Skip to main content

COVID-19 Resources

What people with cancer should know:

Guidance for cancer researchers:

Get the latest public health information from CDC:

Get the latest research information from NIH:

Grant Details

Grant Number: 5R01CA157528-06 Interpret this number
Primary Investigator: Schwartzman, Armin
Organization: University Of California, San Diego
Project Title: Multiple Testing Methods for Random Fields and High-Dimensional Dependent Data
Fiscal Year: 2017


DESCRIPTION (provided by applicant): Large-scale multiple testing has become ubiquitous in the search for disease and health risk markers using high-throughput technologies. While statistical methods for multiple testing often assume independence between the tests, many real situations exhibit dependence and an underlying structure. Examples of spatial structure are one-dimensional (1D) in the case of proteomic data; 2D in the case of environmental data; and 3D in the case of brain imaging data. Ignoring correlation in the analysis may lead to a different set and ordering of discovered features, resulting in increased error rates and potential missing of important features. There is a need to characterize the effect of correlation in multiple testing and incorporate it into the analysis. The goal of this proposal is to develop multiple testing methods that incorporate the correlation in the data in order to increase statistical power, control error rates and obtain appropriately interpretable results. This is done in two different ways. (1) In Aims 1 and 2, we assume a spatial structure and stationary ergodic correlation, where the signal of interest consists of a relatively small number of unimodal peaks. We use random field theory to compute p-values for testing the heights of local maxima of the observed data after smoothing. We develop these methods in complexity from 1D to 3D domains, and from peaks of equal width to peaks of unequal width. We then adapt and apply these methods to various types of data obtained from high-throughput technologies, specifically: mass- spectrometry data for identifying protein biomarkers of cancer; climate model output data for identification of geographical regions at risk for heat stress as a result of climate change; and brain imaging data for identification of anatomical regions involved in abnormal cognitive development. (2) In Aim 3, we assume a general correlation structure, not necessarily stationary or ergodic, and propose a conditional marginal analysis, where correlation is incorporated through conditioning on the observed marginal distribution of likely null cases. Although not exclusively, emphasis throughout is placed on false discovery rate inference. This proposal provides a unified view of signal detection for random fields that applies broadly to a large class of problems ranging from proteomics to medical imaging to environmental monitoring. From a statistical point of view, it provides a new answer to the problem of controlling FDR in random fields. By taking advantage of the dependence structure, the methods developed in this proposal offer higher statistical power in the search for markers, so that a smaller number of false markers will be tested in follow-up studies.


Spatial confidence sets for raw effect size images.
Authors: Bowring A. , Telschow F. , Schwartzman A. , Nichols T.E. .
Source: NeuroImage, 2019 12; 203, p. 116187.
EPub date: 2019-09-15.
PMID: 31533067
Related Citations

Peak p-values and false discovery rate inference in neuroimaging.
Authors: Schwartzman A. , Telschow F. .
Source: NeuroImage, 2019-08-15; 197, p. 402-413.
EPub date: 2019-04-24.
PMID: 31028923
Related Citations

Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields.
Authors: Cheng D. , Schwartzman A. .
Source: Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, 2018 Nov; 24(4B), p. 3422-3446.
EPub date: 2018-04-18.
PMID: 31511762
Related Citations

Confidence regions for spatial excursion sets from repeated random field observations, with an application to climate.
Authors: Sommerfeld M. , Sain S. , Schwartzman A. .
Source: Journal of the American Statistical Association, 2018; 113(523), p. 1327-1340.
EPub date: 2018-06-12.
PMID: 31452557
Related Citations

A Geospatial Epidemiologic Analysis of Nontuberculous Mycobacterial Infection: An Ecological Study in Colorado.
Authors: Lipner E.M. , Knox D. , French J. , Rudman J. , Strong M. , Crooks J.L. .
Source: Annals of the American Thoracic Society, 2017 Oct; 14(10), p. 1523-1532.
PMID: 28594574
Related Citations

