Sexual Role and Transmission of HIV Type 1 among Men Who Have Sex with Men, in Peru

Abstract

In Latin America, men who have sex with men (MSM) have traditionally practiced role segregation—that is, the adoption of a fixed role (insertive or receptive) rather than a versatile role (both practices) during anal sex. Previous modeling has shown that role segregation may yield a lower incidence of human immunodeficiency virus (HIV) type 1 infection, compared with role versatility; however, the modeling assumed no risk of acquiring HIV-1 during insertive sex, which is now recognized as unlikely. We reexamine the issue by use of a deterministic model incorporating bidirectional transmission and data from a cohort study of MSM in Lima, Peru, to demonstrate the potential effects of role segregation on the trajectory of the HIV-1 epidemic. In Lima, 67% of MSM reported segregated roles in their recent male partnerships. A population of MSM with identical contact rates but complete role versatility would have twice the prevalence of HIV-1 infection throughout the epidemic’s first 3 decades. Preferential mixing among versatile MSM does not change overall prevalence but affects which individuals become infected.

Most epidemiological research focuses on the relationships between individual-level attributes and behaviors, on the one hand, and individual- or population-level phenomena, on the other hand. For sexually transmitted infections (STIs), these are connected through the patterns occurring at an intermediate level—that is, the network of partnerships. The analysis of partnership patterns has begun to play an important role in STI research during the past 2 decades, initially through the study of mixing matrices [1, 2] and more recently in analyses of more-detailed network patterns [3, 4]. Here, we examine a mixing pattern arising from individual-level factors and having implications for STI transmission among men who have sex with men (MSM), namely, sexual role segregation. In Latin America, MSM have traditionally chosen a fixed role over time for their po sition in anal sex, by being identified as either the insertive or the receptive partner but not both. These role identities constrain who can have sex with whom in MSM partnerships, which, in turn, can strongly influence the trajectory of the HIV-1 epidemic in the population as a whole.

Role segregation among MSM has been described for a variety of settings, including Mediterranean Europe [5], Amsterdam [6], and Seattle (M. Golden, personal communication), but is perhaps best documented in Latin America [7–11]. Trichopoulos et al. [5] first noted the potential for role segregation to influence HIV-1 transmission dynamics. They argued that, in populations with role segregation, those most easily infected (receptive partners) are in turn less likely to transmit infection, slowing the chain of infection. In populations with role versatility, on the other hand, the person who is easily infected through unprotected receptive anal (URA) sex can then efficiently transmit infection through unprotected insertive anal (UIA) sex. Wiley and Herschkorn [12] modeled a version of role segregation and role assortativity (in which versatile MSM may choose each other as partners more or less than expected by chance) as a system of differential equations, solving explicitly at virus introduction and equilibrium. Their model showed the strong effects of both role segregation and role assortativity on endemic prevalence. Van Druten et al. [6] also modeled HIV-1 transmission but allowed for temporal changes in role category, incorporating data from Amsterdam on the reported roles of MSM during 2 consecutive 6-month intervals. However, they did not extend their analysis to the dynamics of long-term epidemics. In both modeling studies, the risk of HIV-1 acquisition from UIA sex was assumed to be 0. However, evidence now shows that UIA sex poses a nonnegligible risk of infection for the insertive partner [13].

In this article, we reexamine the potential effects of role segregation and patterns of role assortativity among MSM, on the HIV-1 epidemic. We use a mathematical model similar to that of Wiley and Herschkorn [12] but distinct in a number of important details, including the incorporation of bidirectional virus transmission. We use data on role behavior and partner selection from a partnership cohort study of MSM in Lima, Peru (a population in which seroprevalence has been previously estimated at 18.5% [14]), both to formulate the specific details of the model and to interpret the results in an empirical context.

In addition, we examine 2 related issues that help to clarify the context for role segregation and its implications. The argument for the importance of versatility suggests that it should be a population-level risk factor, rather than an individual-level one. If all MSM had the same number of partners, the prevalence of HIV-1 among receptive MSM (who have the riskier role) would be expected to be highest. Nevertheless, this pattern was observed in only 1 of 3 early studies in Mexico of the prevalence of HIV-1 among MSM that addressed sexual role [7], whereas 2 of the studies [15, 16] found the highest prevalence among versatile MSM. One explanation could be that versatile MSM average more unprotected sexual contacts than do nonversatile MSM. Another explanation could be that mixing is assortative by role: versatile MSM preferentially choose other versatile MSM as partners, whereas MSM who practice role segregation choose each other as partners, thus demonstrating role assortativity. Given the transmission-amplification effect of versatility, HIV-1 infection would then spread more rapidly among versatile MSM, even with the same level of activity in both groups. Thus, one goal was to examine the data from Peru for evidence supporting each hypothesis.

Our other goal was to examine the interrelationship between the behavior of MSM and sexual identity, since role segregation appears to be a fundamental dimension of both in Latin America. Latino MSM have traditionally identified themselves by using the terms activo or pasivo (i.e., exclusively preferring insertive or receptive anal sex, respectively), rather than the general term for homosexual identity [17]. In the last generation, new categories have become popular descriptors for those preferring a more versatile sexual repertoire (moderno in Peru or internacional in Mexico). The terms themselves suggest that versatility carries some level of sophistication, likely resulting from diffusion of an egalitarian, gay-identified homosexuality from the United States and Europe [8]. Although the identities activo, pasivo, and moderno theoretically equate with insertive, receptive, and versatile behaviors, respectively, in reality men may engage in behavior discordant with their identity for many reasons (experimentation, commercial sex work, or constraints on available partners). Although the behavior, not the identity, directly affects transmission of HIV-1, understanding the identity may help to explain the behavior and to design context-appropriate interventions.

