Modeling Network Populations via Graph Distances

Identification of system-level features in HIV migration within a host

OBJECTIVE

Identify system-level features in HIV migration within a host across body tissues. Evaluate heterogeneity in the presence and magnitude of these features across hosts.

METHOD

Using HIV DNA deep sequencing data generated across multiple tissues from 8 people with HIV, we represent the complex dependencies of HIV migration among tissues as a network and model these networks using the family of exponential random graph models (ERGMs). ERGMs allow for the statistical assessment of whether network features occur more (or less) frequently in viral migration than might be expected by chance. The analysis investigates five potential features of the viral migration network: (1) bi-directional flow between tissues; (2) preferential migration among tissues in the same biological system; (3) heterogeneity in the level of viral migration related to HIV reservoir size; (4) hierarchical structure of migration; and (5) cyclical migration among several tissues. We calculate the Cohran's Q statistic to assess heterogeneity in the magnitude of the presence of these features across hosts. The analysis adjusts for missing data on body tissues.

RESULTS

We observe strong evidence for bi-directional flow between tissues; migration among tissues in the same biological system; and hierarchical structure of the viral migration network. This analysis shows no evidence for differential level of viral migration with respect to the HIV reservoir size of a tissue. There is evidence that cyclical migration among three tissues occurs less frequent than expected given the amount of viral migration. The analysis also provides evidence for heterogeneity in the magnitude that these features are present across hosts. Adjusting for missing tissue data identifies system-level features within a host as well as heterogeneity in the presence of these features across hosts that are not detected when the analysis only considers the observed data.

DISCUSSION

Identification of common features in viral migration may increase the efficiency of HIV cure efforts as it enables targeting specific processes.

Clustering of heterogeneous populations of networks

Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might be different on weekdays and weekends, for instance. Brain networks may differ between healthy patients and those with dementia or other conditions. Here we describe a Bayesian analysis framework for such data that allows for the fact that network measurements may be reflective of multiple possible structures. We define a finite mixture model of the measurement process and derive a Gibbs sampling procedure that samples exactly from the full posterior distribution of model parameters. The end result is a clustering of the measured networks into groups with similar structure. We demonstrate the method on both real and synthetic network populations.