Authors: Cheng D. , Schwartzman A. .
Source: Annals of statistics, 2017 Apr; 45(2), p. 529-556.
EPub date: 2019-05-16.
PMID: 31527989
Related Citations

autoimage: Multiple Heat Maps for Projected Coordinates.
Authors: French J.P. .
Source: The R journal, 2017; 9(1), p. 284-297.
EPub date: 2017-05-10.
PMID: 29147579
Related Citations

Assessing NARCCAP climate model effects using spatial confidence regions.
Authors: French J.P. , McGinnis S. , Schwartzman A. .
Source: Advances in statistical climatology, meteorology and oceanography, 2017; 3(2), p. 67-92.
EPub date: 2017-07-14.
PMID: 28936474
Related Citations

FDR control of detected regions by multiscale matched filtering.
Authors: Kachouie N.N. , Lin X. , Schwartzman A. .
Source: Communications in statistics: Simulation and computation, 2017; 46(1), p. 127-144.
EPub date: 2014-12-23.
PMID: 31501637
Related Citations

Nonparametric Bootstrap of Sample Means of Positive-Definite Matrices with an Application to Diffusion-Tensor-Imaging Data Analysis.
Authors: Ellingson L. , Groisser D. , Osborne D. , Patrangenaru V. , Schwartzman A. .
Source: Communications in statistics: Simulation and computation, 2017; 46(6), p. 4851-4879.
EPub date: 2017-02-03.
PMID: 31452576
Related Citations

The Empirical Distribution of a Large Number of Correlated Normal Variables.
Authors: Azriel D. , Schwartzman A. .
Source: Journal of the American Statistical Association, 2015-09-01; 110(511), p. 1217-1228.
EPub date: 2014-09-25.
PMID: 26858467
Related Citations

Distribution of the Height of Local Maxima of Gaussian Random Fields.
Authors: Cheng D. , Schwartzman A. .
Source: Extremes, 2015-06-01; 18(2), p. 213-240.
EPub date: 2014-12-11.
PMID: 26478714
Related Citations

False Discovery Control in Large-Scale Spatial Multiple Testing.
Authors: Sun W. , Reich B.J. , Cai T.T. , Guindani M. , Schwartzman A. .
Source: Journal of the Royal Statistical Society. Series B, Statistical methodology, 2015-01-01; 77(1), p. 59-83.
PMID: 25642138
Related Citations

Detection of Local DNA Copy Number Changes in Lung Cancer Population Analyses Using A Multi-Scale Approach.
Authors: Kachouie N.N. , Lin X. , Christiani D.C. , Schwartzman A. .
Source: Communications in statistics. Case studies, data analysis and applications, 2015; 1(4), p. 206-216.
EPub date: 2016-07-18.
PMID: 31489360
Related Citations

Voxelwise multivariate analysis of multimodality magnetic resonance imaging.
Authors: Naylor M.G. , Cardenas V.A. , Tosun D. , Schuff N. , Weiner M. , Schwartzman A. .
Source: Human brain mapping, 2014 Mar; 35(3), p. 831-46.
EPub date: 2013-02-13.
PMID: 23408378
Related Citations

Authors: Schwartzman A. , Jaffe A. , Gavrilov Y. , Meyer C.A. .
Source: The annals of applied statistics, 2013; 7(1), p. 471-494.
PMID: 25411587
Related Citations

Paradoxical results of adaptive false discovery rate procedures in neuroimaging studies.
Authors: Reiss P.T. , Schwartzman A. , Lu F. , Huang L. , Proal E. .
Source: NeuroImage, 2012 Dec; 63(4), p. 1833-40.
EPub date: 2012-07-27.
PMID: 22842214
Related Citations

Comment on "Estimating False Discovery Proportion Under Arbitrary Covariance Dependence" by Fan et al.
Authors: Schwartzman A. .
Source: Journal of the American Statistical Association, 2012; 107(499), p. 1039-1041.
PMID: 24976660
Related Citations

Authors: Schwartzman A. , Gavrilov Y. , Adler R.J. .
Source: Annals of statistics, 2011-12-01; 39(6), p. 3290-3319.
PMID: 23576826
Related Citations

Back to Top