SUBJECTS AND METHODS

Study population

In this first wave of a local-network longitudinal cohort study, we recruited MSM in Lima through outreach on the street, visits to businesses frequented by MSM, and flyers and ads in public and private settings frequented by MSM. Eligibility criteria included having had anal sex with a man in the previous 12 months, being HIV-1 negative (self-reported or as determined by testing at screening), being available for follow-up for at least 1 year, and having at least 1 of the following 5 high-risk criteria: (1) having 15 partners during the previous 6 months; (2) not using a condom during the last episode of anal sex; (3) trading sex for money during the previous 12 months; (4) having an STI at any point during the previous 6 months (self-reported or as determined by testing at screening); or (5) having a known HIV-1–positive partner during the previous 6 months. Questionnaires were administered by means of computer-assisted self-interviewing, to circumvent potential unwillingness to discuss sensitive issues face-to-face with a stranger, to skip unnecessary questions and clarify ambiguity en route, and to reduce transcription error. Staff recorded 4155 outreach contacts in the identification of 350 eligible MSM who expressed willingness to enroll. Of these, 254 MSM (73%) enrolled; 16 did not complete initial screening; 12 were deemed psychologically unable to provide informed consent; 31 tested positive for HIV-1 at screening; 6 were unavailable for follow-up; and 31 did not fulfill the risk criteria, despite initial statements to the contrary. Our own familiarity with the study population leads us to believe that both the recruitment strategies and study criteria disproportionately excluded married MSM who self-identified as heterosexual; these men are less versatile than those in our cohort, but they provide a bridge for HIV-1 transmission to women [14]. Informed consent was obtained from all subjects. The study was approved by the Human Subjects Committee of the University of Washington (Seattle), the Institutional Review Board of the US Naval Medical Research Center Detachment (Lima), and the Institutional Ethics Committee of the Asociación Civil Impacta Salud y Educación and the Asociación Via Libre (Lima).

The men were asked about their sexual identity and role identity (e.g., How do you classify yourself with respect to your sexuality? Homosexual, bisexual, heterosexual? What is your sexual role in the bedroom? Activo, pasivo, moderno?). Participants were asked to indicate the total number of male sex partners (oral and anal, receptive and insertive, and protected and unprotected) that they had had in the previous 3 months and the total number of female sex partners (oral, vaginal, and anal). The questionnaire included a local-network module [18] with detailed partner-specific questions on sex acts and the perceived role identities of partners, for the 3 most recent partners. Men were classified as insertive, receptive, or versatile on the basis of the detailed partner-specific data, since the 3-month data did not distinguish between insertive and receptive partners. Respondents classified as versatile reported at least 1 episode each of insertive and receptive anal sex with any of their last 3 male partners (either the same or different partners). In determining role behavior, we excluded female partners, who accounted for only 21 (3.5%) of 603 partners.

Development of the model for estimating effect of role segregation and role assortativity on the prevalence of HIV-1

We used a compartmental deterministic modeling framework, described by the series of ordinary differential equations spec-ified in the Appendix; here, we summarize its basic form and assumptions. The population was divided into 6 transmission-related states, defined by 3 roles (insertive, receptive, and versatile) and 2 categories of HIV-1 status (negative and positive). Individuals were assumed to pass through these states as a function of 3 life events: entrance into the sexually active pool of MSM, in 1 of the 3 roles; seroconversion; and departure from the sexually active pool of MSM (because of general aging, death, or AIDS-related death). We assumed no movement between role classes; they were considered to be fixed. The introduction of new HIV-1–negative individuals occurred at a constant rate; these individuals were assigned to role classes in proportion to the initial class sizes. Removal due to causes other than AIDS occurred, on average, 30 years after introduction to the sexually active pool, whereas HIV-1–negative individuals were removed 8 years after seroconversion.

Modeling infection transmission requires defining both the number of contacts between individuals in each group and the probability of infection, given a serodiscordant contact. For the latter factor, we assumed a 5-fold difference in infectivity between URA and UIA sex, on the basis of data reported by Vittinghoff et al. [13] (see Appendix), and conducted a brief sensitivity analysis for this difference. The former factor is itself a function of overall contact rate, group size, and role assortativity (i.e., the degree to which versatile MSM preferentially choose each other as partners, rather than those who practice role segregation, and vice versa). By definition, contact between 2 insertive or 2 receptive partners is nonexistent, and the def inition of random mixing under this constraint is not trivial. Wiley and Herschkorn [12] define random mixing as all non-prohibited partnerships being equally likely. However, this definition implies that versatile MSM have considerably more partners than do MSM who practice role segregation, since versatile MSM have more potential partnerships. We did not observe this pattern in our sample population. In our model, we instead assumed that the average number of partners for versatile MSM is the same as that for the entire population. In addition to being more consistent with our empirical findings, this assumption also provided a more neutral position for measuring the effects of versatility. We then defined a continuum for the examination of the effect of role assortativity. At one extreme is completely proportional (“random”) mixing, in which each versatile MSM is equally likely to partner with any other member of the population. At the other extreme is complete assortativity, in which versatile MSM partner only with other versatile MSM. The scale for the level of role assortativity was from 0 to 1, between the random and assortative end points, respectively. The relative size of the population of receptive MSM always declined initially over time, compared with that of insertive MSM, because of differences in infection transmission; the result is that receptive MSM have more partners and insertive MSM have fewer partners, compared with versatile MSM, which matched our data.

We explored output for a variety of versatility fractions, levels of role assortativity, and average rates of contact. The fraction of the population that is versatile and the level of role assortativity were each run at 11 levels (0.0–1.0, with a step of 0.1). The rate of unprotected anal contact had 5 values (unprotected anal contact with 18, 21, 24, 27, and 30 partners/year), which ranged above and below the mean value of 23.4 (rounded to 24) obtained from the data from Peru (table 1). In all model runs, the initial population size was 10,000 individuals; the initial prevalence of HIV-1 was 0.01 for each group; the initial nonversatile population was equally divided between insertive and receptive partners; and the number of new HIV-1–negative individuals was 2/day. We used a balanced study design, by observing the behavior of the system for all 605 combinations (11 × 11 × 5) of parameter values. We interpreted the results for the parameter combinations resembling the data from Peru and obtained approximations that summarize the output across the full range of combinations of parameter input.

