title: Nonparametric Bayes modeling for case control studies with many predictors.
abstract: It is common in biomedical research to run case-control studies involving high-dimensional predictors, with the main goal being detection of the sparse subset of predictors having a significant association with disease. Usual analyses rely on independent screening, considering each predictor one at a time, or in some cases on logistic regression assuming no interactions. We propose a fundamentally different approach based on a nonparametric Bayesian low rank tensor factorization model for the retrospective likelihood. Our model allows a very flexible structure in characterizing the distribution of multivariate variables as unknown and without any linear assumptions as in logistic regression. Predictors are excluded only if they have no impact on disease risk, either directly or through interactions with other predictors. Hence, we obtain an omnibus approach for screening for important predictors. Computation relies on an efficient Gibbs sampler. The methods are shown to have high power and low false discovery rates in simulation studies, and we consider an application to an epidemiology study of birth defects.
authors.affiliation: Department of Biostatistics, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A.
authors.forename: Jing
authors.initials: J
authors.lastname: Zhou
authors.affiliation: Department of Biostatistics, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A.|Carolina Population Center, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A.
authors.forename: Amy H
authors.initials: AH
authors.lastname: Herring
authors.affiliation: Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A.
authors.forename: Anirban
authors.initials: A
authors.lastname: Bhattacharya
authors.affiliation: Carolina Population Center, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A.|Department of Epidemiology, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A.
authors.forename: Andrew F
authors.initials: AF
authors.lastname: Olshan
authors.affiliation: Departments of Statistical Science, Electrical and Computer Engineering, and Mathematics, Duke University, Durham, North Carolina 27708, U.S.A.
authors.forename: David B
authors.initials: DB
authors.lastname: Dunson
mesh_terms: D001499:Bayes Theorem; D016022:Case-Control Studies; D003198:Computer Simulation; D000013:Congenital Abnormalities / Q000453:epidemiology*; D003627:Data Interpretation, Statistical; D006801:Humans; D015994:Incidence; D007231:Infant, Newborn; D015233:Models, Statistical; D015203:Reproducibility of Results; D018570:Risk Assessment / Q000379:methods; D018401:Sample Size; D012680:Sensitivity and Specificity; D018709:Statistics, Nonparametric
keywords: Bayesian nonparametrics; Big data; Epidemiology; Retrospective likelihood; Sparse parallel factor analysis model; Tensor factorization