The Annals of Applied Statistics

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

Ryan Admiraal and Mark S. Handcock

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation

References

  • Adimora, A. A. and Schoenbach, V. J. (2002). Contextual factors and the black–white disparity in heterosexual HIV transmission. Epidemiology 13 707–712.
  • Adimora, A. A. and Schoenbach, V. J. (2005). Social context, sexual networks, and racial disparities in rates of sexually transmitted infections. J. Infect. Dis. 191 S115–S122.
  • Adimora, A. A., Schoenbach, V. J. and Doherty, I. A. (2006). HIV and African Americans in the southern United States: Sexual networks and social context. Sex. Transm. Dis. 33 S39–S45.
  • Adimora, A. A., Schoenbach, V. J. and Doherty, I. A. (2007). Concurrent sexual partnerships among men in the United States. Am. J. Publ. Health 97 2230–2237.
  • Admiraal, R. and Handcock, M. S. (2016). Supplement to “Modeling concurrency and selective mixing in heterosexual partnership networks with applications to sexually transmitted diseases.” DOI:10.1214/16-AOAS963SUPP.
  • Anderson, R. M. (1992). Some aspects of sexual behavior and the potential demographic impact of AIDS in developing countries. Social Science and Medicine 34 271–280.
  • Anderson, R. M., Gupta, S. and Ng, W. (1990). The significance of sexual partner contact networks for the transmission dynamics of HIV. J. Acquir. Immune Defic. Syndr. 3 417–429.
  • Aral, S. O., Hughes, J. P., Stoner, B., Whittington, W., Handsfield, H. H., Anderson, R. M. and Holmes, K. K. (1999). Sexual mixing patterns in the spread of gonococcal and chlamydial infections. Am. J. Publ. Health 89 825–833.
  • Barndorff-Nielsen, O. (2014). Information and Exponential Families in Statistical Theory. Wiley, Chichester.
  • Busenberg, S. and Castillo-Chavez, C. (1989). Interaction, pair formation and force of infection terms in sexually transmitted diseases. In Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics 83 289–300. Springer, Berlin.
  • Carnegie, N. B. and Morris, M. (2011). Size matters: Concurrency and the epidemic potential of HIV in small networks. PLoS One 7 e43048.
  • Castillo-Chavez, C. and Blythe, S. P. (1989). Mixing framework for social/sexual behavior. In Mathematical and Statistical Approaches to AIDS Epidemiology (C. Castillo-Chavez, ed.). Lecture Notes in Biomathematics 83 275–288. Springer, Berlin.
  • Centers for Disease Control and Prevention (2015). Sexually Transmitted Diseases: Data & Statistics. Available at http://www.cdc.gov/std/stats/default.htm, 2015. Accessed: December 1, 2015.
  • Chick, S. E., Adams, A. L. and Koopman, J. S. (2000). Analysis and simulation of a stochastic, discrete-individual model of STD transmission with partnership concurrency. Math. Biosci. 166 45–68.
  • Demographic and Health Surveys Program (2015). HIV/AIDS Survey Indicators Database. Available at http://hivdata.dhsprogram.com, 2015. Accessed: December 1, 2015.
  • Doherty, I. A., Shiboski, S., Ellen, J. M., Adimora, A. A. and Padian, N. S. (2006). Sexual bridging socially and over time: A simulation model exploring the relative effects of mixing and concurrency on viral sexually transmitted infection transmission. Sex. Transm. Dis. 33 368–373.
  • Eaton, J. W., Hallett, T. B. and Garnett, G. P. (2011). Concurrent sexual partnerships and primary HIV infection: A critical interaction. AIDS Behav. 15 687–692.
  • Eaton, J. W., McGrath, N. and Newell, M.-L. (2012). Unpacking the recommended indicator for concurrent sexual partnerships. AIDS 26 1037–1039.
  • Garnett, G. and Anderson, R. M. (1993a). Contact tracing and the estimation of sexual mixing patterns: The epidemiology of Gonococcal infections. Sex. Transm. Dis. 20 181–191.
  • Garnett, G. P. and Anderson, R. M. (1993b). Factors controlling the spread of HIV in heterosexual communities in developing countries: Patterns of mixing between different age and sexual activity classes. Philosophical Transactions: Biological Sciences 342 137–159.
  • Garnett, G. P., Hughes, J. P., Anderson, R. M., Stoner, B. P., Aral, S. O., Whittington, W. L., Handsfield, H. H. and Holmes, K. K. (1996). Sexual mixing patterns of patients attending sexually transmitted diseases clinics. Sex. Transm. Dis. 23 248–257.
  • Ghalanos, A. and Theussls, S. (2012). Rsolnp: General Non-linear Optimization Using Augmented Lagrange Multiplier Method. Available at CRAN.R-project.org/package=Rsolnp. Version 1.14.
  • Ghani, A. C. and Garnett, G. P. (2000). Risks of acquiring and transmitting sexually transmitted diseases in sexual partner networks. Sex. Transm. Dis. 27 579–587.
