Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data

TL;DR

This paper introduces a Bayesian functional mixed model framework for analyzing quantitative image data, enabling flexible, automatic inference on image features while controlling false discoveries, with applications demonstrated in proteomics.

Contribution

It presents a unified, isomorphic modeling approach for functional mixed models, including wavelet-based methods, for complex and irregular quantitative image data analysis.

Findings

Efficient, automatic analysis of complex image data.

Ability to identify image regions associated with factors.

Control of false discovery rate in inferences.

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.