Modeling concurrency and selective mixing in heterosexual partnership networks with applications to sexually transmitted diseases

Abstract

Network-based models for sexually transmitted disease transmission rely on initial partnership networks incorporating structures that may be related to risk of infection. In particular, initial networks should reflect the level of concurrency and attribute-based selective mixing observed in the population of interest. We consider momentary degree distributions as measures of concurrency and propensities for people of certain types to form partnerships with each other as a measure of attribute-based selective mixing. Estimation of momentary degree distributions and mixing patterns typically relies on cross-sectional survey data, and, in the context of heterosexual networks, we describe how this results in two sets of reports that need not be consistent with each other. The reported momentary degree distributions and mixing totals are related through a series of constraints, however. We provide a method to incorporate those in jointly estimating momentary degree distributions and mixing totals. We develop a method to simulate heterosexual networks consistent with these momentary degree distributions and mixing totals, applying it to data obtained from the National Longitudinal Study of Adolescent Health. We first use the momentary degree distributions and mixing totals as mean value parameters to estimate the natural parameters for an exponential-family random graph model and then use a Markov chain Monte Carlo algorithm to simulate person-level heterosexual partnership networks.

A simulation-based framework for assessing the feasibility of respondent-driven sampling for estimating characteristics in populations of lesbian, gay and bisexual older adults

“…Building on the work of Admiraal and Handcock (2016), we first define a model for the unobserved social network structure that depends on several unknown parameters, and then relate these parameters to the pilot data described in Section 2.…”

“…In our application to LGB older adults, i indexes gay (i=G) or bisexual (i=B) sexual identity and j indexes male (j=M) or female (j=W) gender identity. As in Admiraal and Handcock (2016), we assume that social network structure is characterized by degree distributions, the distribution of alters per ego, and mixing totals, the propensity of egos to have alters of various types.…”

“…This kind of network data is very coarse, but nonetheless contains information about the distribution of contacts per subject in the population, that is, the degree distribution, and how egos’ characteristics relate to the characteristics of their alters, that is, mixing totals. When alter counts are relatively small and the characteristics relevant to the social network structure are observed for egos and alters, this kind of data has been used to estimate measures of the structure of the population network [Admiraal and Handcock (2016)]. However, aggregated egocentric data often includes very large alter counts and is “asymmetric” in practice.…”

“…More characteristics are observed for egos than alters in asymmetric data, for example, gender identity of egos may be observed while alter counts are pooled over gender identities. This is problematic because gender identity is relevant to network structure; the method given by Admiraal and Handcock (2016) will not allow gender identity to be used in modeling measures of the population network structure if gender identity is not observed for alters. Accordingly, we extend the work of Admiraal and Handcock (2016) to develop a novel statistical approach for estimating unknown social network structures from asymmetric aggregated social network data with large alter counts.…”

Network Inference From Grouped Observations Using Hub Models

“…In this work, the network structure for the population is latent. Admiraal and Handcock (2016) fit exponential-family random graph models (ERGMs) to latent heterosexual partnership networks, with degree distributions and mixing totals being sufficient statistics in the exponential family. Those statistics for the underlying population are inferred from crosssectional survey data.…”