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Original article
Improved measures of racial mixing among men who have sex with men using Newman's assortativity coefficient
  1. Daniel D Bohl1,
  2. Willi McFarland2,
  3. H Fisher Raymond2
  1. 1School of Public Health, University of California, Berkeley, California, USA
  2. 2San Francisco Department of Public Health, San Francisco, California, USA
  1. Correspondence to H Fisher Raymond, San Francisco Department of Public Health, 25 Van Ness Avenue, Suite 500, San Francisco, CA 94102-6033, USA; hfisher.raymond{at}sfdph.org

Abstract

Objective To measure sexual mixing among racial groups of men who have sex with men (MSM).

Methods The authors explore its potential impacts, making two methodological advancements over previous work. First, the authors pioneer the use of Newman's assortativity coefficient to characterise mixing among MSM. Second, the authors examine mixing at the level of primary ties and at the level of secondary ties.

Results Results from the 1142-participant sample suggest that MSM are highly assortative by all races at the secondary level.

Conclusions Networks of MSM may be more tightly contracted around racial groupings than previously supposed. These groupings may lead to increased HIV transmission in certain racial groups.

  • Men who have sex with men
  • sexual mixing
  • race/ethnicity
  • assortativity
  • HIV
  • herpes
  • men
  • epidemiology
  • AIDS
  • HSV-2
  • street youth
  • homosexual
  • sexual behaviour
  • risk behaviours

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Introduction

There exist substantial racial disparities in both prevalence and incidence of HIV among men who have sex with men (MSM) in the USA—in particular, black MSM have relatively high rates,1 2 while Asian/Pacific Islander MSM have relatively low rates.3 4 Racial disparities generally cannot be explained by differences in individual risk behaviours (ie, condom use, number of sexual partners, etc); however, recent studies suggest that they may be explained by differences in the sexual networks in which MSM of the various races participate.5–9 One such study by Raymond et al8 examined levels of same-race sexual partnering among MSM and found that black MSM have a threefold higher level of same-race sexual partnering than would be expected from partnering by chance alone, while MSM of other races have much lower levels. The association may imply that the networks of black MSM are more tightly interconnected than those of MSM of other races, which could potentiate both more rapid spread and higher sustained prevalence of infection with HIV.

This piece is an extension of and methodological improvement upon Raymond et al.8 There are two primary improvements. First, Raymond et al sampled individuals from the population of MSM and asked about the race of their five most recent partners. In doing so, the authors were, in essence, sampling the partnerships—or, in network terminology, the primary ties—of the sexual network of MSM. Each primary tie consisted of a participant paired with one of the partners he described. However, sexual networks are defined by the natures of their primary ties and by the natures of their secondary ties, each of which is composed of two primary ties that share one common individual. For example, individuals' partners' other partners' HIV statuses can have a substantial impact on their risks of acquiring HIV. However, the extent to which individuals tend to connect partners of the same or different HIV statuses cannot be characterised by merely observing sampled primary ties. Rather, one must investigate the HIV statuses of sets of three connected individuals or secondary ties. In parallel, we posit, in addition to studying the extent to which MSM select partners of their own race, it is also helpful to characterise the extent to which MSM, who are tied at the secondary level, share the same race.

Second, Raymond et al8 examined sexual mixing by comparing, for each race, the number of observed same-race sexual partnerships among the sample to the number of same-race partnerships expected, given a hypothetical random mixing scenario. However, a more sophisticated approach is to evaluate sexual mixing from the perspective of assortativity. Assortativity is a measure of the correlations between properties of entities in a network that are tied together. For example, in a sexual network in which there is high assortativity at the level of primary ties, persons tend to choose partners of their same race; in a sexual network in which there is no assortativity, persons tend to choose partners without respect to race; in a sexual network in which there is disassortativity, persons tend to choose partners of races different than their own. Assortativity can be characterised using Newman's assortativity coefficient, described in detail in a paper published by Newman.10 The coefficient ranges from 1 to −1, where 1 is perfect assortativity (every tie connects individuals of the same types) and 0 is no assortativity or random mixing, and some value between 0 and −1 (the value varies) is perfect disassortativity (every tie connects individuals of different types).

In this context, among the sample of MSM examined in Raymond et al8 and using Newman's methods of characterising assortativity from sampled ties, we characterise the extent to which MSM who are tied at the primary level share the same race, as well as characterise the extent to which MSM who are tied at the secondary level share the same race.

