Voxelwise single-subject analysis of imaging metabolic response to therapy in neuro-oncology

Genomics data analysis via spectral shape and topology

Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and to retain information that may be lost using standard dimension-reduction algorithms. We propose a novel workflow to process and analyze RNA-seq data from tumor and healthy subjects integrating Mapper, differential gene expression, and spectral shape analysis. Precisely, we show that a Gaussian mixture approximation method can be used to produce graphical structures that successfully separate tumor and healthy subjects, and produce two subgroups of tumor subjects. A further analysis using DESeq2, a popular tool for the detection of differentially expressed genes, shows that these two subgroups of tumor cells bear two distinct gene regulations, suggesting two discrete paths for forming lung cancer, which could not be highlighted by other popular clustering methods, including t-distributed stochastic neighbor embedding (t-SNE). Although Mapper shows promise in analyzing high-dimensional data, tools to statistically analyze Mapper graphical structures are limited in the existing literature. In this paper, we develop a scoring method using heat kernel signatures that provides an empirical setting for statistical inferences such as hypothesis testing, sensitivity analysis, and correlation analysis.

Statistical assessment of treatment response in a cancer patient based on pre-therapy and post-therapy FDG-PET scans

This work arises from consideration of sarcoma patients in which fluorodeoxyglucose positron emission tomography (FDG-PET) imaging pre-therapy and post-chemotherapy is used to assess treatment response. Our focus is on methods for evaluation of the statistical uncertainty in the measured response for an individual patient. The gamma distribution is often used to describe data with constant coefficient of variation, but it can be adapted to describe the pseudo-Poisson character of PET measurements. We propose co-registering the pre-therapy and post- therapy images and modeling the approximately paired voxel-level data using the gamma statistics. Expressions for the estimation of the treatment effect and its variability are provided. Simulation studies explore the performance in the context of testing for a treatment effect. The impact of misregistration errors and how test power is affected by estimation of variability using simplified sampling assumptions, as might be produced by direct bootstrapping, is also clarified. The results illustrate a marked benefit in using a properly constructed paired approach. Remarkably, the power of the paired analysis is maintained even if the pre-image and post- image data are poorly registered. A theoretical explanation for this is indicated. The methodology is further illustrated in the context of a series of fluorodeoxyglucose-PET sarcoma patient studies. These data demonstrate the additional prognostic value of the proposed treatment effect test statistic. Copyright © 2016 John Wiley & Sons, Ltd.