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Abstract
Patterns of risk in injecting drug user (IDU) networks have been a key focus of network approaches to HIV transmission histories. New network modeling techniques allow for a reexamination of these patterns with greater statistical accuracy and the comparative weighting of model elements. This paper describes the results of a reexamination of network data from the SFHR and P90 data sets using Exponential Random Graph Modeling. The results show that “transitive closure” is an important feature of IDU network topologies, and provides relative importance measures for race/ethnicity, age, gender, and number of risk partners in predicting risk relationships.
RÉSUMÉ
Les modèles de risque en matière d'injection utilisateurs de drogues (UDI) des réseaux ont été un élément clé de la logique de réseau à l'histoire de transmission du VIH. De nouvelles techniques de modélisation de réseaux de permettre une ré-examen de ces motifs avec précision statistique plus grande et la pondération comparative des éléments du modèle. Cet article décrit les résultats d'un réexamen des données du réseau de la SFHR et P90 ensembles de données à l'aide de modélisation graphique exponentielle aléatoire (ERGM). Les résultats montrent que la «fermeture transitive» est une caractéristique importante de l'UDI topologies de réseau, et prévoit des mesures importance relative de la race/ethnicité, l’âge, le sexe et le nombre de partenaires risque pour la prédiction des relations à risque.
RESUMEN
Los patrones de riesgo en usuarios de drogas inyectables (UDI) redes han sido un elemento clave de los enfoques de la red a las historias de transmisión del VIH. Nuevas técnicas de modelado de red permiten un nuevo examen de estos patrones con mayor precisión estadística y la ponderación comparativa de los elementos del modelo. En este trabajo se describen los resultados de un nuevo examen de los datos de red de la SFHR y datos P90 establece utilizando el modelado gráfico exponencial aleatorio (ERGM). Los resultados muestran que “el cierre transitivo” es una característica importante de la UDI topologías de red, y proporciona medidas de importancia relativa para la raza/etnia, la edad, el género y el número de socios de riesgo en la predicción de las relaciones riesgo.
THE AUTHORS
Kirk Dombrowski is trained as an anthropologist, with a dissertation centered on the impact of native land claims on public health, food security, and household violence. He began working on social network techniques in 2004 after realizing that he needed new ways to think about rural inequality. Since 2006 he has worked closely with Khan, Curtis, and Wendel on techniques that can bridge the gap between on-the-ground fieldwork and network theory/modeling. In September 2013, he joined the Sociology Department at the University of Nebraska-Lincoln to help develop a special doctoral training focused on network analysis and health disparities.
Bilal Khan has been involved in the development of large scale network simulation development for over 15 years, including developmental work CASiNO, SEAN, PRouST, TRON, CHIME, and OPTIPRISM. He is presently Professor of Mathematics and Computer Science at John Jay College. His research areas span networks, algorithms, and graph theory. In recent years, he has developed simulations of networks in the context of fundamental research in wireless communications. He also recently coauthored a book on network simulation, Network Modeling and Simulation: A Practical Perspective.
Ric Curtis is a professor of anthropology at John Jay College of Criminal Justice and has conducted research in New York City since 1978. He was the lead ethnographer on the SFHR project discussed here. He worked with Friedman at NDRI from 1988–1998 where he conducted research on drug injectors for this and a number of studies. He continues to work with drug injectors as a Board of Directors member at 3 New York City harm reduction programs.
Katherine McLean is a PhD student in sociology at the CUNY Graduate Center. Her dissertation, currently in progress, focuses on the production of risk and subjectivity in needle exchange. She graduated with a BA in biology from Columbia and an MS in International Health from Harvard. She has taught courses ranging from Drugs and Society to Culture and Crime at Hunter College, Queens College, and John Jay College. She has been working with SNRG since 2009.
Evan Misshula is a research fellow of the Social Network Research Group at CUNY John Jay and a PhD candidate in Criminal Justice at the CUNY Graduate Center. His interests include simulation, optimal stochastic control, and data mining. His prior work has applied these techniques to political violence, victimization reporting, HIV transmission, and prisoner reentry.
Travis Wendel, JD, PhD, is a Research Associate and Scholar-In-Residence in the Department of Anthropology, John Jay College of Criminal Justice, City University of New York. He has been an ethnographer working with New York City drug users and distributors since 1996. His current activities include serving as Principal Investigator of the New York City National HIV Behavioral Surveillance study, and a study of the repeal of the Rockefeller drug laws in New York State. His research interests center around the social organization of the distribution and consumption of illegal commodities, and the role of social networks in those processes.