Table 1.

Estimated no. of partners with whom respondents had unprotected anal sex, by reported sexual role of respondent.

Characteristic	Role of respondent with last 3 male partners			No anal sex	Total
	Insertive only	Versatile only	Receptive only
No. of respondents	50	84	97	23	254
No. of male partners in last 3 months
Median	2	5	5	1	4
Mean	3.50	12.52	16.99	1.57	11.50
Fraction of recent male partnerships that involved unprotected anal sex	0.40	0.47	0.56	NA	0.47
No. of male partners unprotected during anal sex, mean
In last 3 monthsa	1.4	5.8	9.5	NA	5.5
In last yearb	5.6	23.4	38.0	NA	21.8

NOTE. NA, not applicable.

^aEstimated by multiplying the mean no. of male partners in last 3 months by the fraction of recent male partnerships that involved unprotected anal sex.

^bEstimated by multiplying the mean no. of male partners unprotected during anal sex, in last 3 months, by 4.

Compartmental epidemic models are often examined by solving the underlying system of differential equations explicitly for 2 limits, the introduction of the pathogen (via the construct R₀ [i.e., the basic reproductive number]) and equilibrium. In a population with nonhomogeneous mixing, these limits do not reveal all the dynamics in between, which would be relevant to HIV-1 infection in countries like Peru. Instead, we obtained a numerical solution to the system of equations by using the default mixed Adams/Gear algorithm [19] in Mathematica (version 4.2; Wolfram Research) and examined the results at year 20, which corresponded roughly to the present day. Individual examination of many model runs revealed that they are still characterized by exponentially increasing prevalence. Readers who wish to explore a given set of parameters can obtain the Mathematica code for the model at http://www.stat.washington.edu/~goodreau.

RESULTS

Sexual identity, role identity, and role behavior for Peruvian MSM

Figure 1 shows responses by the cohort of Peruvian MSM for sexual identity, role identity, and role behavior. Only 1 in 3 MSM reported role versatility during anal sex with their last 3 male partners (84 [33.1%] of all 254 respondents; 84 [36.4%] of 231 respondents reporting any anal sex with last 3 partners). Many more reported receptive behavior, rather than insertive behavior, which we believe to be mostly a sampling artifact. Figure 2 cross-tabulates role identity with sexual identity and with role behavior. Sexual identity and role identity are indeed different, with 8 of 9 possible combinations appearing in this small data set. Nevertheless, they are highly interdependent (P<10^-11, Fisher’s exact test): men who self-identified as homosexual also tended to identity as pasivo or moderno, bisexual men tended to identify as activo or moderno, and heterosexual men tended to identify as activo. Concordant combinations of role identity and role behavior (indicated in figure 2B by underlined nos.) were significantly more common than the other combinations (P<.001, likelihood ratio test on nested log-linear models). Still, only approximately two-thirds of MSM reporting anal sex with their last 3 partners (155 [67.4%] of 231) had these concordant combinations. However, use of data for only 3 partners created a bias away from versatility; long-term versatile partners may have performed only 1 role with their last 3 partners by chance. This may explain the large number of moderno/insertive and moderno/receptive combinations (20 and 22 respondents, respectively).

Figure 1.

Sexual identity, role identity, and reported role with last 3 male partners, for cohort of 254 Peruvian men who have sex with men (MSM).

Figure 2.

Association of role identity with sexual identity (A) and role behavior (B). A, P<10^-11, Fisher’s exact test for independence, excluding nonresponders. B, Underlined nos. indicate concordant identity and behavior. Likelihood ratio tests on nested log-linear models were done for (main effects, concordance) vs. (main effects) (P<.001).

The mean numbers of all male partners (regardless of sex act or condom use) for the 3 role groups differed strikingly (P<.001, nonparametric Kruskal-Wallis test; table 1). The data for all 3 groups roughly followed a Poisson distribution, with the additional common phenomenon of heaping at round numbers. (A small number of extreme outliers appeared in the sample, as indicated by the large difference between median and mean values; responses to other questions suggested that most of these men engaged in commercial sex.) To estimate the differentials in unprotected anal sexual contacts by role class, we extrapolated to all partners by using the fractions for anal sex and condom use with the last 3 partners. As shown in table 1, these estimates suggest that, for versatile MSM, the number of unprotected anal sexual contacts with male partners was close to the population mean, with the number for receptive MSM higher and that for insertive MSM lower; thus, the mathematical form for our transmission model was shown to be better supported than that of Wiley and Herschkorn [12], at least by this population. This estimate also suggests that the higher prevalence of HIV-1 found among versatile MSM in some studies may not be due to higher contact rates.

Our cohort included many more receptive MSM than insertive MSM, and receptive MSM reported having had more partners; these 2 observations can only be consistent if versatile partners almost always took the insertive role or if our cohort was biased. Versatile MSM reported having taken the insertive or receptive role in anal sex in 59% (130/220) and 70% (153/ 220) of their recent contacts, respectively; therefore, the former explanation is not tenable. We thus have internal evidence that our cohort was biased away from inclusion of insertive MSM, as suspected. We address the implications of this in our analysis in the Discussion.

