Open Access
June 2011 Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data
Jeffrey S. Morris, Veerabhadran Baladandayuthapani, Richard C. Herrick, Pietro Sanna, Howard Gutstein
Ann. Appl. Stat. 5(2A): 894-923 (June 2011). DOI: 10.1214/10-AOAS407


Image data are increasingly encountered and are of growing importance in many areas of science. Much of these data are quantitative image data, which are characterized by intensities that represent some measurement of interest in the scanned images. The data typically consist of multiple images on the same domain and the goal of the research is to combine the quantitative information across images to make inference about populations or interventions. In this paper we present a unified analysis framework for the analysis of quantitative image data using a Bayesian functional mixed model approach. This framework is flexible enough to handle complex, irregular images with many local features, and can model the simultaneous effects of multiple factors on the image intensities and account for the correlation between images induced by the design. We introduce a general isomorphic modeling approach to fitting the functional mixed model, of which the wavelet-based functional mixed model is one special case. With suitable modeling choices, this approach leads to efficient calculations and can result in flexible modeling and adaptive smoothing of the salient features in the data. The proposed method has the following advantages: it can be run automatically, it produces inferential plots indicating which regions of the image are associated with each factor, it simultaneously considers the practical and statistical significance of findings, and it controls the false discovery rate. Although the method we present is general and can be applied to quantitative image data from any application, in this paper we focus on image-based proteomic data. We apply our method to an animal study investigating the effects of cocaine addiction on the brain proteome. Our image-based functional mixed model approach finds results that are missed with conventional spot-based analysis approaches. In particular, we find that the significant regions of the image identified by the proposed method frequently correspond to subregions of visible spots that may represent post-translational modifications or co-migrating proteins that cannot be visually resolved from adjacent, more abundant proteins on the gel image. Thus, it is possible that this image-based approach may actually improve the realized resolution of the gel, revealing differentially expressed proteins that would not have even been detected as spots by modern spot-based analyses.


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Jeffrey S. Morris. Veerabhadran Baladandayuthapani. Richard C. Herrick. Pietro Sanna. Howard Gutstein. "Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data." Ann. Appl. Stat. 5 (2A) 894 - 923, June 2011.


Published: June 2011
First available in Project Euclid: 13 July 2011

zbMATH: 05961696
MathSciNet: MR2840180
Digital Object Identifier: 10.1214/10-AOAS407

Keywords: 2D gel electrophoresis , Bayesian analysis , False discovery rate , Functional data analysis , functional mixed models , functional MRI , image analysis , isomorphic transformations , proteomics , Wavelets

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.5 • No. 2A • June 2011
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