  • Ghani, A. C., Swinton, J. and Garnett, G. P. (1997). The role of sexual partnership networks in the epidemiology of gonorrhea. Sex. Transm. Dis. 24 45–56.
  • Glynn, J. R., Dube, A., Kayuni, N., Floyd, S., Molesworth, A., Parrott, F., French, N. and Crampin, A. C. (2012). Measuring concurrency: An empirical study of different methods in a large population-based survey in northern Malawi and evaluation of the UNAIDS guidelines. AIDS 26 977–985.
  • Goodreau, S. M. (2011). A decade of modelling research yields considerable evidence for the importance of concurrency: A response to Sawers and Stillwaggon. Journal of the International AIDS Society 14 1–7.
  • Goodreau, S. M., Cassels, S., Kasprzyk, D., Montaño, D. E., Greek, A. and Morris, M. (2012). Concurrent partnerships, acute infection and HIV epidemic dynamics among young adults in Zimbabwe. AIDS Behav. 6 312–322.
  • Grulich, A. E. and Zablotska, I. (2010). Commentary: Probability of HIV transmission through anal intercourse. Int. J. Epidemiol. 39 1064–1065.
  • Gupta, S., Anderson, R. M. and May, R. M. (1989). Networks of sexual contacts: Implications for the pattern of spread of HIV. AIDS 3 807–817.
  • Hamilton, D. T., Handcock, M. S. and Morris, M. (2008). Degree distributions in sexual networks: A framework for evaluating evidence. Sex. Transm. Dis. 35 30–40.
  • Hamilton, D. T. and Morris, M. (2015). The racial disparities in STI in the U.S.: Concurrency, STI prevalence, and heterogeneity in partner selection. Epidemics 11 56–61.
  • Handcock, M. S. (2003). Assessing degeneracy in statistical models of social networks. Working paper, Center for Statistics and the Social Sciences, Univ. of Washington.
  • Handcock, M. S. and Gile, K. J. (2010). Modeling networks from sampled data. Ann. Appl. Stat. 40 285–327.
  • Handcock, M. S., Rendall, M. S. and Cheadle, J. E. (2005). Improved regression estimation of a multivariate relationship with population data on the bivariate relationship. Sociol. Method. 35 291–334.
  • Handcock, M. S., Hunter, D. R., Butts, C. T., Goodreau, S. M. and Morris, M. (2003). statnet: Software tools for the Statistical Modeling of Network Data. Seattle, WA, 2003. Available at http://statnetproject.org.
  • Handcock, M. S., Hunter, D. R., Butts, C. T., Goodreau, S. M., Krivitsky, P. N. and Morris, M. (2013). ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks. The Statnet Project (http://www.statnet.org), 2013. Available at CRAN.R-project.org/package=ergm. R package version 3.1-0.
  • Harris, K. M., Halpern, C. T., Whitsel, E., Hussey, J., Tabor, J., Entzel, P. and Udry, J. R. (2009). The National Longitudinal Study of Adolescent Health: Research Design [www document]. Technical report, Carolina Population Center, University of North Carolina at Chapel Hill, Available at: http://www.cpc.unc.edu/projects/addhealth/design.
  • Helleringer, S., Mkandawire, J. and Kohler, H.-P. (2014). A new approach to measuring partnership concurrency and its association with HIV risk in couples. AIDS Behav. 18 2291–2301.
  • Hudson, C. (1993). Concurrent partnerships could cause AIDS epidemics. International Journal of STD and AIDS 4 349–353.
  • Hunter, D. R. and Handcock, M. S. (2006). Inference in curved exponential family models for networks. J. Comput. Graph. Statist. 15 565–583.
  • Hunter, D. R., Handcock, M. S., Butts, C. T., Goodreau, S. M. and Morris, M. (2008). ergm: A package to fit, simulate and diagnose exponential-family models for networks. J. Stat. Softw. 24 1–11.
  • Hyman, J. M. and Stanley, E. A. (1988). Using mathematical models to understand the AIDS epidemic. Math. Biosci. 90 415–473.
  • Jacquez, J. A., Simon, C. P. and Koopman, J. (1989). Structured mixing: Heterogeneous mixing by the definition of activity groups. In Mathematical and Statistical Approaches to AIDS Epidemiology (C. Castillo-Chavez, ed.). Lecture Notes in Biomathematics 83 301–315. Springer, Berlin.
  • Johnson, L. F., Dorrington, R. E., Bradshaw, D., Pillay-Van Wyk, V. and Rehle, T. M. (2009). Sexual behaviour patterns in South Africa and their association with the spread of HIV: Insights from a mathematical model. Demogr. Res. Monogr. 21 289–339.
  • Julian, D., Bouchard, C., Gagnon, M. and Pomerleau, A. (1992). Insider’s views of marital sex: A dyadic analysis. J. Sex Res. 29 343–360.
  • Kinsey, A. C., Pomeroy, W. B. and Martin, C. E. (1948). Sexual Behavior in the Human Male. W. B. Saunders Company, Philadelphia.
  • Koopman, J. S., Chick, S. E., Riolo, C. S., Adams, A. L., Wilson, M. L. and Becker, M. P. (2000). Modeling contact networks and infection transmission in geographic and social space using GERMS. Sex. Transm. Dis. 27 617–626.
