Measuring heterogeneity in normative models as the effective number of deviation patterns

PLoS One. 2020 Nov 13;15(11):e0242320. doi: 10.1371/journal.pone.0242320. eCollection 2020.

Abstract

Normative modeling is an increasingly popular method for characterizing the ways in which clinical cohorts deviate from a reference population, with respect to one or more biological features. In this paper, we extend the normative modeling framework with an approach for measuring the amount of heterogeneity in a cohort. This heterogeneity measure is based on the Representational Rényi Heterogeneity method, which generalizes diversity measurement paradigms used across multiple scientific disciplines. We propose that heterogeneity in the normative modeling setting can be measured as the effective number of deviation patterns; that is, the effective number of coherent patterns by which a sample of data differ from a distribution of normative variation. We show that lower effective number of deviation patterns is associated with the presence of systematic differences from a (non-degenerate) normative distribution. This finding is shown to be consistent across (A) application of a Gaussian process model to synthetic and real-world neuroimaging data, and (B) application of a variational autoencoder to well-understood database of handwritten images.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Autistic Disorder / diagnostic imaging
  • Humans
  • Models, Statistical*
  • Neuroimaging

Grants and funding

Ruth Wagner Memorial Fund (AN). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.