genes/biomarkers that are associated with clinical outcome. This framework uses a hierarchical modeling technique to combine the data obtained from multiple platforms …
A Bayesian Model Averaging Approach For Observational Gene Expression Studies, Xi Kathy Zhou, Fei Liu, Andrew J. Dannenberg
A Bayesian Model Averaging Approach For Observational Gene Expression Studies, Xi Kathy Zhou, Fei Liu, Andrew J. Dannenberg
COBRA Preprint Series
Identifying differentially expressed (DE) genes associated with a sample characteristic is the primary objective of many microarray studies. As more and more studies are carried out with observational rather than well controlled experimental samples, it becomes important to evaluate and properly control the impact of sample heterogeneity on DE gene finding. Typical methods for identifying DE genes require ranking all the genes according to a pre-selected statistic based on a single model for two or more group comparisons, with or without adjustment for other covariates. Such single model approaches unavoidably result in model misspecification, which can lead to increased error …
Clustering With Exclusion Zones: Genomic Applications, Mark Segal, Yuanyuan Xiao, Fred Huffer
Clustering With Exclusion Zones: Genomic Applications, Mark Segal, Yuanyuan Xiao, Fred Huffer
Mark R Segal
Methods for formally evaluating the clustering of events in space or time, notably the scan statistic, have been richly developed and widely applied. In order to utilize the scan statistic and related approaches, it is necessary to know the extent of the spatial or temporal domains wherein the events arise. Implicit in their usage is that these domains have no “holes”—hereafter “exclusion zones”—regions in which events a priori cannot occur. However, in many contexts, this requirement is not met. When the exclusion zones are known, it is straightforward to correct the scan statistic for their occurrence by simply adjusting the …
Minimum Description Length Measures Of Evidence For Enrichment, Zhenyu Yang, David R. Bickel
Minimum Description Length Measures Of Evidence For Enrichment, Zhenyu Yang, David R. Bickel
COBRA Preprint Series
In order to functionally interpret differentially expressed genes or other discovered features, researchers seek to detect enrichment in the form of overrepresentation of discovered features associated with a biological process. Most enrichment methods treat the p-value as the measure of evidence using a statistical test such as the binomial test, Fisher's exact test or the hypergeometric test. However, the p-value is not interpretable as a measure of evidence apart from adjustments in light of the sample size. As a measure of evidence supporting one hypothesis over the other, the Bayes factor (BF) overcomes this drawback of the p-value but lacks …
The Strength Of Statistical Evidence For Composite Hypotheses: Inference To The Best Explanation, David R. Bickel
The Strength Of Statistical Evidence For Composite Hypotheses: Inference To The Best Explanation, David R. Bickel
COBRA Preprint Series
A general function to quantify the weight of evidence in a sample of data for one hypothesis over another is derived from the law of likelihood and from a statistical formalization of inference to the best explanation. For a fixed parameter of interest, the resulting weight of evidence that favors one composite hypothesis over another is the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function over the parameter of interest. Since the weight of evidence is generally only known up to a nuisance parameter, it is approximated by replacing the likelihood function with …
Survival Prediction For Brain Tumor Patients Using Gene Expression Data, Vinicius Bonato
Survival Prediction For Brain Tumor Patients Using Gene Expression Data, Vinicius Bonato
Dissertations & Theses (Open Access)
Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. …
Wavelet-Based Functional Linear Mixed Models: An Application To Measurement Error–Corrected Distributed Lag Models, Elizabeth J. Malloy, Jeffrey S. Morris, Sara D. Adar, Helen Suh, Diane R. Gold, Brent A. Coull
Wavelet-Based Functional Linear Mixed Models: An Application To Measurement Error–Corrected Distributed Lag Models, Elizabeth J. Malloy, Jeffrey S. Morris, Sara D. Adar, Helen Suh, Diane R. Gold, Brent A. Coull
Jeffrey S. Morris
Frequently, exposure data are measured over time on a grid of discrete values that collectively define a functional observation. In many applications, researchers are interested in using these measurements as covariates to predict a scalar response in a regression setting, with interest focusing on the most biologically relevant time window of exposure. One example is in panel studies of the health effects of particulate matter (PM), where particle levels are measured over time. In such studies, there are many more values of the functional data than observations in the data set so that regularization of the corresponding functional regression coefficient …
Members’ Discoveries: Fatal Flaws In Cancer Research, Jeffrey S. Morris
Members’ Discoveries: Fatal Flaws In Cancer Research, Jeffrey S. Morris
Jeffrey S. Morris
A recent article published in The Annals of Applied Statistics (AOAS) by two MD Anderson researchers—Keith Baggerly and Kevin Coombes—dissects results from a highly-influential series of medical papers involving genomics-driven personalized cancer therapy, and outlines a series of simple yet fatal flaws that raises serious questions about the veracity of the original results. Having immediate and strong impact, this paper, along with related work, is providing the impetus for new standards of reproducibility in scientific research.
