1. The Relative Contribution of Sex and Drug Ties to STI-relevant Network Connectivity James Moody & jimi adams Duke & Ohio State University Sunbelt XXVI – Annual Meetings of the International Network for Social Network Analysis – Vancouver, BC Thanks to Steve Muth, Martina Morris, John Potterat, Rich Rothenberg & the network modeling group at UW. Supported by NIH grants DA12831 and HD41877

2. Background: STI Epidemic transmission rests on at least two network points: a)The network must connect a wide portion of the population, which is ultimately a question of network reach – how do type of ties affect: - The size of the largest component (potential extent) - The redundancy of the network (robustness for transmission) b) A disease has to pass from an infected to a susceptible at the dyad level -The likelihood of a dyadic transmission rests on the type of tie. While difficult to estimate: p( transmission | sexual ties) < p( transmission drug ties)

3. Connectivity & Tie Type Structural constraints for connectivity by type of tie: Heterosexual networks cannot have closed triangles, which makes cliques impossible. This limits “recursion” and helps spread ties quickly to the wider population. Drug-sharing ties allow closed triads, which are the building blocks for cliques. These are essential for building robust structures.

4. African Americans have substantially higher rates of STIs than whites –National Surveys of Women and Men: “any STI ever” approximately double at bivariate and OR 2-3 more likely in multivariate analyses (Tanfer et al. 1995) –Bacterial STIs as much as 10-20 times more frequent (Aral 1996) –New cases of HIV/AIDS are strongly disproportionately high among African Americans Why? –AA have more partners, greater concurrency rates, and strongly differential core/non-core mixing patterns. –There may also be a difference in type of tie that provides a micro- structural analog to mixing pattern differences. Race, Connectivity & Tie Type

5. Men Women Dyadic Transmission Routes Proportion of AIDS Cases among Adults and adolescents, by Transmission Category and Race/Ethnicity Cumulative through 2003—United States

6. Can difference in the types of ties help explain race differences in STI rates? While we know different types of ties facilitate the dyadic transmission of BBIs, there is less understanding of how different types of ties bridge population groups. If race correlates with type of dyadic contact, and type of contact affects transmission rates, then we might get some purchase on the population heterogeneity of STI rates.

7. Method: We approach this problem as a general question of network connectivity. How do different types of relations knit together a population? We can assess the connectivity contributions of each type of tie by selectively removing ties from a network and assessing the change in a number of connectivity-relevant measures. That is: a) Select at random n ties of type k b) calculate the connectivity measures on the resulting network c) repeat this many times (here 500 at each setting). We do this for Sex, Drug, Sex & Drug, and random ties, removing between 2% and 12% of the total ties observed in the network. How do different types of ties connect a network?

8. Colorado Springs – Project 90 CDC Funded HIV Transmission Risk in high risk population: –Prostitutes and their sex partners (heterosexual) –IDU 595 respondents –Face-to-face interviews –5 year open cohort design –Link tracing design with an ego-network module (linked ego-nets) to assess the size, structure and epidemic potential of the high-risk partnership network We examine two networks: The “respondent only” network of ties among respondents The “full reach” network of ties that include nominations outside the respondent set. Data

9. Tie Type Connectivity Contributions Measuring connectivity: Size of the largest component Captures the ultimate potential extent of STI diffusion Relative size of the largest bi-component A measure of the extent of the most robust portion of the network Relative average distance among pairs in the networks Transmission likelihood is higher if there are many shortcuts in the network. We measure this relative to the largest component. Transitivity Ratio As ties revert back on themselves (“recursion”) transmission is reinforced, but not spread as widely. Racial Segregation index Freeman’s segregation index. Extent of cross race ties compared to random (1 = completely segregated, 0 = random mixing).

10. Project 90: Respondent only Contact Network

11. Frequency Distribution of Tie Type Tie TypeR-R TiesAll Ties Sex Only 200 (15.4) 2400 (17.3) Drug Only 853 (65.8) 9686 (69.7) Sex & Drug 243 (18.8) 1815 (13.1) (Numbers presented are counts and column-percentages)

12. Distribution of Tie Type

13. Frequency Distribution of Tie Type by Racial Mixing R-R TiesAll Ties Sex Only Drug Only Sex& Drug Sex Only Drug Only Sex& Drug WW812918610204507835 BB17148412471521244 BW44196564781112305

14. Node-level Mixing by Tie-Type Sex Only Drug Only Both Only Bridge Only Both & Bridge White1283 (35.2) 1022 (28.1) 42 (1.2) 944 (25.9) 353 (9.7) Black418 (34.6) 365 (30.2) 12 (1.0) 305 (25.3) 108 (8.9) Total2009 (34.5) 1717 (29.5) 68 (1.2) 1503 (25.8) 530 (9.1) (Numbers presented are counts and row-percentages)

