According to the US Centers for Disease Control and Prevention, more than 500,000 Americans have died of AIDS since the epidemic began,1 and more than 1 million Americans are currently infected with HIV.2 Men who have sex with men continue to be the group most affected by HIV/AIDS in the United States. In 2005, half (50%) of newly diagnosed, reportable HIV infections nationwide were transmitted through male-male sexual contact.1 In King County, Washington (comprising Seattle and many of its suburbs), men who have sex with men comprise two-thirds (64%) of cases identified since 2003,3 and there is evidence that high-risk behaviors4 and STI incidence5–8 are rising in this population.
Commercial sex venues catering exclusively to men, including gay bathhouses and sex clubs, have operated in the United States for at least a century.9 Bathhouses and sex clubs differ in some respects, but both charge entrance fees, admit only men, and allow sex on premises.10 In the early 1980s, commercial sex venues were widely considered to facilitate the spread of HIV.11–13 A committee convened by the National Research Council concluded that commercial sex venues were analogous to “shooting galleries” used by injection drug users, in that they “promote transmission-related behavior at a rate far beyond that possible outside these settings.”14 Sharply contentious efforts to close or regulate commercial sex venues were made by local health officials across the United States.15 Opponents of closures argued that the policy would simply move unsafe sex into other sites more out of reach of HIV prevention efforts.16
Lacking epidemiologic evidence relating commercial sex venue characteristics and HIV risk,17 cities have often had to choose among policy approaches based on anecdotal evidence. An increase in direct HIV prevention and testing and in basic epidemiologic research, within commercial sex venues, began in the 1990s and continues to the present,18–26 but the fraction of new infections attributable to commercial sex venues remains unknown.
This analysis applies mathematical modeling to data from 3 recent surveys to examine the impact that commercial sex venues have on the HIV epidemic among men who have sex with men in one large US county. These include 2 probability surveys that present the first description of commercial sex venue patrons and their behavior throughout an entire US county or metropolitan area,10 including relatively detailed information on HIV risk behaviors, both in commercial sex venues and elsewhere.
Our primary aim is to estimate a range for the number of HIV infections attributable to the presence of commercial sex venues in King County, given a set of plausible scenarios. This requires the simulation of HIV incidence among King County men who have sex with men in several theoretical, counterfactual scenarios in which commercial sex venues no longer exist, and in a scenario reflecting conditions as reported in recent years. We explore a range of assumptions about the degree to which current commercial sex venue contacts would be forgone or replaced, and we assume that those replaced would match the behaviors that commercial sex venue patrons reported engaging in outside of commercial sex venues.
To simulate HIV transmission in the various scenarios, we constructed a series of compartmental, discrete-time deterministic mathematical models, specified and solved in Stella (Isee Systems, Lebanon, NH). Model equations comprised initial conditions (eg, proportions of men initially uninfected) and transition-related parameters (eg, partnership formation rate, patterns of serostatus-based partner selection, per-sex act infectivity). Our discrete-time simulation time step was one day, reflected in all rates calculated from our data.
A key resource was data from a recent pair of surveys of probability samples of commercial sex venue patrons in King County, conducted in 2004 and 2006.10 These surveys sampled men from 3 commercial sex venues in King County. To estimate many of our model parameters, we conducted descriptive statistical analyses of the more in-depth 2004 survey data to identify self-reported HIV prevalence among commercial sex venue patrons, and frequency of unprotected anal intercourse by self-reported serostatus. The surveys also asked commercial sex venue attendees about their use of other venues for meeting sexual partners, and the rates of sexual contact, acts, and condom use at those venues—information we use in our counterfactual scenarios.
Our findings were supplemented with information from a 2003 population-based, random-digit-dial survey of Seattle men who have sex with men.27 This survey informed several key parameter estimates, particularly regarding the makeup and behaviors of men who do not visit commercial sex venues.