Methods

We analysed data from Assort!, a study of serosorting, conducted in 2008. Assort! recruited MSM in San Francisco during 2008 using time–location sampling, a venue-based method developed to sample hard-to-reach populations throughout the USA and the world.11–18 Formative research mapped venues and times where MSM congregate to generate a list of venue–day–time (VDT) periods from which a random sample was drawn. At each randomly selected VDT period, research staff systematically intercepted men entering a predetermined area, assessed eligibility and invited eligible men to participate. Eligibility criteria were being men, age 18 years or older, a resident of the San Francisco or nine other Bay Area counties and approached by the staff at the randomly selected VDT period.

Through self-administered hand-held computers, participants were first asked questions about their own race/ethnicity, other demographic characteristics and sexual risk factors. They were then asked similar questions about each of up to their five most recent partners in the previous 6 months. The self-reports of race/ethnicity for both participants and partners were categorised as ‘Asian’ (for ‘Asian’ or ‘Native Hawaiian/Pacific Islander’), ‘African–American’, ‘Caucasian’ or ‘Latino’ (for ‘Latino/Hispanic’). Only participants classified as MSM (defined as either identifying as gay or bisexual or having had anal or oral sex with a man during the previous 12 months) and only partners described as men were included in this analysis.

To determine HIV status of participants, on-site pre-test counselling was done and oral fluid specimens were collected for HIV testing. To determine the HIV serostatus of partners, we asked each participant about each partner, ‘To the best of your knowledge, what was this partner's HIV status when you had sex for the first time?’

Primary ties (or sexual partnerships) that were included in the study consisted of each participant paired with each of the partners he described; hence, each participant described between 0 and 5 primary ties. Secondary ties that were included in the analysis consisted of each partner described by a participant paired with each of the other partners described by that participant; hence, each participant could describe between 0 and 10 secondary ties (figure 1).

Figure 1

An example participant with five partners, contributing five primary ties and 10 secondary ties to the analysis.

Data were tabulated in Stata V.11.0, and Newman's assortativity coefficient was calculated from those tabulations in Excel 2008 using the following equation from Newman10:r=ieiiιaibi1ιaibi,(1)where i is a given race, eii is the frequency of ties connecting two MSM of race i and ai and bi are the frequency of MSM of race i (for primary ties, ai corresponds to frequencies among participants and bi to frequencies among partners; for secondary ties, ai corresponds to frequencies among the more recent partners and bi to frequencies among the less recent partners).

First, among primary ties, the assortativity coefficient was calculated for assortativity by all four races and then for assortativity by each race alone. This was then repeated among secondary ties, with an additional analysis stratified on whether or not the participant was of each race in question. Finally, in order to investigate whether any of the observed assortativity by race is driven by serosorting, we conducted parallel investigations among only ties in which participants tested negative for HIV and partners were reported to be ‘negative’ for HIV by the participant.

The variance of the estimate of the mean and corresponding 95% CIs were calculated using the following equation from Newman10:σr2=1Miaibi+[iaibi]2iai2biiaibi21iaibi,(2)where σr2 is the variance and M is the total number of ties. However, because this equation assumes that the ties were independently sampled, M was modified to account for potential similarity between ties that were reported by the same participant. We made the most conservative assumption—that the ties of each participant are identical. Correspondingly, in calculating SEs, we reduced M from the number of ties to the number of participants describing ties at the given level, inflating the SEs and, correspondingly, the 95% CIs, appropriately.

The study was reviewed and approved by the Institutional Review Board of the University of California, San Francisco.

Results

Two thousand five hundred and fifty-eight individuals were approached, 1769 were eligible, 1305 completed the survey and 1213 were classified as MSM. One thousand one hundred and forty-two MSM could be classified as one of the four races, and all further analyses were conducted among only them. Of these, 160 (14.0%) were categorised as Asian, 98 (8.6%) as African–American, 243 (21.3%) as Latino and 641 (56.1%) as Caucasian. Also of these, 959 participants reported at least one partner, in sum describing 3473 partners, or primary ties. On average, Asian participants described 2.8 eligible partners (95% CI 2.5 to 3.2), African–American 2.9 (95% CI 2.5 to 3.2), Latino 3.1 (95% CI 2.8 to 3.3) and Caucasian 3.1 (95% CI 3.0 to 3.3). Among partners, 496 partners (14.3%) were categorised as Asian, 248 (7.1%) as African–American, 464 (13.4%) as Latino and 2265 (65.2%) as Caucasian. Table 1 displays the numbers of primary ties tabulated by participant and partner race.

Table 1

Numbers of participants and partners by race, constituting 3473 primary ties

Table 2 displays similar information for secondary ties (discussed in the paragraph that follows).

