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.
This proposal provides a unified view of feature detection in high-throughput data that applies to a large class of problems ranging from cancer proteomics to medical imaging to environmental monitoring. By taking advantage of the dependence structure, the methods developed in this proposal offer higher statistical power in the search for markers, facilitating the discovery of new true markers and reducing the number of false markers to be tested in follow-up studies.
|French, Joshua P (2017) autoimage: Multiple Heat Maps for Projected Coordinates. R J 9:284-297|
|French, Joshua P; McGinnis, Seth; Schwartzman, Armin (2017) Assessing NARCCAP climate model effects using spatial confidence regions. Adv Stat Climatol Meteorol Oceanogr 3:67-92|
|Lipner, Ettie M; Knox, David; French, Joshua et al. (2017) A Geospatial Epidemiologic Analysis of Nontuberculous Mycobacterial Infection: An Ecological Study in Colorado. Ann Am Thorac Soc 14:1523-1532|
|Cheng, Dan; Schwartzman, Armin (2015) Distribution of the Height of Local Maxima of Gaussian Random Fields. Extremes (Boston) 18:213-240|
|Azriel, David; Schwartzman, Armin (2015) The Empirical Distribution of a Large Number of Correlated Normal Variables. J Am Stat Assoc 110:1217-1228|
|Naylor, Melissa G; Cardenas, Valerie A; Tosun, Duygu et al. (2014) Voxelwise multivariate analysis of multimodality magnetic resonance imaging. Hum Brain Mapp 35:831-46|
|Schwartzman, Armin; Jaffe, Andrew; Gavrilov, Yulia et al. (2013) MULTIPLE TESTING OF LOCAL MAXIMA FOR DETECTION OF PEAKS IN CHIP-SEQ DATA. Ann Appl Stat 7:471-494|
|Schwartzman, Armin (2012) Comment on ""Estimating False Discovery Proportion Under Arbitrary Covariance Dependence"" by Fan et al. J Am Stat Assoc 107:1039-1041|
|Schwartzman, Armin; Gavrilov, Yulia; Adler, Robert J (2011) MULTIPLE TESTING OF LOCAL MAXIMA FOR DETECTION OF PEAKS IN 1D. Ann Stat 39:3290-3319|