1. Sexual Network Constraints on STD Flow The role of Sexual Networks in HIV spread by James Moody The Ohio State University Presented at The UNC Center for Aids Research Conference: Methods of Study in Human Sexuality: Relevance to AIDS Research Chapel Hill, May 5, 2001

2. Overview I. Introduction Why networks matter Basic network data types II. Network Topology Mixing Patterns in ego networks Reachability properties Location properties III. Timing Sexual Networks Network Development Directional Constraint IV. Problems, Limitations & Future Directions Data, Data, Data Linking non-sexual relations to sexual networks Sampling, Simulation & Estimation VI. Conclusion

3. Why Networks Matter Intuitive: STDs travel through intimate interpersonal contact We should do better explaining disease spread if we take this into account. Less intuitive: The pattern of intimate contact can have global effects on disease spread that could not be detected looking only at individual behavior. Work making this point: Klovdahl, A. S. 1985. "Social Networks and the Spread of Infectious Diseases: The AIDS Example." Social Science Medicine 21:1203-16. Morris, M. 1993. "Epidemiology and Social Networks: Modeling Structured Diffusion." Sociological Methods and Research 22:99-126. Rothenberg, et al. 1997 “Using Social Network and Ethnographic Tools to Evaluate Syphilis Transmission” Sexually Transmitted Diseases 25: 154-160

4. Basic network data People treated as nodes, relations (sex or drug use) as lines among nodes. Network data are represented in multiple, often unfamiliar, ways: Graphical - Often intuitive, but cumbersome to work with beyond intuition Adjacency Matrix - An n by n matrix, X, where X ij = 1 if i has had sex w. j - Can also be valued, with X ij = k, where k is a count Adjacency List - An n row list of each actor’s relations - Contains the row information of X Edge List - An m row list of sender receiver and value of the relation - Contains each element of X

5. Types of network data: Ego-network Have data on a respondent (ego) and their reports of people they are connected to (alters). May include estimates of connections among alters National Health and Social Life Survey, Laumann et al. Partial network Ego networks plus some amount of tracing to reach partners of partners. Something less than full account of connections among all pairs of actors in the relevant population Colorado Springs, Potterat, Rothenberg, et al. Urban and Rural Networks Project (Trotter, Rothenberg, et al.) Complete (Udry, Bearman, et al.) Data on all actors within a particular (relevant) boundary Never exactly ‘complete’ Basic network data

6. Partner’s partner Trace Relation Alter Relation Examples: linked levels of data Respondent Partner Primary Relation

7. Why Sexual Networks Matter: Consider the following (much simplified) scenario: Probability that actor i infects actor j (p ij )is a constant over all relations = 0.6 S & T are connected through the following structure: S T The probability that S infects T through either path would be: 0.090.09

8. Probability of infection over independent paths: The probability that an infectious agent travels from i to j is assumed constant at p ij. The probability that infection passes through multiple links (i to j, and from j to k) is the joint probability of each (link1 and link2 and … link k) = p ij d where d is the path distance. To calculate the probability of infection passing through multiple paths, use the compliment of it not passing through any paths. The probability of not passing through path l is 1-p ij d, and thus the probability of not passing through any path is (1-p ij d ) k, where k is the number of paths Thus, the probability of i infecting j given k independent paths is: Why matter Distance

9. Probability of infection over non-independent paths: - To get the probability that I infects j given that paths intersect at 4, I calculate Using the independent paths formula.formula

10. Why Sexual Networks Matter: Now consider the following (similar?) scenario: S T Every actor but one has the exact same number of partners The category-to-category mixing is identical The distance from S to T is the same (7 steps) S and T have not changed their behavior Their partner’s partners have the same behavior But the probability of an infection moving from S to T is: = 0.148 Different outcomes & different potentials for intervention

11. Network Topology: Ego Networks Mixing Matters The most commonly collected network data are ego-centered. While limited in the structural features, these do provide useful information on broad mixing patterns & relationship timing. Consider Laumann & Youm’s (1998) treatment of sexual mixing by race and activity level, using data from the NHSLS, to explain the differences in STD rates by race They find that two factors can largely explain the difference in STD rates: Intraracially, low activity African Americans are much more likely to have sex with high activity African Americans than are whites Interracially, sexual networks tend to be contained within race, slowing spread between races