  • Kretzschmar, M. and Caraël, M. (2012). Is concurrency driving HIV transmission in Sub-Saharan African sexual networks? The significance of sexual partnership typology. AIDS Behav. 16 1746–1752.
  • Kretzschmar, M. and Morris, M. (1996). Measures of concurrency in networks and the spread of infectious disease. Math. Biosci. 133 165–195.
  • Krivitsky, P. N. (2012). Exponential-family random graph models for valued networks. Electron. J. Stat. 6 1100–1128.
  • Krivitsky, P. N. and Handcock, M. S. (2014). A separable model for dynamic networks. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76 29–46.
  • Mah, T. L. and Halperin, D. T. (2010). Concurrent sexual partnerships and the HIV epidemics in Africa: Evidence to move forward. AIDS Behav. 14 11–16.
  • Morin, B. R., Perrings, C., Levin, S. and Kinzig, A. (2014). Disease risk mitigation: The equivalence of two selective mixing strategies on aggregate contact patterns and resulting epidemic spread. J. Theoret. Biol. 363 262–270.
  • Morris, M. (1991). A log-linear modeling framework for selective mixing. Math. Biosci. 2 349–377.
  • Morris, M. (1994). Epidemiology and social networks: Modeling structured diffusion. In Advances in Social Network Analysis: Research in the Social and Behavioral Sciences (S. Wasserman and J. Galaskiewicz, eds.) 26–52. Sage Publications, Thousand Oaks.
  • Morris, M. (1995). Data driven network models for the spread of infectious disease. In Epidemic Models: Their Structure and Relation to Data (D. Mollison, ed.) 302–322. Cambridge Univ. Press, Cambridge.
  • Morris, M. (1997). Sexual networks and HIV. AIDS 11 S209–S216.
  • Morris, M., Epstein, H. and Wawer, M. (2010). Timing is everything: International variations in historical sexual partnership concurrency and HIV prevalence. PLoS ONE 5 31–33.
  • Morris, M., Goodreau, S. M. and Moody, J. (2007). Sexual networks, concurrency, and STD/HIV. In Sexually Transmitted Diseases, 4th ed. (K. K. Holmes, P. F. Sparling, W. E. Stamm, P. Piot, J. N. Wasserheit, L. Corey and D. H. Watts, eds.) 109–125. McGraw-Hill, New York.
  • Morris, M. and Kretzschmar, M. (1995). Concurrent partnerships and transmission dynamics in networks. Social Networks 17 299–318.
  • Morris, M. and Kretzschmar, M. (1997). Concurrent partnerships and the spread of HIV. AIDS 5 641–648.
  • Morris, M. and Kretzschmar, M. (2000). A microsimulation study of the effect of concurrent partnerships on the spread of HIV in Uganda. Math. Popul. Stud. 8 109–133. The population dynamics of the HIV epidemic: Projections.
  • Morris, M., Kurth, A. E., Hamilton, D. T., Moody, J. and Wakefield, S. (2009). Concurrent partnerships and HIV prevalence disparities by race: Linking science and public health practice. Am. J. Publ. Health 99 1023–1031.
  • Ochs, E. P. and Binik, Y. M. (1999). The use of couple data to determine the reliability of self-reported sexual behavior. J. Sex Res. 36 374–384.
  • R Core Team (2013). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2013. Available at http://www.R-project.org/.
  • Rendall, M. S., Admiraal, R., DeRose, A., DiGiulio, P., Handcock, M. S. and Racioppi, F. (2008). Population constraints on pooled surveys in demographic hazard modeling. Stat. Methods Appl. 17 519–539.
  • Sawers, L. (2013). Measuring and modelling concurrency. Journal of the International AIDS Society 16 1–20.
  • Seal, D. W. (1997). Interpartner concordance of self-reported sexual behavior among college dating couples. The Journal of Sex Research 34 39–55.
  • Shalizi, C. R. and Rinaldo, A. (2013). Consistency under sampling of exponential random graph models. Ann. Statist. 41 508–535.
  • Snijders, T. A. B. (2001). The statistical evaluation of social network dynamics. Sociol. Method. 31 361–95.
  • UNAIDS Reference Group on Estimates, Modelling, and Projections (2009). Consultation on Concurrent Sexual Partnerships: Recommendations from a meeting of the UNAIDS Reference Group on Estimates, Modelling and Projections held in Nairobi, Kenya, April 20–21st 2009.
  • Watts, C. H. and May, R. M. (1992). The influence of concurrent partnerships on the dynamics of HIV/AIDS. Math. Biosci. 108 89–104.
  • World Health Organization (2013). Number of people (all ages) living with HIV: Estimates by WHO region. Available at http://apps.who.int/gho/data/view.main.22100WHO?, 2013. Accessed: December 1, 2015.
  • Ye, Y. (1987). Interior algorithms for linear, quadratic, and linearly constrained non-linear programming Ph.D. Thesis, Stanford Univ., Dept. of EES.

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.