Our models were parameterized using only recent data sets, because our models are intended to represent the current biobehavioral system of HIV spread among Seattle men who have sex with men. Our models are not intended to capture the full trajectory of the HIV epidemic in this population (either into the past or the distant future) because we do not believe that sexual behavior has been or will remain constant over long time frames, especially regarding the use of commercial sex venues versus alternative venues.
We constructed 2 general classes of models: one reflecting current HIV transmission among King County men who have sex with men (main model), and the other modeling transmission in counterfactual situations in which commercial sex venues no longer exist (counterfactual model). Certain important model assumptions were speculative, so we varied their respective parameters, some individually and some in a combined sensitivity analysis, as detailed below. We describe the general model structure and its assumptions here; more mathematical detail can be found in the eAppendix (http://links.lww.com/EDE/A381).
The main model included 10 compartments of men who have sex with men, distinguished by commercial sex venue patron status (L), sexual activity level inside and outside commercial sex venues (A), and HIV serostatus (H) (Fig. 1). We categorized commercial sex venue patrons by their activity levels both within commercial sex venues (high/low) and outside those venues (high/low). High activity for either location was defined as reporting 2+ unprotected anal intercourse partners there in the previous 3 months. Commercial sex venue patrons' activity level was defined by their combination of inside- and outside-commercial sex venue activity levels (4 combinations total). Due to the limited information available from the 2003 population-based survey, all noncommercial sex venue-patron men who have sex with men were placed into one activity class. The 5 total activity classes were each further subdivided into susceptible (HIV-negative) and infected (HIV-positive).
The initial distribution of men across the 10 compartments (nah) was based primarily on self-reported HIV prevalence and unprotected anal intercourse contact rates in the 2004 commercial-sex-venue survey (for commercial sex venue compartments) and HIV prevalence in the 2003 population survey (for noncommercial sex venue compartments). We calculated the initial sizes of the total commercial sex venue population and sexually active noncommercial sex venue population using a previous estimate of the number of men who have sex with men in King County,28 and findings from the 2003 population survey regarding sexual activity and frequency of visiting commercial sex venues in the previous year. The distribution was adjusted for the presence of undiagnosed HIV-positive men, and for a bias towards frequent commercial sex venue visitors in the 2004 commercial-sex-venue survey (eAppendix, http://links.lww.com/EDE/A381). Table 1 details model notation; many variables should be indexed by time, although we omit this for notational simplicity. Tables 2 and 329,30 summarize initial conditions and parameter values for the main model.
The model contains 3 types of transitions: HIV acquisition, entry, and exit. We assumed no movement among activity classes. We detail each transition type in turn.
Movement from HIV-negative to HIV-positive compartments is a function of (1) sexual activity levels of each compartment; (2) patterns of mixing by serostatus given these activity levels; and (3) per-partnership HIV transmissibility for commercial sex venue and noncommercial sex venue partnerships. We included only unprotected anal intercourse in the model because this behavior is widely believed to be the predominant route of male-to-male sexual HIV transmission.31
Separate commercial-sex-venue and outside-commercial-sex-venue unprotected anal intercourse partnership formation rates (clah) were defined for each activity-level/HIV-status combination, based on reports by men in each respective group from the 2004 commercial-sex-venue survey and the 2003 population survey. These rates were adjusted for the presence of undiagnosed HIV-positive men; commercial sex venue rates were also adjusted for a bias towards frequent commercial sex venue visitors in the 2004 survey. The final unprotected anal intercourse partnership formation rates for each group in the main model (Table 3) equal the 5% trimmed mean number of unprotected anal intercourse partners per day for each activity-level/HIV-status group in the adjusted datasets. We used trimmed means due to small numbers of subjects in certain activity level-HIV status groups in the survey. See the eAppendix (http://links.lww.com/EDE/A381) for more detail. From these values, we specified the total number of contacts for all men in activity class a, with serostatus h in location l at a given time (= clah nah), which we call dlah.