12. Network Topology: Ego Networks In addition to general category mixing, ego-network data can provide important information on: Local clustering (if there are relations among ego’s partners. Not usually relevant in heterosexual populations, though very relevant to IDU populations) Number of partners -- by far the simplest network feature, but also very relevant at the high end Relationship timing, duration and overlap By asking about partner’s behavior, you can get some information on the relative risk of each relation. For example, whether a respondents partner has many other partners (though data quality is often at issue).

13. Network Topology: Ego Networks Studies making successful use of ego-network data include: Reinking et al. 1994. “Social Transmission Routes of HIV. A combined sexual network and life course perspective.” Patient Education and Counseling 24:289-297. Aral et al. 1999. “Sexual Mixing Patterns in the Spread of Gonococcal and Chlamydial Infections.” American Journal of Public Health 89: 825- 833. Martin and Dean 1990 (Longitudinal AIDS Impact Project). “Development of a community sample of gay men for an epidemiologic study of aids.” American Behavioral Science 33:546-61. Morris and Dean. 1994. “The effects of sexual behavior change on long- term hiv seroprevalence among homosexual men.” American Journal of Epidemiology 140:217-32.

14. Network Topology: Partial and Complete Networks Once we move beyond the ego-network, we can start to identify how the pattern of connection changes the disease risk for actors. Two features of the network’s shape are known to be important: Connectivity and Centrality. Connectivity refers to how actors in one part of the network are connected to actors in another part of the network. Reachability: Is it possible for actor i to infect actor j? This can only be true if there is an unbroken (and properly time ordered) chain of contact from one actor to another. Given reachability, three other properties are important: Distance Number of paths Distribution of paths through actors (independence of paths)

15. Reachability example: All romantic contacts reported ongoing in the last 6 months in a moderate sized high school (AddHealth) Male Female 12 9 63 2 (From Bearman, Moody and Stovel, n.d.)

16. 288 People in largest component 42 steps maximum distance Mean distance between non-connected pairs is 16 steps Mean number within 3 steps is: 9.7 45 people are biconnected (in the center ring).

17. Network Topology: Distance & number of paths Given that ego can reach alter, distance determines the likelihood of an infection passing from one end of the chain to another. Disease spread is never certain, so the probability of transmission decreases over distance. Disease transmission increases with each alternative path connecting pairs of people in the network.

18. 0 0.2 0.4 0.6 0.8 1 1.2 23456 Path distance probability Probability of infection by distance and number of paths, assume a constant p ij of 0.6 10 paths 5 paths 2 paths 1 path

19. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 23456 Path distance probability Probability of infection by distance and number of paths, assume a constant p ij of 0.3

20. S T S T Return to our first example: 2 paths 4 paths

21. Reachability in Colorado Springs (Sexual contact only) High-risk actors over 4 years 695 people represented Longest path is 17 steps Average distance is about 5 steps Average person is within 3 steps of 75 other people 137 people connected through 2 independent paths, core of 30 people connected through 4 independent paths (Node size = log of degree)

22. Centrality refers to (one dimension of) where an actor resides in a sexual network. Local: compare actors who are at the edge of the network to actors at the center Global: compare networks that are dominated by a few central actors to those with relative involvement equality Network Topology: Centrality and Centralization

23. Centrality example: Add Health Node size proportional to betweenness centrality Graph is 45% centralized

24. Centrality example: Colorado Springs Node size proportional to betweenness centrality Graph is 27% centralized

25. Network Topology: Centrality and Centralization Rothenberg, et al. 1995. "Choosing a Centrality Measure: Epidemiologic Correlates in the Colorado Springs Study of Social Networks." Social Networks: Special Edition on Social Networks and Infectious Disease: HIV/AIDS 17:273-97. Found that the HIV positive actors were not central to the overall network Bell, D. C., J. S. Atkinson, and J. W. Carlson. 1999. "Centrality Measures for Disease Transmission Networks." Social Networks 21:1-21. Using a data-based simulation on 22 people, found that simple degree measures were adequate, relative to complexity Poulin, R., M.-C. Boily, and B. R. Masse. 2000. "Dynamical Systems to Define Centrality in Social Networks." Social Networks 22:187-220 Method that allows one to compare across non-connected portions of a network, applied to a network of 40 people w. AIDS Measures research:

26. Timing Sexual Networks A focus on contact structure often slights the importance of network dynamics. Time affects networks in two important ways: 1) The structure itself goes through phases that are correlated with disease spread Wasserheit and Aral, 1996. “The dynamic topology of Sexually Transmitted Disease Epidemics” The Journal of Infectious Diseases 74:S201-13 Rothenberg, et al. 1997 “Using Social Network and Ethnographic Tools to Evaluate Syphilis Transmission” Sexually Transmitted Diseases 25: 154-160 2) Relationship timing constrains disease flow a) by spending more or less time “in-host” b) by changing the potential direction of disease flow

27. Sexual Relations among A syphilis outbreak Jan - June, 1995 Rothenberg et al map the pattern of sexual contact among youth involved in a Syphilis outbreak in Atlanta over a one year period. (Syphilis cases in red) Changes in Network Structure

28. Sexual Relations among A syphilis outbreak July-Dec, 1995

29. Sexual Relations among A syphilis outbreak July-Dec, 1995

30. Data on drug users in Colorado Springs, over 5 years

35. What impact does this kind of timing have on disease flow? The most dramatic effect occurs with the distinction between concurrent and serial relations. Relations are concurrent whenever an actor has more than one sex partner during the same time interval. Concurrency is dangerous for disease spread because: a) compared to serially monogamous couples, and STDis not trapped inside a single dyad b) the std can travel in two directions - through ego - to either of his/her partners at the same time

36. 0 400 800 1200 01234567 Concurrency and Epidemic Size Morris & Kretzschmar (1995) Monogamy Disassortative AssortativeRandom Population size is 2000, simulation ran over 3 ‘years’

37. Concurrency and disease spread Variable Constant Concurrent K 2 Degree Correlation Bias Coefficient 84.18 357.07 440.38 -557.40 982.31 Adjusting for other mixing patterns: Each.1 increase in concurrency results in 45 more positive cases

38. B C E DF A 2 - 5 3 - 7 0 - 1 8 - 9 3 - 5 A hypothetical Sexual Contact Network

39. B C E DF A The path graph for a hypothetical contact network

40. Direct Contact Network of 8 people in a ring

41. Implied Contact Network of 8 people in a ring All relations Concurrent

42. Implied Contact Network of 8 people in a ring Mixed Concurrent 2 2 1 1 2 2 3 3

43. Implied Contact Network of 8 people in a ring Serial Monogamy (1) 1 2 3 7 6 5 8 4

44. Implied Contact Network of 8 people in a ring Serial Monogamy (2) 1 2 3 7 6 1 8 4

45. Implied Contact Network of 8 people in a ring Serial Monogamy (3) 1 2 1 1 2 1 2 2

46. Timing Sexual Networks Network dynamics can have a significant impact on the level of disease flow and each actor’s risk exposure This work suggests that: a) Disease outbreaks correlate with ‘phase-shifts’ in the connectivity level b) Interventions focused on relationship timing, especailly concurrency, could have a significant effect on disease spread c) Measure and models linking network topography to disease flow should account for the timing of romantic relationships

47. Problems, Limitations & Future Directions Data Theoretically, STDs travel through a complete network, and thus that would be the ideal data to have. Practically, this is extremely difficult and very expensive Ego-network data are the easiest to collect, but limited. They cannot capture extended effects of network structure Partial network data is thus the most realistic hope we have for combining network insights with data. Future strategies should focus on developing methods for selecting partial network data that maximizes network coverage & developing statistical and simulation techniques that can bridge the local/partial data and global data divide

48. Linking non-sexual relations to sexual networks Problems, Limitations & Future Directions Consider another look at the data from Colorado Springs: The circled node is HIV positive.

49. Linking non-sexual relations to sexual networks