Role assortativity is considered in figure 3, which shows the role identities of respondents cross-tabulated with the presumed role identities of partners; note that respondents may have been included in the data up to 3 times. Although the validity of perceived partner role remains uncertain, we note that 43.5% (110/253) of respondents reported moderno identity and that they perceived 46.6% (122/262) of their partners as being moderno, suggesting proportional mixing. However, activo and pasivo respondents perceived only 10.8% and 4.6% of their partners, respectively, as moderno, which is lower than the 39% and 32% expected with proportional mixing in this population. Thus, the evidence for role assortativity in this population was equivocal. Both sampling and imperfect knowledge of partner identity are likely to have been responsible.

Figure 3.

Respondent role identity and respondent’s perception of partner’s role identity (n = 582), for any of the last 3 partners.

Effect of proportion of versatile MSM and of role assortativity on HIV-1 endemic prevalence and relative prevalence by role behavior groups

Figure 4 shows prevalence over time in simulated populations resembling our Peruvian cohort, with 30% of MSM being versatile and both versatile MSM and the MSM population as a whole having an average of 24 unprotected anal sexual contacts per year (line A). Because of the conflicting evidence for role assortativity in the data for the Peruvian cohort, these model runs were based on random mixing. Line B shows a population with the same contact rate but 100% versatility. For the first 30 years of the epidemic, the prevalence of HIV-1 in these 2 populations differed roughly by a factor of 2; endemic prevalence in the simulation modeled on the Peruvian cohort was ~20% lower than that in the population with complete versatility. This implies that role segregation in a population resembling our Peruvian cohort can keep the prevalence of HIV-1 among MSM at approximately one-half what it would be without that segregation, for decades. If MSM were segregated even more, as they may have been in the past, the prevalence of HIV-1 would be lower (line C, same contact rate but 10% versatility), although the difference was not nearly as large. For comparison, figure 5 shows results for the same model runs for 3 other ratios between insertive and receptive infectivity. For each, the average of insertive and receptive infectivity was the same; thus, the curve is the same for the population with complete versatility, across models. Not surprisingly, the effect of segregation was strongly influenced by the ratio between the 2 probabilities of transmission and becomes quite weak by ~1:2.

Figure 4.

HIV-1 prevalence in 3 simulated populations of men who have sex with men (MSM), by year of epidemic. The mean no. of partners/ year was 24 in all populations, and the proportion of MSM with versatile sexual behavior was 30% (line A; comparable to the Peruvian cohort), 100% (line B), and 10% (line C). All populations had random mixing and a 5-fold difference in infectivity, for receptive vs. insertive behavior.

Figure 5.

HIV-1 prevalence in simulated populations of men who have sex with men, by year of epidemic. Models were run with a 2-fold (A) and a 10-fold (B) difference in infectivity, for receptive vs. insertive behavior, and with no infectivity for insertive behavior (C). All populations had random mixing. In each graph, the 3 lines correspond to the same parameter sets as in figure 4.

We summarized the full set of simulations by looking at 2 metrics of epidemic progression: the prevalence of HIV-1 at year 20 of the epidemic and the prevalence ratio between versatile and receptive MSM at year 20. The former summarized the risk for the population as a whole, whereas the latter provided relative risk for individuals in the 2 role groups with the most risk. The relative-risk measure was undefined when the population contained all versatile or no versatile MSM; thus, its analysis was based on only 495 (5 × 9 × 11) of the 605 model runs. The natural logarithm of each output measure is plotted in figure 6 as a function of 1 input. Overall prevalence appeared to be primarily a function of contact rate (which separates the points into 5 discrete areas) and versatility fraction (which has a strong positive correlation with log prevalence, within each contact-rate class). The relative-risk measure appeared to be primarily a function of role assortativity, however.

Figure 6.

Disease prevalence at year 20 of epidemic, across all model runs. A, Natural log of overall HIV-1 prevalence in 605 model runs. This is seen to be mostly a function of contact rate (which determines section in which points are plotted) and the initial fraction of the population that is versatile (which possesses a strong positive correlation with the log value for HIV-1 prevalence within each contact level). B, Relative-risk measure (described in Results) as a function of role assortativity.

These relationships can be quantified by regression of each on the 3 input variables. This is a relatively uncommon (but valid) use of regression analysis; rather than explaining uncertainty in the outputs, we defined a linear approximation for our nonlinear system, which allowed a condensed description of versatility’s effects on the epidemic. Since we were not explaining any uncertainty, significance tests had no meaning; instead, the balanced design of the inputs made them uncor-related, and the R² value associated with each input provided an independent measure of the variation in the prevalence of HIV-1 explained by each input. Outputs were expressed by log values, only because this transformation improved the linear predictive power of the inputs. Tables 2 and 3 show the 2 models. The R² values and the figures clearly indicate that overall prevalence was most strongly determined by contact rate and, to a lesser extent, the prevalence of versatility. On the other hand, the relative risk measured by the prevalence of HIV-1 ratio between versatile and receptive MSM was mostly determined by role assortativity. We also examined linear models with 2- and 3-way interaction effects among the predictor variables. For overall prevalence at year 20, including all interaction terms increased R² from 0.983 to 0.984 for overall prevalence and from 0.865 to 0.882 for the prevalence ratio between versatile and receptive MSM. Given this small increase, we excluded these models from further analysis, to simplify interpretation.

Table 2.

Determinants of prevalence of HIV-1 at year 20 of epidemic, in 605 simulated populations.

Factor	Coefficient	R 2a
Intercept	–6.768	...
Contact rate, partners/year	0.181b	0.807
Versatility fraction, by decile	1.128c	0.173
Mixing scale, by decile	0.148d	0.003
Total	...	0.983

^aFraction of the variance in log prevalence at year 20, across model runs, as explained by each factor. The balanced design of the simulated parameter sets meant that the predictors were uncorrelated and that the individual R² values did not vary in relation to order of input.

^bIncrease in the natural log of prevalence of HIV-1 at year 20, when contact rate was increased by 1 partner/year.

^cIncrease in the natural log of prevalence of HIV-1 at year 20, when versatility fraction was increased by 10%.