Statistical Contributions To Proteomic Research, Jeffrey S. Morris, Keith A. Baggerly, Howard B. Gutstein, Kevin R. Coombes
Statistical Contributions To Proteomic Research, Jeffrey S. Morris, Keith A. Baggerly, Howard B. Gutstein, Kevin R. Coombes
Jeffrey S. Morris
Proteomic profiling has the potential to impact the diagnosis, prognosis, and treatment of various diseases. A number of different proteomic technologies are available that allow us to look at many proteins at once, and all of them yield complex data that raise significant quantitative challenges. Inadequate attention to these quantitative issues can prevent these studies from achieving their desired goals, and can even lead to invalid results. In this chapter, we describe various ways the involvement of statisticians or other quantitative scientists in the study team can contribute to the success of proteomic research, and we outline some of the …
Informatics And Statistics For Analyzing 2-D Gel Electrophoresis Images, Andrew W. Dowsey, Jeffrey S. Morris, Howard G. Gutstein, Guang Z. Yang
Informatics And Statistics For Analyzing 2-D Gel Electrophoresis Images, Andrew W. Dowsey, Jeffrey S. Morris, Howard G. Gutstein, Guang Z. Yang
Jeffrey S. Morris
Whilst recent progress in ‘shotgun’ peptide separation by integrated liquid chromatography and mass spectrometry (LC/MS) has enabled its use as a sensitive analytical technique, proteome coverage and reproducibility is still limited and obtaining enough replicate runs for biomarker discovery is a challenge. For these reasons, recent research demonstrates the continuing need for protein separation by two-dimensional gel electrophoresis (2-DE). However, with traditional 2-DE informatics, the digitized images are reduced to symbolic data though spot detection and quantification before proteins are compared for differential expression by spot matching. Recently, a more robust and automated paradigm has emerged where gels are directly …
Bayesian Random Segmentationmodels To Identify Shared Copy Number Aberrations For Array Cgh Data, Veerabhadran Baladandayuthapani, Yuan Ji, Rajesh Talluri, Luis E. Nieto-Barajas, Jeffrey S. Morris
Bayesian Random Segmentationmodels To Identify Shared Copy Number Aberrations For Array Cgh Data, Veerabhadran Baladandayuthapani, Yuan Ji, Rajesh Talluri, Luis E. Nieto-Barajas, Jeffrey S. Morris
Jeffrey S. Morris
Array-based comparative genomic hybridization (aCGH) is a high-resolution high-throughput technique for studying the genetic basis of cancer. The resulting data consists of log fluorescence ratios as a function of the genomic DNA location and provides a cytogenetic representation of the relative DNA copy number variation. Analysis of such data typically involves estimation of the underlying copy number state at each location and segmenting regions of DNA with similar copy number states. Most current methods proceed by modeling a single sample/array at a time, and thus fail to borrow strength across multiple samples to infer shared regions of copy number aberrations. …
Resampling-Based Multiple Hypothesis Testing With Applications To Genomics: New Developments In The R/Bioconductor Package Multtest, Houston N. Gilbert, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit
Resampling-Based Multiple Hypothesis Testing With Applications To Genomics: New Developments In The R/Bioconductor Package Multtest, Houston N. Gilbert, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
The multtest package is a standard Bioconductor package containing a suite of functions useful for executing, summarizing, and displaying the results from a wide variety of multiple testing procedures (MTPs). In addition to many popular MTPs, the central methodological focus of the multtest package is the implementation of powerful joint multiple testing procedures. Joint MTPs are able to account for the dependencies between test statistics by effectively making use of (estimates of) the test statistics joint null distribution. To this end, two additional bootstrap-based estimates of the test statistics joint null distribution have been developed for use in the …
Sparse Linear Discriminant Analysis For Simultaneous Testing For The Significance Of A Gene Set/Pathway And Gene Selection, Michael C. Wu, Lingson Zhang, Zhaoxi Wang, David C. Christiani, Xihong Lin
Sparse Linear Discriminant Analysis For Simultaneous Testing For The Significance Of A Gene Set/Pathway And Gene Selection, Michael C. Wu, Lingson Zhang, Zhaoxi Wang, David C. Christiani, Xihong Lin
Harvard University Biostatistics Working Paper Series
No abstract provided.
Identification Of Yeast Transcriptional Regulation Networks Using Multivariate Random Forests, Yuanyuan Xiao, Mark Segal
Identification Of Yeast Transcriptional Regulation Networks Using Multivariate Random Forests, Yuanyuan Xiao, Mark Segal
Mark R Segal
The recent availability of whole-genome scale data sets that investigate complementary and diverse aspects of transcriptional regulation has spawned an increased need for new and effective computational approaches to analyze and integrate these large scale assays. Here, we propose a novel algorithm, based on random forest methodology, to relate gene expression (as derived from expression microarrays) to sequence features residing in gene promoters (as derived from DNA motif data) and transcription factor binding to gene promoters (as derived from tiling microarrays). We extend the random forest approach to model a multivariate response as represented, for example, by time-course gene expression …
The Strength Of Statistical Evidence For Composite Hypotheses With An Application To Multiple Comparisons, David R. Bickel
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 …
Estimation And Testing For The Effect Of A Genetic Pathway On A Disease Outcome Using Logistic Kernel Machine Regression Via Logistic Mixed Models, Dawei Liu, Debashis Ghosh, Xihong Lin
Estimation And Testing For The Effect Of A Genetic Pathway On A Disease Outcome Using Logistic Kernel Machine Regression Via Logistic Mixed Models, Dawei Liu, Debashis Ghosh, Xihong Lin
Harvard University Biostatistics Working Paper Series
No abstract provided.