Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology

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dc.citation.firstpage2197en_US
dc.citation.issueNumber4en_US
dc.citation.journalTitleThe Annals of Applied Statisticsen_US
dc.citation.lastpage2227en_US
dc.citation.volumeNumber12en_US
dc.contributor.authorLi, Mengen_US
dc.contributor.authorSchwartzman, Arminen_US
dc.date.accessioned2019-01-09T17:21:12Zen_US
dc.date.available2019-01-09T17:21:12Zen_US
dc.date.issued2018en_US
dc.description.abstractIn 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.en_US
dc.identifier.citationLi, Meng and Schwartzman, Armin. "Standardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncology." <i>The Annals of Applied Statistics,</i> 12, no. 4 (2018) The Institute of Mathematical Statistics: 2197-2227. https://doi.org/10.1214/18-AOAS1149.en_US
dc.identifier.digitalSTANDARDIZATIONen_US
dc.identifier.doihttps://doi.org/10.1214/18-AOAS1149en_US
dc.identifier.urihttps://hdl.handle.net/1911/105025en_US
dc.language.isoengen_US
dc.publisherThe Institute of Mathematical Statisticsen_US
dc.rightsArticle 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.en_US
dc.titleStandardization of multivariate Gaussian mixture models and background adjustment of PET images in brain oncologyen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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