^dIncrease in the natural log of prevalence of HIV-1 at year 20, with a 10% increase along the mixing scale. The mixing scale refers to the position along the continuum between random role mixing (0) and complete assortative role mixing (1).

Table 3.

Determinants of relative risk of HIV-1 infection, for versatile men who have sex with men (MSM) vs. receptive MSM, at year 20 of epidemic in 495 simulated populations.

Factor	Coefficient	R 2a
Intercept	–0.377	...
Contact rate, partners/year	–0.002b	0.001
Versatility fraction, by decile	–0.107c	0.006
Mixing scale, by decile	1.035d	0.858
Total	...	0.865

^aFraction of the variance in the natural log of (prevalence of HIV-1 among versatile MSM/prevalence of HIV-1 among receptive MSM) at year 20, across model runs, as explained by each factor. The balanced design of the simulated parameter sets meant that the predictors were uncorrelated and that the individual R² values did not vary in relation to order of input.

^bIncrease in the natural log of (prevalence of HIV-1 among versatile MSM/prevalence of HIV-1 among receptive MSM) at year 20, when contact rate was increased by 1 partner/year.

^cIncrease in the natural log of (prevalence of HIV-1 among versatile MSM/prevalence of HIV-1 among receptive MSM) at year 20, when versatility fraction was increased by 10%.

^dIncrease in the natural log of (prevalence of HIV-1 among versatile MSM/prevalence of HIV-1 among receptive MSM) at year 20, with a 10% increase along the mixing scale. The mixing scale refers to the position along the continuum between random role mixing (0) and complete assortative role mixing (1).

DISCUSSION

This study extended earlier findings showing that role segregation can be an important population-level risk factor for the prevalence of HIV-1. We found that this relationship holds even when infection from receptive to insertive partners was significant and when an empirically grounded definition of random mixing was used. We also found that, in the presence of bidirectional transmission, role assortativity remained an individual-level risk factor but not a population-level risk factor, whereas Wiley and Herschkorn [12] found it to be both. With unidirectional infectivity, all cases of infection were generated by versatile MSM; thus, patterns of role assortativity would be expected to matter more in this scenario. In Peru, we found both strong role segregation and evidence that role behavior is intertwined with, but not identical to, role identity. This work suggested the importance of efforts to monitor trends in role segregation among MSM over time and, in the process, of not assuming that role identity is a perfect marker for role behavior.

We observed that versatile MSM had fewer partners than did receptive MSM and found mixed evidence for role assortativity, thus providing no clear support for either explanation of higher prevalence among versatile MSM in some Latin American studies [15, 16]. The observation of fewer partners for versatile MSM led to our model formulation, which then introduced the assumption that versatile MSM always have fewer partners than receptive MSM. An alternative explanation for observed differentials in number of partners is that more-cautious men have converted from receptive behavior with the advent of mes sages regarding HIV-1 infection prevention, leaving a disproportionate number of risk-prone men as receptive partners. In this scenario, receptive MSM were likely to have had more partners in the past than were versatile MSM. As our longitudinal data become available, we may have more insight into the evidence for each explanation; if this alternate explanation is true, our model will have overestimated the differences in prevalence among receptive MSM versus that among versatile MSM.

The Lima study excluded HIV-1–positive men, as well as low-risk HIV-1–negative men. HIV-1–positive men presumably have high levels of risk activity; thus, exclusion of these 2 groups could mean that estimates of average number of partners were not strongly biased. However, we suspect that the missing population, with low numbers of partners, is considerably larger than that with high numbers of partners. This assumption is based, in part, on our prior awareness and on internal evidence of undersampling of insertive MSM who self-identified as heterosexual and who have comparatively low numbers of partners. Thus, our estimates of number of partners would be too high, suggesting that we overestimated prevalence. The actual predicted level of prevalence was not of primary interest to us in this study, however, especially given that the values adopted for infectivity were themselves ad hoc. We are concerned with the relative effect on prevalence created by changes in versatility and role assortativity; the magnitude by which these effects would change in a population sampled differently is not clear, but the direction of each effect and its relative importance in determining different outcome measures should not change.

Our model treated all sex partners as homogeneous, rather than distinguishing between steady and short-term or commercial and noncommercial partners, and excluded female partners altogether. These different components of the risk network are qualitatively different, and future work should consider their separate effects. Cáceres et al. [10, 11] have conducted ethnographic research among men who trade sex for money or favors, in Lima, and have provided much insight into the relationship between these activities and role behavior, female partnership, class, and economic status, which might be incorporated into future modeling efforts. We also assumed that men never change their role class over time, either in response to the epidemic as described above or not. Van Druten et al. [6] point to the importance of role change, and longitudinal cohort studies, such as Carrier’s work in Guadalajara [8], have found increases in versatile behavior over time, although more work is needed to determine whether such increases represent period or cohort effects. As these complexities are added to models of epidemics, we believe that the use of agent-based or network approaches allowing for more-direct modeling of the influence on HIV-1 transmission dynamics of behavior at the individual, rather than the group, level will become fruitful [3, 4, 20, 21].

We assumed constant infectivity over the course of infection. Evidence is now mounting that infectivity correlates with virus load [22–24], which may mean that transmission is concentrated during a relatively small window after initial infection; the introduction of highly active antiretroviral therapy may further curtail infectivity. If these results are corroborated, short-term versatility should play a much greater role in transmission dynamics than has been demonstrated in the present study, since easy transmission would require the same man taking the receptive and insertive roles in rapid succession. With concentrated infectivity, even moderate increases in versatility should have the power to fuel a growing HIV-1 infection epidemic, and public health interventions addressing this will become more important. This simply reiterates the need for more work both collecting empirical data on and modeling the effects of versatility among MSM, under temporally varying infectivity.