We assumed proportional mixing by activity class, but preferential selection of sex partners by HIV status (serosorting). To parameterize the latter, we used data from the 2004 commercial-sex-venue survey, and a method described previously32 based on the odds ratio in the 2 × 2 table of apparent serostatus for insertive and receptive partners. In calculating this odds ratio, we assigned positive or negative serostatus to partners whose status was reported as unknown by respondents, based on the proportion of partnerships reported by self-identified positive and negative men, respectively. A single odds ratio, calculated using data from all partnerships, was used, given the considerable overlap in confidence intervals for the 4 odds ratios for the data disaggregated by activity level and location. The resulting value (ORaa' = 2.82) reflects the increased odds of selecting an unprotected anal intercourse partner of one's own HIV status.
This odds ratio, combined with the dlah values derived in the previous step and the assumption of random mixing by activity class, define a unique set of contact rates for each pair of compartments in each location. For the full process of determining these rates given the odds ratio and marginal contact rates, see the eAppendix (http://links.lww.com/EDE/A381). From these values we calculate the number of unprotected anal intercourse partners of discordant HIV status for each compartment per timestep (αlaiar).
The number of discordant unprotected anal intercourse partnerships among HIV-negative compartments was multiplied by a value representing per-partnership HIV transmission probability to arrive at the number of new HIV infections. The per-partnership transmission probability was calculated using the formulas (1−(1−βR)zR) and (1−(1−βI)zI), where βR and βI represent per-act probability of HIV transmission for receptive and insertive unprotected anal intercourse, respectively, and zR and zI equal the number of receptive and insertive acts of unprotected anal intercourse per partnership. We assumed one such act per commercial-sex-venue partnership. We assumed no seropositioning and complete role versatility, such that in serodiscordant relationships, the seronegative partner was insertive 50% of the time. The mean number of acts of unprotected anal intercourse partnerships initiated outside of commercial sex venues is not well-documented—so we systematically varied this from 2 to 20; here we assumed in each case that half the acts in each partnership were insertive for each partner. The per-act HIV transmission probabilities for insertive and receptive unprotected anal intercourse were derived from previous findings.30 Our calculation of these probabilities is presented in the eAppendix (http://links.lww.com/EDE/A381).
Entry and Exit
HIV transmission dynamics were simulated over a 10-year period in each model run. Departure occurred with constant probability (εah), based on an expected membership in the population of 40 years for HIV-negative men and 10 years postinfection for HIV-positive men. Numbers of men entering each compartment (ωah) were set to equal numbers of departures from the system leaving each respective compartment during a one-year simulation run without entry. This ensures a roughly steady-sized population.
Model equations. The difference equations resulting from this model are:
with all notation defined in Table 1. The time index (t) is included for the n values only for ease of presentation.
The structure, assumptions, and initial conditions for the counterfactual model equal the main model in nearly every way. The sole difference is the partnership formation rates for commercial-sex-venue men, modified to estimate behaviors in a counterfactual setting without commercial sex venues.
The mean number of commercial-sex-venue partnerships—including those in which unprotected anal intercourse did or did not occur—was identified for each of the activity-level/HIV-status groups from the 2004 commercial-sex-venue survey. Again, 5% trimmed means were used, due to some small subgroup sizes. These mean partnerships were assumed to be measures of the number of “replaceable” partnerships for each group member in a counterfactual scenario.
Calculation of Replacement Partnerships
We assumed that the best evidence of counterfactual behaviors with these “replaceable” partners lies in the indicators of past sexual behaviors outside of commercial sex venues among the men who go to commercial sex venues. In the 2004 survey, subjects were asked to report their recent sexual behavior, including unprotected anal intercourse, with partners met through 12 types of noncommercial sex venue sources, such as bars, parties, parks, friends, and the Internet. This allowed for a determination of the proportion of sexual partnerships initiated through each source, and the probability that a partnership of each type would involve unprotected anal intercourse. The sum of the product of these 2 sets of numbers provided a weighted average for each activity-level/HIV-status group, representing the probability that any given sexual partnership outside of commercial sex venues would result in unprotected anal intercourse for members of each group. Table 4 shows estimates of the 2 sets of probabilities.
