The Annals of Applied Statistics

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, and Howard Gutstein

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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.

Article information

Ann. Appl. Stat. Volume 5, Number 2A (2011), 894-923.

First available in Project Euclid: 13 July 2011

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Zentralblatt MATH identifier

Bayesian analysis false discovery rate functional data analysis functional mixed models functional MRI image analysis isomorphic transformations proteomics 2D gel electrophoresis wavelets


Morris, Jeffrey S.; Baladandayuthapani, Veerabhadran; Herrick, Richard C.; Sanna, Pietro; Gutstein, Howard. Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data. Ann. Appl. Stat. 5 (2011), no. 2A, 894--923. doi:10.1214/10-AOAS407.

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Supplemental materials

  • Supplementary material A: Computational details for wavelet-space implementation of ISO-FMM for image data. Computational details for wavelet implementation of the ISO-FMM for image data, including empirical Bayes method for estimating regularization parameters, MCMC details and Metropolis–Hastings details for covariance parameters.
  • Supplementary material B: Supplementary figures. Supplementary figures, including a virtual 2d gel simulated from the model, a demonstration of the spatial covariance structure induced by the model and 8 plots containing zoomed-in results from analysis of application data in certain interesting regions of the gel.
  • Supplementary material C: Spatial covariance structure in image WFMM. Basic illustration of spatial covariance structure induced by ISO-FMM with 2D wavelet transforms and independence assumed in the wavelet space. Basic demonstration described, and some plots provided. Movie file spatial_covariance.wvm also available as supplementary material to further illustrate these results.
  • Supplementary material D: Movie file illustrating spatial covariance structure of ISO-WFMM with 2D wavelet transform. Windows movie file illustrating the nonstationary spatial covariance structure induced by the ISO-FMM with 2D wavelet bases, with independence assumed among wavelet coefficients. Description of data yielding this movie is provided in the file “Spatial Covariance Structure in Image WFMM.pdf,” also available as supplementary material.