What should those working to stop transmission of HIV-1 do in light of these findings? The first approach that might come to mind is an intervention to reduce the prevalence of role versatility among MSM. We argue that, in general, this is not the approach to take. Versatility in Latin America appears to be related to a rising sense of comfort with gay identity, and, if this is the case, seeking to change this role behavior may be both difficult and, ultimately, counterproductive. In addition, unless versatile MSM are highly assortative, versatility is not an individual-level risk factor for acquiring HIV-1. Instead, we believe that the results of the present study emphasize the need to consider role versatility when targeting prevention messages, such as condom use or reduction in number of partners, especially in resource-poor settings where targeting may be most practical. All else being equal, an intervention adopted by versatile MSM should have more impact than the same intervention adopted by a cross-section of the MSM population. Versatility can be easily identified in clinic venues; if research identifies strong correlates to versatility (e.g., age or income group), these also could form the basis for targeted interventions that take advantage of this added impact. We will examine some of these covariates for the Peruvian cohort in a future article. If role assortativity is high (the evidence here was equivocal), then the power of this approach should increase, since risk will be concentrated among versatile MSM. Of course, the value of this approach rests on the assumption that versatile MSM acquire partners for unprotected anal sex as frequently as MSM in general. This assumption will need to be examined in a given population before this approach is adopted; if versatile MSM already have fewer partners or higher rates of condom use than do MSM who practice role segregation, this approach may not be an effective avenue to pursue. Our study also emphasizes the importance of incorporating role segregation into any model that seeks to understand patterns of HIV-1 transmission in Latin America or anywhere that role segregation is high. Most importantly, it emphasizes that we still know little about role segregation and versatility, despite the importance of these components in the identity and behavior of MSM in some regions and their potential for being major factors in determining the course of the HIV-1 epidemic in communities of MSM around the world.

APPENDIX

DERIVATION OF FORMULAS

The sexually active population of men who have sex with men (MSM) was divided into 6 transmission-related states, by sexual role behavior and HIV-1 status: insertive, HIV-1 positive (i+); insertive, HIV-1 negative (i—); receptive, HIV-1 positive (r+); receptive, HIV-1 negative (r—); versatile, HIV-1 positive (v+); and versatile, HIV-1 negative (v—). We defined the change in the size of each role group over a unit of time as a system of ordinary differential equations and initial conditions, as follows.

Notation

Let n represent the total population; n_x the total number in role group x (x ∈ i,r,v); and n_x+ and n_x– the number of HIV-1– positive and –negative individuals, respectively, with role x. We use c_xy to represent the average number of partners a member of group x has from group y per year and c̵ to represent the average number of partners per year in the whole population. Let C_xy = n_xc_xy/ which indicates the total number of partnerships between all members of group x and group y; note that C_xy must equal C_yx for all x and y. β_xy represents the probability of transmission, per partnership, between an HIV-1–negative individual in group x and an HIV-1–positive individual in group y;β_ins represents the probability of infection for an HIV-1–negative individual having unprotected insertive anal (UIA) sex with an HIV-1–positive individual; and β_rec represents the probability of infection for an HIV-1–negative individual having unprotected receptive anal (URA) sex with an HIV-1–positive individual. The number of new HIV-1–negative individuals introduced into the population per unit of time is indicated by μ, which also can be indexed by role class. The general rate of departure from the population is γ, and the rate of departure due to an AIDS-specific cause is γ′. Note that all these variables should be indexed by time; for simplicity, we will drop this factor, except when referring to initial conditions (t = 0).

Initial Conditions

For all simulated populations, n(0) = 10,000, n_i(0) = n_r(0), and initial prevalence of HIV-1 is 0.01 for each group. We systematically varied n_v(0), as explained in the text (Subjects and Methods), yielding the following initial conditions:

$$\begin{array}{cc}\hfill n_{\mathrm{v}+}\left(0\right)=& 0.01\times n_{\mathrm{v}}\left(0\right),\hfill \\ \hfill n_{\mathrm{v}-}\left(0\right)=& 0.99\times n_{\mathrm{v}}\left(0\right),\hfill \\ \hfill n_{\mathrm{i}+}\left(0\right)=& n_{\mathrm{r}+}\left(0\right)=0.01\times [10,000-n_{\mathrm{v}}\left(0\right)]∕2,\text{and}\hfill \\ \hfill n_{\mathrm{i}-}\left(0\right)=& n_{\mathrm{r}-}\left(0\right)=0.99\times [10,000-n_{\mathrm{v}}\left(0\right)]∕2.\hfill \end{array}$$

Population Change

Introductions and removals

We assumed that μis constant and independent of population size (μ = 2), since introductions represent sexual debut, rather than birth, of member of current population. Introductions were divided among the HIV-1–negative states according to initial sizes of groups: that is, μ_x = μn_x(0)/n(0). Removals were dependent on population size: γ = 1/(30 χ 365) removals/person/day, and γ′ = 1/(10 χ 365) removals/HIV-1–positive person/day. Lacking data on entry into the sexually active population of MSM in Lima, we specified the entry rate as higher than the removal rate, given Lima's rapid general growth. In the absence of disease, this meant that the MSM population initially would grow by 4%/year. Examination of alternate scenarios showed that, in this case, changing the entry rate can have strong effects on total population size but not on prevalence of HIV-1, either overall or within each group (data not shown).

