Abstract
Data collected from omics technologies have revealed pervasive heterogeneity and stochasticity of molecular states within and between phenotypes. A prominent example of such heterogeneity occurs between genome-wide mRNA, microRNA, and methylation profiles from one individual tumor to another, even within a cancer subtype. However, current methods in bioinformatics, such as detecting differentially expressed genes or CpG sites, are population-based and therefore do not effectively model intersample diversity. Here we introduce a unified theory to quantify sample-level heterogeneity that is applicable to a single omics profile. Specifically, we simplify an omics profile to a digital representation based on the omics profiles from a set of samples from a reference or baseline population (e.g., normal tissues). The state of any subprofile (e.g., expression vector for a subset of genes) is said to be "divergent" if it lies outside the estimated support of the baseline distribution and is consequently interpreted as "dysregulated" relative to that baseline. We focus on two cases: single features (e.g., individual genes) and distinguished subsets (e.g., regulatory pathways). Notably, since the divergence analysis is at the individual sample level, dysregulation can be analyzed probabilistically; for example, one can estimate the probability that a gene or pathway is divergent in some population. Finally, the reduction in complexity facilitates a more "personalized" and biologically interpretable analysis of variation, as illustrated by experiments involving tissue characterization, disease detection and progression, and disease-pathway associations.