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dc.contributor.authorLi, Meng
Schwartzman, Armin
dc.date.accessioned 2019-01-09T17:21:12Z
dc.date.available 2019-01-09T17:21:12Z
dc.date.issued 2018
dc.identifier.citation Li, Meng and Schwartzman, Armin. "Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology." The Annals of Applied Statistics, 12, no. 4 (2018) 2197-2227. https://doi.org/10.1214/18-AOAS1149.
dc.identifier.urihttps://hdl.handle.net/1911/105025
dc.description.abstract In brain oncology, it is routine to evaluate the progress or remission of the disease based on the differences between a pre-treatment and a post-treatment Positron Emission Tomography (PET) scan. Background adjustment is necessary to reduce confounding by tissue-dependent changes not related to the disease. When modeling the voxel intensities for the two scans as a bivariate Gaussian mixture, background adjustment translates into standardizing the mixture at each voxel, while tumor lesions present themselves as outliers to be detected. In this paper, we address the question of how to standardize the mixture to a standard multivariate normal distribution, so that the outliers (i.e., tumor lesions) can be detected using a statistical test. We show theoretically and numerically that the tail distribution of the standardized scores is favorably close to standard normal in a wide range of scenarios while being conservative at the tails, validating voxelwise hypothesis testing based on standardized scores. To address standardization in spatially heterogeneous image data, we propose a spatial and robust multivariate expectation-maximization (EM) algorithm, where prior class membership probabilities are provided by transformation of spatial probability template maps and the estimation of the class mean and covariances are robust to outliers. Simulations in both univariate and bivariate cases suggest that standardized scores with soft assignment have tail probabilities that are either very close to or more conservative than standard normal. The proposed methods are applied to a real data set from a PET phantom experiment, yet they are generic and can be used in other contexts.
dc.language.iso eng
dc.rights Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.title Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology
dc.type Journal article
dc.citation.journalTitle The Annals of Applied Statistics
dc.citation.volumeNumber 12
dc.citation.issueNumber 4
dc.identifier.digital STANDARDIZATION
dc.contributor.publisher The Institute of Mathematical Statistics
dc.type.dcmi Text
dc.identifier.doihttps://doi.org/10.1214/18-AOAS1149
dc.type.publication publisher version
dc.citation.firstpage 2197
dc.citation.lastpage 2227


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