Infections

The number of new infections that pass from members of group y to members of group x per unit of time is given by

$$t_{xy}=\{\begin{array}{cc}\frac{C_{xy}{n}_{x-}{n}_{y+}{b}_{xy}}{n_x{n}_y},\hfill & x\ne y\hfill \\ \frac{2C_{xx}{n}_{x-}{n}_{x+}{b}_{xx}}{n_x^2},\hfill & x=y\hfill \end{array}\phantom{\}},$$

which indicates the total number of partnerships between individuals in groups x and y (C_xy) times the fraction of those partnerships with the necessary serodiscordance ([n_x–] χ [n_x–/n_x, when x ≠y, and 2 χ [n_x–/n_x] χ [n_x+/n_x], when x = y) times the probability of seroconversion given contact between an HIV-1–negative individual in group x and an HIV-1–positive individual in group y (b_xy). The total number of new infections in group x equals this value summed over the 3 y groups: t_x = Σ_y∈[i,r,v] t_xy. Since 2 insertive MSM and 2 receptive MSM cannot partner, C_ii = C_rr = 0, and these 2 terms drop out of their respective equations. Thus, there are only 4 unique values when C ≠ 0 (C_ir, C_iv, C_rv, and C_vv), which are derived below.

We begin with the assertion (derived from our data from Peru [table 1]) that the average number of partners for versatile MSM equals the average number of partners for the whole population c̵, which we call the “versatile mean constraint.” We now examine 2 extremes under this constraint, namely, complete proportional choice of partner by role and complete assortative mixing by role. In the first case (proportional mixing), the probability that each of a versatile individual's partnerships is with a member of group x ∈ {i,v,r} is n_x/n. This implies that $C_{\mathrm{iv}\left(\mathrm{p}\right)}=\stackrel{‒}{c}{n}_{\mathrm{v}}{n}_{\mathrm{i}}∕n,C_{\mathrm{rv}\left(\mathrm{p}\right)}=\stackrel{‒}{c}{n}_{\mathrm{v}}{n}_{\mathrm{r}}∕n$, and $C_{\mathrm{vv}\left(\mathrm{p}\right)}=\stackrel{‒}{c}{n}_{\mathrm{v}}^2∕2n$, where “(p)” indicates proportional mixing. The 2 in the denominator of the equation for C_vv(p) prevents double counting of versatile/versatilepartnerships, in this homogeneous class. (In all these derivations, we assumed that the population was large enough that we could ignore the fact that, for versatile/versatile relationships, we are sampling without replacement.) The only remaining group of partnerships is insertive/receptive, which must equal the total number in the population (c̵n/2) minus that in each other group. This simplifies to $C_{\mathrm{ir}\left(\mathrm{p}\right)}=\stackrel{‒}{c}(n∕2+n_{\mathrm{v}}^2∕2n-n_{\mathrm{v}})$.

Under complete assortative mixing by role, versatile MSM only choose other versatile MSM; thus, the only 2 possible partnership types are versatile/versatile and insertive/receptive. Here, the versatile mean constraint implies that C_vv(a) = c̵n_v/2 and C_ir(a) = c̵n/2 — c̵n_v/2 = [c̵(n_i + n_r)]/2, where “(a)” indicates assortative mixing.

We define an assortativity scale h on the interval (0,1), which measures the distance a population lies between the extremes of complete proportional and assortative mixing. Thus, the total number of partnerships of a type is C_xy = hC_xy(a) + (1 — h)C_xy(p). The statistical properties of this ad hoc measure are not obvious, and inferences about population differences based on it would suffer from low interpretability. It does possess the strength of allowing the quantity of each partnership type to take any value between the maximum and minimum values that satisfy the constraint C_xy = C_yxGx,y and the versatile mean constraint.

β_rec and β_ins are set to 0.025 and 0.005, respectively. The exact magnitude of risk for either URA or UIA sex is still not known, partly owing to temporal and host-specific heterogeneity in susceptibility and infectivity. Vittinghoff et al. [13] estimated a per-contact infectivity of 0.0082 for URA sex with a known HIV-1–positive individual but could not obtain a similar estimate for UIA sex with a HIV-1–positive individual. They estimated the per-act risk of UIA sex with a partner of unknown or known positive serostatus to be slightly 120% of that of URA sex with a partner of unknown or known positive serostatus (0.0006 vs. 0.0027, respectively). This ratio does not necessarily apply to sex acts with HIV-1–positive individuals only, since the probability that a partner of unknown serostatus is HIV-1–positive could depend on whether they are engaging in UIA sex, versus URA sex. Nevertheless, we adopted this approximate ratio but chose higher absolute magnitudes, because the estimates determined by Vittinghoff et al. were per act, whereas we considered infectivity per partnership; because higher estimates have appeared in the literature [25]; and because our estimates did not attribute substantial risk to other sex acts (protected anal or unprotected oral sex). For insertive/receptive, versatile/receptive, and insertive/versatile partnerships, the role of each member is predetermined, and serodiscordant partnerships of these types have a probability of transmission of β_ins if the insertive partner is HIV-1–negative and β_rec if the receptive partner is HIV-1–negative. For serodiscordant versatile/versatile partnerships, role is not predetermined; we assumed that versatile partners do not jointly select roles on the basis of serostatus, so that the probability of transmission is (β_ins + β_rec)/2 (however, see [26]).

Assembling introductions, infections, and removals thus yields the following differential equations:

$$\begin{array}{cc}\hfill \frac{d{n}_{\mathrm{i}-}}{dt}=& ({\mu }_{\mathrm{i}}-\gamma n_{\mathrm{i}-})-\frac{{\beta }_{\mathrm{ins}}{n}_{\mathrm{i}-}{n}_{\mathrm{r}+}}{n_{\mathrm{i}}{n}_{\mathrm{r}}}\left[\stackrel{‒}{c}\left(\frac{n}{2}+\frac{n_{\mathrm{v}}^2}{2n}-n_{\mathrm{v}}\right)(1-h)+\stackrel{‒}{c}\left(\frac{n_{\mathrm{i}}-n_{\mathrm{r}}}{2}\right)h\right]-\left(\frac{{\beta }_{\mathrm{ins}}{n}_{\mathrm{i}-}{n}_{\mathrm{v}+}}{n_{\mathrm{i}}{n}_{\mathrm{v}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{i}}{n}_{\mathrm{v}}}{n}\right)(1-h)\hfill \\ \hfill \frac{d{n}_{\mathrm{r}-}}{dt}=& ({\mu }_{\mathrm{r}}-\gamma n_{\mathrm{r}-})-\frac{{\beta }_{\mathrm{rec}}{n}_{\mathrm{r}-}{n}_{\mathrm{i}+}}{n_{\mathrm{i}}{n}_{\mathrm{r}}}\left[\stackrel{‒}{c}\left(\frac{n}{2}+\frac{n_{\mathrm{v}}^2}{2n}-n_{\mathrm{v}}\right)(1-h)+\stackrel{‒}{c}\left(\frac{n_{\mathrm{i}}-n_{\mathrm{r}}}{2}\right)h\right]-\left(\frac{{\beta }_{\mathrm{rec}}{n}_{\mathrm{r}-}{n}_{\mathrm{v}+}}{n_{\mathrm{r}}{n}_{\mathrm{v}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{r}}{n}_{\mathrm{v}}}{n}\right)(1-h)\hfill \\ \hfill \frac{d{n}_{\mathrm{v}-}}{dt}=& ({\mu }_{\mathrm{v}}-\gamma n_{\mathrm{v}-})-\left(\frac{{\beta }_{\mathrm{rec}}{n}_{\mathrm{v}-}{n}_{\mathrm{i}+}}{n_{\mathrm{v}}{n}_{\mathrm{i}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{v}}{n}_{\mathrm{i}}}{n}\right)(1-h)-\left(\frac{{\beta }_{\mathrm{ins}}{n}_{\mathrm{v}-}{n}_{\mathrm{r}+}}{n_{\mathrm{v}}{n}_{\mathrm{r}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{v}}{n}_{\mathrm{r}}}{n}\right)(1-h)\hfill \\ & -\left(\frac{{\beta }_{\mathrm{ins}}+{\beta }_{\mathrm{rec}}}{2}\right)\left(\frac{2n_{\mathrm{v}-}{n}_{\mathrm{v}+}}{n_{\mathrm{v}}^2}\right)\left[\frac{\stackrel{‒}{c}{n}_{\mathrm{v}}^2}{2n}(1-h)+\left(\frac{c^{-}{n}_{\mathrm{v}}}{2}\right)h\right]\hfill \\ \hfill \frac{d{n}_{\mathrm{i}+}}{dt}=& (-\gamma n_{\mathrm{i}+}-{\gamma }^{\prime }{n}_{\mathrm{i}+})+\frac{{\beta }_{\mathrm{ins}}{n}_{\mathrm{i}-}{n}_{\mathrm{r}+}}{n_{\mathrm{i}}{n}_{\mathrm{r}}}\left[\stackrel{‒}{c}\left(\frac{n}{2}+\frac{n_{\mathrm{v}}^2}{2n}-n_{\mathrm{v}}\right)(1-h)+\stackrel{‒}{c}\left(\frac{n_{\mathrm{i}}+n_{\mathrm{r}}}{2}\right)h\right]+\left(\frac{{\beta }_{\mathrm{ins}}{n}_{\mathrm{i}-}{n}_{\mathrm{v}+}c}{n_{\mathrm{i}}{n}_{\mathrm{v}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{i}}{n}_{\mathrm{v}}}{n}\right)(1-h)\hfill \\ \hfill \frac{d{n}_{\mathrm{r}+}}{dt}=& (-\gamma n_{\mathrm{r}+}-{\gamma }^{\prime }{n}_{\mathrm{r}+})+\frac{{\beta }_{\mathrm{rec}}{n}_{\mathrm{r}-}{n}_{\mathrm{i}+}}{n_{\mathrm{i}}{n}_{\mathrm{r}}}\left[\stackrel{‒}{c}\left(\frac{n}{2}+\frac{n_{\mathrm{v}}^2}{2n}-n_{\mathrm{v}}\right)(1-h)+\stackrel{‒}{c}\left(\frac{n_{\mathrm{i}}+n_{\mathrm{r}}}{2}\right)h\right]+\left(\frac{{\beta }_{\mathrm{rec}}{n}_{\mathrm{r}-}{n}_{\mathrm{v}+}}{n_{\mathrm{r}}{n}_{\mathrm{v}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{r}}{n}_{\mathrm{v}}}{n}\right)(1-h)\hfill \\ \hfill \frac{d{n}_{\mathrm{v}+}}{dt}=& (-\gamma n_{\mathrm{v}+}-{\gamma }_{\mathrm{v}+}^{\prime })+\left(\frac{{\beta }_{\mathrm{rec}}{n}_{\mathrm{v}-}{n}_{\mathrm{i}+}}{n_{\mathrm{v}}{n}_{\mathrm{i}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{v}}{n}_{\mathrm{i}}}{n}\right)(1-h)+\left(\frac{{\beta }_{\mathrm{ins}}{n}_{\mathrm{v}-}{n}_{\mathrm{r}+}}{n_{\mathrm{v}}{n}_{\mathrm{i}}}\right)\left(\frac{\stackrel{‒}{c}{n}_{\mathrm{v}}{n}_{\mathrm{i}}}{n}\right)(1-h)\hfill \\ & +\left(\frac{{\beta }_{\mathrm{ins}}+{\beta }_{\mathrm{rec}}}{2}\right)\left(\frac{2n_{\mathrm{v}-}{n}_{\mathrm{v}+}}{n_{\mathrm{v}}^2}\right)\left[\frac{\stackrel{‒}{c}{n}_{\mathrm{v}}^2}{2n}(1-h)+\left(\frac{c^{-}{n}_{\mathrm{v}}}{2}\right)h\right]\hfill \end{array}$$

The model is then solved for different values of n_v(0) (initial prevalence of versatility), h (role assortativity), and c̵ (contact rate), as discussed in the text (Subjects and Methods).