Samuel R. Friedman is Director of HIV/AIDS Research at National Development and Research Institutes, Inc. and the Director of the Interdisciplinary Theoretical Synthesis Core in the Center for Drug Use and HIV Research, New York City. He also is associated with the Department of Epidemiology, Johns Hopkins University, and with the Dalla Lana School of Public Health, University of Toronto. Dr. Friedman is an author of about 400 publications on HIV, hepatitis C, hepatitis C, STI, and drug use epidemiology and prevention. Honors include the International Rolleston Award of the International Harm Reduction Association (2009), the first Sociology AIDS Network Award for Career Contributions to the Sociology of HIV/AIDS (2007), and a Lifetime Contribution Award, Association of Black Sociologists (2005). He has published many poems in a variety of publications and a book of poetry (Seeking to make the world anew: Poems of the Living Dialectic. 2008. Lanham, Maryland: Hamilton Books).
Notes
2 The analysis was undertaken by the authors as part of a larger project aimed at creating a large scale, dynamic simulation of IDU networks capable of modeling the transmission HIV through time. The purpose of the ERGM analysis was to discover trends in connectivity previously unanalyzed in the SFHR and P90 data set that could form the basis of the network dynamics in the simulation. The discovery of a list of relevant variables and their influence on the making of new connections could be used to guide the simulation and help maintain real-world-viability across changes induced by network dynamism.
3 Conversely, when network structural features are being modeled—say, for example, the role of already existing mutual connections in the probability of tie formation between two nodes—the question necessarily involves the examination of dyadic dependence. In this case, the assumption reverses and the likelihood of the additional tie is assumed to occur independent of consideration of the attributes of the endpoints of that edge. Thus the attribute independence assumption applies only to attribute-based consideration and allows for the differentiation of node-based and network-based influences on network topology. This independence assumption is important to the discussion that follows, where the relative importance of network-structural versus attribute-based influences on tie formation is a central feature of the analysis.
4 Here, we use self-estimated degree of study informants, however, rather than the degree of the node in the discovered network. In this case the value of θ will indicate the extent to which those with high or low numbers of partners tend to associate primarily with others who also claim similar numbers of partners.
5 As above, Exponential Random Graph Modeling (ERGM) is relatively recent phenomena in Social Network Analysis, though its roots go back to the 1970s and 1980s (Frank & Strauss Citation1986). Until recently, the estimating of likelihood errors remained problematic in network terms (Strauss & Ikeda Citation1990); Handcock, Citation2003). But in the last several years, these problems have been overcome with the use of Maximum Likelihood Estimating procedures for use in network contexts (Handcock, Citation2003; Handcock, Hunter, Butts, Goodreau & Morris, Citation2008; Snijders et al., Citation2006). Since this time, ERGM has been used in a number of innovative network analyses. The ERGM package used here that which is implemented as part of the ERGM/Statnet package in R (Handcock et al. Citation2008).
6 Because the two studies used different criteria for injection drug use partnering (injection partners in the SFHR study, and needle partners in the P90 study), and two very different time periods (30 days versus 5 years, respectively), we refer to this under the label “injection partners,” which is the more inclusive of the two and subsumes the latter—needle partners are by definition injection partners but not vice versa. Because this data was closely related to subjects self-estimated degree in the drug couse network, we did not attempt to normalize the time frame. We note, however, that the number of injection partners over longer periods of time in the SFHR network (as seen in retrospective data also collected at the time) appears relatively steady.
7 Thus, by way of example, in a univariate analysis of the baseline measure of edges (or connection likelihood) in the SFHR network (Table 1a), the odds that a particular, randomly chosen pair of nodes in the network will share a connection is e−6.34 (see line 1). Yet if that pair of randomly chosen nodes both happen to be already connected to a third node, such that their connection would complete a transitive closure triangle, the odds of there being a connection between them increase by e3.42 (line 2) against a now adjusted “edges” value of e−6.26. As such, the odds an edge appearing between a pair of randomly chosen nodes where transitive closure would result from their joining is e−6.26+3.42 = e−2.84.
8 While such a finding may ask the question of whether something other than heterosexual risk was determining the connectivity trends of women, the analysis in Step 2 shows that the level of homophily shown by women in the P90 data set can be largely explained by differences in the average number of risk partners for women over and above that of men.