Table 2

Numbers of partner As and partner Bs by race, constituting 5749 secondary ties

Newman's coefficients for assortativity by race at the level of primary ties are shown in table 3. The assortativity coefficient for overall assortativity by race at the level of primary ties was 0.06 (95% CI 0.03 to 0.09). The assortativity coefficient for assortativity by Asian race was 0.03 (95% CI 0.00 to 0.06), by African–American was 0.21 (95% CI 0.19 to 0.24), by Latino was 0.06 (95% CI 0.03 to 0.09) and by Caucasian was 0.03 (95% CI −0.02 to 0.07).

Table 3

Assortativity by race among primary and secondary ties between MSM, San Francisco, 2008

At least two partnerships were described by 791 participants, in sum describing 5749 secondary ties. Table 2 displays the numbers of secondary ties tabulated by partner A and partner B race. Newman's coefficients for assortativity by race at the level of secondary ties are shown in table 3. The assortativity coefficient for overall assortativity by race at the level of secondary ties was 0.36 (95% CI 0.33 to 0.40). The assortativity coefficient for assortativity by Asian race was 0.46 (95% CI 0.43 to 0.50), by African–American 0.27 (95% CI 0.24 to 0.29), by Latino 0.17 (95% CI 0.13 to 0.20) and by Caucasian 0.43 (95% CI 0.39 to 0.48). When the participant was of the race in question, the assortativity coefficient for assortativity by Asian race was 0.36 (95% CI 0.27 to 0.46), by African–American 0.39 (95% CI 0.24 to 0.55), by Latino 0.16 (95% CI 0.09 to 0.24) and by Caucasian 0.41 (95% CI 0.35 to 0.47). When the participant was not of the race in question, the assortativity coefficient for assortativity by Asian race was 0.48 (95% CI 0.44 to 0.52), by African–American 0.17 (95% CI 0.15 to 0.20), by Latino 0.16 (95% CI 0.13 to 0.20) and by Caucasian 0.47 (95% CI 0.39 to 0.54). For assortativity by Asian, Latino and Caucasian at the level of secondary ties, the coefficient did not differ whether or not the participant was of the race in question (95% CIs for the two strata overlap). However, for assortativity by African–American, the coefficient was significantly higher when the participant was of the race in question compared with when the participant was not of the race in question (95% CIs for the two strata do not overlap).

The final analysis was conducted to investigate the contribution of serosorting to the observed assortativity by race. For this analysis, 652 participants who were not infected with HIV reported on 1739 primary ties in which the partner was also not infected with HIV. Similarly, 433 participants who were not infected with HIV reported on 2211 secondary ties in which both partners were not infected with HIV. Newman's assortativity constants for assortativity by race among these ties are shown in table 4.

Table 4

Assortativity by race among primary and secondary ties between HIV-uninfected MSM, San Francisco, 2008

Discussion

We applied Newman's method of characterising assortativity to a sexual network of MSM in San Francisco in order to characterise the extent to which members of the same race are connected to each other at the levels of primary and secondary ties. Consistent with previous findings using different methods,5 6 8 we find that assortativity by African–American is relatively high at the primary level, having an assortativity coefficient of 0.21 (95% CI 0.19 to 0.24), while assortativity by Asian, Hispanic and Caucasian is much lower, having positive assortativity coefficients that do not exceed 0.06 and/or that have 95% CIs not excluding 0. These results suggest that at the partnership level, MSM assort by African–American but not by Asian, Latino or Caucasian. As discussed previously,8 the high levels of assortativity may imply that the networks of black MSM are more highly interconnected than those of other MSM, which could potentiate both the more rapid spread and higher sustained prevalence of infection with HIV.

Unlike previous analyses, we extended our exploration of racial mixing to the level of secondary ties, addressing the question: To what extent do MSM have partners who are of the same race as each other? We find that assortativity by all four races at the level of secondary ties is substantially higher than would be expected from random mixing (all four assortativity constants are relatively high and all four 95% CIs exclude 0). Importantly, for assortativity by Asian, Latino and Caucasian, because there was little or no assortativity at the level of primary ties, the high levels of assortativity at the secondary level are probably not driven by MSM selecting partners of their same race. Rather, the high levels are likely the result of a tendency on the parts of many MSM to select partners of a particular race (no more or less likely to be their own race compared with random mixing) and, hence, to select partners of the same race as each other. For these three races, high levels of assortativity are present even when the shared partner is not of the race in question (see stratified assortativity constants), reinforcing that the association is a product of MSM selecting partners of the same race as each other over-and-above any same-race preference observed among primary ties.