To arrive at counterfactual unprotected anal intercourse partnership formation rates for each activity-level/HIV-status group, the weighted average probability of unprotected anal intercourse for noncommercial-sex-venue partnerships was multiplied by the number of “replaceable” partnerships for each group (Table 5). The degree to which these partnerships would, indeed, be replaced one-for-one (or in some smaller proportion) in a counterfactual scenario is entirely unknown. We therefore systematically varied the degree of replacement of partners by multiplying the commercial sex venue partnership rates by 1.00, 0.75, 0.50, 0.25, and 0—to arrive at a set of alternate counterfactual scenarios with these different levels of commercial sex venue partnership replacement. (Table 6 shows the 100% replacement rates.) For the sake of mathematical tractability, we assumed that the replacement partnerships in the counterfactual scenarios occurred entirely between pairs of men who had been commercial sex venue patrons in the main model. Just as we assumed that each commercial sex venue unprotected anal intercourse partnership consists of a single unprotected anal intercourse act, we defined replacement unprotected anal intercourse partnerships as consisting of one unprotected anal intercourse act.
For each counterfactual scenario, we defined the “attributable number” as the difference in the 10-year cumulative number of new HIV infections between the main model and the counterfactual scenario.
To explore the effect of parameter-value uncertainty on simulated HIV transmission, and to assess the importance of each parameter on HIV incidence, we performed sensitivity analyses using Latin hypercube sampling methods.33–35 Each of the 8 commercial-sex-venue patron unprotected anal intercourse partnership formation rates, the noncommercial-sex-venue partnership formation rate, and the log of the serosorting odds ratio were subjected to the variability generated by Latin hypercube sampling. We used the Crystal Ball (Oracle Corp., Denver, CO) add-in for Microsoft Excel (Microsoft Corp., Redmond, VA) to perform this sampling. One hundred sampling iterations were run, providing 100 sets of unique parameter values. Further details, including selection of the distributions for each variable, are in the eAppendix (http://links.lww.com/EDE/A381).
The 100 sets of parameter values were entered into Stella for both the main model and each of the 5 counterfactual scenarios, generating 600 total outcomes. We used the attributable number across scenarios as our dependent variable, and modeled this as a function of input parameters using SPSS 16.0 (SPSS, Inc., Chicago, IL). First, we assessed monotonicity by examining scatterplots of each parameter variable by the attributable number outcome. Separate analyses were run using the sensitivity analysis data for the main model and 5 counterfactual models. We then performed partial correlation analysis to identify statistical relationships between parameter inputs and outcomes, and, where applicable, to identify the strength and direction of the linear relationship between each parameter and the model outcome (partial correlation analysis results are presented in the eAppendix, http://links.lww.com/EDE/A381).
Main Model Calibration
The annual number of incident HIV cases simulated by the main model ranged from approximately 550 to 900 cases in the scenario assuming 20 unprotected anal intercourse acts per noncommercial-sex-venue partnership, down to only 100 assuming 2 acts of unprotected anal intercourse per noncommercial-sex-venue partnership (Fig. 2). The actual number of new HIV cases among men who have sex with men in King County appears to have been between 200 and 300 cases annually in recent years.3 Our models assigning 5 to 10 unprotected anal intercourse acts per noncommercial-sex-venue partnership projected HIV incidence close to that range. The true mean number of unprotected anal intercourse acts per partnerships involving unprotected anal intercourse is unknown, but a preliminary analysis of data collected from 2 recent population-based studies of men who have sex with men in King County found that the number is likely to be between 2 and 9 (T. Menza, written communication, January 2008). Our findings are consistent with this estimate.
