Omics and Cardiometabolic Disease Risk Prediction

Risk assessments are integral for the prevention and management of cardiometabolic disease (CMD). However, individuals may develop CMD without traditional risk factors, necessitating the development of novel biomarkers to aid risk prediction. The emergence of omic technologies, including genomics, proteomics, and metabolomics, has allowed for assessment of orthogonal measures of cardiometabolic risk, potentially improving the ability for novel biomarkers to refine disease risk assessments. While omics has shed light on novel mechanisms for the development of CMD, its adoption in clinical practice faces significant challenges. We review select omic technologies and cardiometabolic investigations for risk prediction, while highlighting challenges and opportunities for translating findings to clinical practice.

A co-analytic maximal set of orthogonal measures

We prove that if V = L then there is a maximal orthogonal (i.e., mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.

Orthogonal measures and absorbing sets for Markov chains

For a general state space Markov chain on a space (X, [Bscr ](X)), the existence of a Doeblin decomposition, implying the state space can be written as a countable union of absorbing ‘recurrent’ sets and a transient set, is known to be a consequence of several different conditions all implying in some way that there is not an uncountable collection of absorbing sets. These include([Mscr ]) there exists a finite measure which gives positive mass to each absorbing subset of X;([Gscr ]) there exists no uncountable collection of points (xα) such that the measures Kθ(xα, ·)[colone ](1−θ)ΣPn(xα, ·)θn are mutually singular;([Cscr ]) there is no uncountable disjoint class of absorbing subsets of X.We prove that if [Bscr ](X) is countably generated and separated (distinct elements in X can be separated by disjoint measurable sets), then these conditions are equivalent. Other results on the structure of absorbing sets are also developed.