For assortativity by African–American, because there was a high level of assortativity at the primary level, the high level of assortativity at the secondary level is likely a product of both the tendency for MSM to select partners who are of the same race as each other and a tendency for MSM to select partners who are of the same race as their own. These two contributing factors can each be observed by stratifying on the race of the shared partner: assortativity by African–American at the level of secondary ties is significantly higher when the shared partner is African–American compared with when the shared partner is not African–American (95% CIs do not overlap), suggesting that assortativity by African–American at the primary level tightens the network at the secondary level. Yet, even when the shared partner is not African–American, the 95% CI excludes 0, indicating that assortativity is above what would be expected from random mixing, and that an important component of the assortativity by African–American among secondary ties also arises from the tendency for MSM to select partners who are of the same race as each other.

The investigation limited to ties in which both partners and participants were not infected with HIV yielded several interesting results. For assortativity by all races at the primary level, the assortativity constant was similar to that among all ties, suggesting that serosorting does not significantly drive assortativity by all races. However, the 95% CI for assortativity by African–American limited to uninfected MSM fell below and excluded the CI for assortativity by African–American among all ties. Nevertheless, assortativity by African–American remained above that by the other races in the limited analysis. This suggests that part—but far from all—of the assortativity by African–American observed at the primary level is driven by men choosing partners of their own HIV status. That is, the observed, particularly strong preference of many men for partners that match their own African–American or not-black racial category may be driven in part by the desire to match HIV statuses. No such differences between the limited and complete analyses were observed at the secondary level.

Taken together, these results imply that individuals of the same race are connected secondarily far more often than would be predicted from either random mixing or observed levels of same-race partnering at the primary level. The associations seem to result from a preference on the parts of MSM for selecting partners who are of a particular race and, hence, a tendency for MSM to select partners who are of the same race as each other—a preference that exists above-and-beyond any preference to select partners who are of the same race as their own. The results suggest that the sexual networks of MSM are far more contracted around minority groupings than might be otherwise assumed, which could be hazardous for all racial groups. While the evidence presented here does not yet warrant any recommendations to public health practitioners, it does raise the question of whether work to integrate the sexual networks across racial lines might serve to decrease rates of HIV. Because assortative mixing has been shown to increase sexually transmitted disease burden within ethnic groups where disease prevalence is already elevated,19 the tightening observed at the secondary level might be particularly harmful for MSM in groups with already elevated prevalence (ie, black MSM). While not alone giving rise to it, this amplifying factor could play a previously unrecognised yet powerful role in enhancing and maintaining the disparity in rates of HIV between races.

There are several limitations to this study. First, our findings carry with them all the caveats of a cross-sectional self-report survey, including the potential for sampling bias, reporting bias and unmeasured confounders. In particular, any bias in the reporting of partner race could have substantial impacts on our results. Additionally, our survey did not define the duration or concurrency of partnerships, information that is potentially important to further defining network risk. These factors are, however, studied extensively elsewhere.6 7 Finally, our findings may not be applicable outside of San Francisco. Nonetheless, because our associations were strong and robust and because we conservatively adjusted 95% CIs for clustering by participant, we believe that our results do reflect high-quality estimates of these phenomena among MSM in San Francisco.

We conclude by pointing out that data derived from sampled individuals can never fully describe a network; unfortunately, data fully describing social networks are difficult to obtain. However, we emphasise that our partner-by-partner approach to the questionnaire, along with our partner-to-partner approach to the analysis, promotes a better understanding of the network than can any approach that only examines assortativity (or any network phenomena) at the primary level. We hope our findings will encourage those interested in understanding the disparities between races to continue to consider the extent to which the sexual networks of individuals are modulating subpopulation-level risk for infection with HIV. Moreover, we hope this exercise demonstrates the benefits of characterising assortativity beyond the level of primary ties and that these methodological advances can be applied in other fields to research questions that also require the elucidation of mixing patterns from networks that can only be sampled.

Key messages

  • Sexual networks of men who have sex with men are concentrated racially.

  • Racially concentrated networks may increase risk of HIV infection if a particular group has higher HIV prevalence.

  • Measures of mixing may help understand differences in HIV prevalence and incidence.

References

Footnotes

  • Funding This study was funded by the National Institute of Mental Health (Grant number: R01MH077509).

  • Competing interests None.

  • Ethics approval University of California, San Francisco CHR.

  • Provenance and peer review Not commissioned; externally peer reviewed.