AUTOMATED ANALYSIS OF QUANTITATIVE IMAGE DATA USING ISOMORPHIC FUNCTIONAL MIXED MODELS, WITH APPLICATION TO PROTEOMICS DATA

Abstract

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 opiate 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.

Fig 1

Compression Plot:Plot of minimum proportion of energy preserved for EACH image vs. number of wavelet coefficients (T*) for example 2-DE data set.

Fig 2

Illustration of Compression: Heatmap of a raw uncompressed gel image and corresponding compressed images with P = 0.99, 0.975 and 0.95 (top), along with corresponding posterior discovery images (Posterior probability of 1.5-fold expression, bottom) for differences between animals in control and long cocaine access groups.

Fig 3

Virtual Gel Plot of single gel from data example (left panel) and a virtual gel (right panel), found by sampling randomly from the posterior predictive distribution of the ISO-FMM used to fit the sample data. Note that the ISO-FMM is able to sufficiently capture the structure of real 2D gels so that the virtual gel looks very much like a real gel that could have come from the example data set.

Fig 4

ISO-FMM results: Heatmaps of posterior mean of overall mean gel (M(t₁, t₂), upper left) and control vs. long cocaine access effect gel (C₁₃(t₁, t₂), upper right), plus probability discovery plot (p^1.5(t₁, t₂), lower left) and regions of gel flagged as significant (FDR< 0.10, 1.5-fold, lower right). Higher intensities are indicated by hotter colors, lower intensities by cooler colors.

Fig 5

Specific Results 1: Posterior mean of overall mean gel (upper left), effect gel (upper right), probability discovery plot (lower left), and indicating ISO-FMM flagged regions (lower right) for region marked by small box in Figure 4, with pinnacles for detected spots marked (x), and differential expression in Pinnacle analysis indicated by a (o). Note that region flagged by ISO-FMM corresponds to visible spot also detected by Pinnacle analysis

Fig 6

Specific Results 2: Posterior mean of overall mean gel (upper left), effect gel (upper right), probability discovery plot (lower left), and indicating ISO-FMM flagged regions (lower right) for region marked by large box in Figure 4, with pinnacles for detected spots marked (x), and differential expression in Pinnacle analysis indicated by a (o). Note that regions flagged by ISO-FMM correspond to tails of visible spots that themselves are not differentially expressed. These results are not found by the Pinnacle analysis.