15. Odds Ratios for presence of Ties Based on Dyad Racial Similarity (RR dyads only) Any TiesSex Only Ties Drug Only Ties Sex & Drug Ties Same Race1.66 (<.001) 1.41 (0.046) 1.67 (0.004) 1.85 (<.001) Both White1.29 (0.09) 1.36 (0.067) 1.25 (0.112) 1.38 (0.064) Both Black4.78 (<.001) 2.26 (0.008) 5.19 (<.001) 5.21 (0.002) Both Hispanic 1.68 (0.026) 0.71 (0.64) 1.64 (0.07) 2.71 (0.006) (Values in parentheses are QAP p-values for the relevant dyadic logit model)

16. Effect of Edge Removal on Size of the Giant Component Results

17. Relative size is (observed size) / (giant component size) Effect of edge removal on Relative Size of the Largest Bicomponent Results

18. Relative distance is (observed distance) / (giant component size) Effect of edge removal on Relative Average Distance Between Nodes Results

19. Effect of edge removal on Graph Transitivity Ratio Results

20. Segregation is Freeman’s (1972) Segregation Index using a 4 category race variable Effect of edge removal on Racial Segregation Index Results I

21. Summary RR only network: Across all connectivity measures, sex ties create the greatest extent. Removing sex ties:  Quickly decreases the size of the largest component  Leaves the network with a relatively larger biconnected core  Increases average distance faster than drug or random ties  Increases the transitivity (redundancy) of the network  Increases the racial segregation of the network. This suggests that, within the respondent sample, sex ties create “tendrils” that reach out into the wider population, but do so in a relatively sparse way, with (comparatively) fewer re-connections to the strongest core(s) of the network. Relations that have both sex and drug content are often distinct from random, but not in a consistently “negative” manner. Here, there appear to act in a middling role.

22. Results: Full Contact Network

24. Race-specific Contour distributions

25. Note the distribution of edge types. The large “eastern” cluster is where most of the sex is happening in this network. Results: Full Contact Network Tie-specific edge distributions

26. Full Network Results

31. Summary of full network effects: The overall story is much the same: the most dramatic effects on connectivity are due to sex ties. Sex ties spread the network to the widest population, but that connectivity is somewhat fragile: it does not involve the same level of redundancy that drug ties have. The seemingly unique role of “both” ties identified in the RR network are not nearly as pronounced in the full network. The segregation effects are consistent with the RR network findings, but two points worth noting: a)The base level of segregation is higher. This means that sampled nodes were more likely to have cross race ties than non-sampled nodes. b) while sex ties play the same role here as in the RR only network, the effect is not as strong (note the scale of that last figure), suggesting that the race x tie-type effect may not be as strong as suggested in the RR network.

33. Network Transmission of STI & Relation Type The probability of dyadic transmission varies by relation type: Source: Australian National Council on AIDS, Hepatitis C and Related Diseases, Bulletin No. 28, July 2001: Table 2

35. Explanations for Racial STD Differences Individual Risk: –Concurrency is significantly higher for blacks than whites –Others have suggested numerous other pathways affecting individual risk, including poverty, healthcare access and use and community prevalence rates (e.g., Aral 1996; CDC 1995) and drug use (Kottiri et al 2002) –Number of sexual partnerships (Santelli et al 1998)

36. Racial Differences in Numbers of Sexual Partners >1 66 Odds ratios, controlling for age, residence, marital status, alcohol and drug use, and age at first intercourse (Source Santelli et al 1998) (*’s – difference significant for p<0.05)

37. Explanations for Racial STD Differences Individual Risk: –Concurrency measures (Morris and Kretzchmar 1995) are significantly higher for blacks than whites (Adimora et al. 2002; Billy et al. 1993; Manhart et al. 2002; Ford and Norris 1997) –Others have suggested numerous other pathways affecting individual risk, including poverty, healthcare access and use and community prevalence rates (e.g., Aral 1996; CDC 1995) and drug use (Kottiri et al 2002) –Numbers of sexual partnerships (Santelli et al 1998) Epidemiological models based on individual behaviors alone misestimate STI risk (Aral 2002), and sexual network structure can explain differences not observed through individual level modeling, such as: –Network bridges can spread an STI into a population where it was not otherwise present (Morris et al. 1996) Observed more frequently for blacks than whites (Laumann and Youm 1999) –“Sexual segregation” can isolate an STI in a particular population