## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 10, Number 4 (2016), 2021-2046.

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

Ryan Admiraal and Mark S. Handcock

#### 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.

#### Article information

**Source**

Ann. Appl. Stat., Volume 10, Number 4 (2016), 2021-2046.

**Dates**

Received: November 2013

Revised: June 2016

First available in Project Euclid: 5 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1483606850

**Digital Object Identifier**

doi:10.1214/16-AOAS963

**Mathematical Reviews number (MathSciNet)**

MR3592047

**Zentralblatt MATH identifier**

06688767

**Keywords**

Heterosexual partnership networks exponential-family random graph models constrained maximum likelihood estimation National Longitudinal Survey of Adolescent Health

#### Citation

Admiraal, Ryan; Handcock, Mark S. Modeling concurrency and selective mixing in heterosexual partnership networks with applications to sexually transmitted diseases. Ann. Appl. Stat. 10 (2016), no. 4, 2021--2046. doi:10.1214/16-AOAS963. https://projecteuclid.org/euclid.aoas/1483606850

#### Supplemental materials

- Supplement to “Modeling concurrency and selective mixing in heterosexual partnership networks with applications to sexually transmitted diseases.”. We provide a full exposition of common measures of concurrency, studies providing evidence for the importance of concurrency in explaining disparities in the spread of sexually transmitted diseases and studies refuting this conclusion. We additionally present details for estimating natural parameters from mean value parameters for exponential-family random graph models, and we provide a full simulation study that demonstrates the usefulness of our method in generating networks consistent with populations having drastically different levels of concurrency and selective mixing patterns.Digital Object Identifier: doi:10.1214/16-AOAS963SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.