Attributable Number Findings
Figure 3 summarizes the attributable number of incident HIV cases in the counterfactual models under the scenarios with 5 and 10 unprotected anal intercourse acts per replacement partnership (Fig. 3). Each line per panel plots a different value for level of partnership replacement in the absence of commercial sex venues. In both cases, replacement of 50% or more of commercial sex venue partners resulted in yearly attributable number values below zero. That is, for these scenarios our model predicts a net increase in the number of incident HIV infections in the absence of commercial sex venues in every year. Only when replacement drops to 25% does the attributable number approximate zero, indicating that this scenario would result in little or no change in HIV incidence. The only counterfactual scenario that consistently projected fewer annual infections than the main model was that representing zero replacement partnerships. In no case, however, did these yearly margins reach even 30 additional HIV infections. We performed these analyses for each additional scenario (ie, 2, 10, and 20 acts of unprotected anal intercourse per replacement partnership), with similar qualitative findings.
Figure 4 presents yearly attributable number estimates from the sensitivity analyses. Results from each set of 100 parameter values selected in the Latin hypercube sampling are shown, assuming 10 acts of unprotected anal intercourse per partnership, and applied to the 100%, 75%, 50%, 25%, and 0% replacement levels. Most attributable numbers—at all time points, in each replacement scenario—fall within 20 incident cases of the corresponding main findings (Fig. 3, 20 acts). Nearly all of the attributable number estimates from the 25% replacement scenario were close to zero, consistent with the main results noted above. Each of the scenarios assigning 50% or greater replacement of commercial sex venue partners predicted higher HIV incidence in the absence of commercial sex venues, with near unanimity across the 100 sets of sensitivity analysis outcomes.
Under our model assumptions, commercial sex venues in King County appear to contribute little to the local HIV epidemic among men who have sex with men. If commercial sex venues ceased to exist in King County, and commercial-sex-venue patrons were to forego as many as 75% of their lost commercial-sex-venue contacts, overall HIV incidence would not likely decrease from its current level. If, in the absence of commercial sex venues, would-be commercial-sex-venue patrons were to replace even half of their missed bathhouse and sex club contacts, it appears that HIV incidence among men who have sex with men might increase slightly. Under no scenario did we find that even 25 new cases of HIV per year could be attributed to the presence of commercial sex venues in the region. These qualitative findings were relatively insensitive to a variety of key assumptions.
Our findings are largely a reflection of the types of HIV risk behaviors that respondents in the 2004 King County commercial-sex-venue survey reported engaging in, both inside and outside of bathhouses and sex clubs. Specifically, commercial-sex-venue patrons were less likely to report having anal sex—protected and unprotected—with partners met in bathhouses and sex clubs than with partners met within other popular venues. For example, of respondents with exactly one partner during their recent bathhouse or sex club visit, the proportion reporting unprotected anal intercourse with their most recent sex partner was 22% for Internet partners, 20% for bar partners, and 10% for commercial sex venue partners. The pattern is reversed for oral sex (64%, 71%, and 85%, respectively). Also worth noting is that only 18% of the 2003 population-survey respondents attended a commercial sex venue in the previous year. Of those who had, 42% reported visiting only once or twice a year, and fewer than 10% stated that they visited commercial sex venues more than once a month (MR Golden, written communication, September 2007). Thus, the population of routine commercial-sex-venue patrons is a relatively small segment of men who have sex with men in King County.
A number of limitations may affect the accuracy and generalizability of the study findings. We modeled HIV transmission probabilities as homogenous within a specific type of act (unprotected insertive anal intercourse and unprotected receptive anal intercourse). In reality, this probability varies by factors such as stage of infection36 and antiretroviral therapy.37 We also imagine that the true network of sexual partnerships among men who have sex with men in King County is more complicated than we have considered. However, in general these factors might be expected to affect both our main model and our counterfactual model in the same direction and in a generally similar way, and our main finding represented the relative magnitude of these 2 scenarios. Thus, although all of these represent additional features of importance to HIV epidemiology generally, we feel confident that they would not strongly alter our qualitative findings.
Many of the parameter values in our models are based on a 2004 survey with a low participation rate (30%), which calls into question the representativeness of our parameter values within the full King County commercial sex venue-patron population. However, this survey has been compared statistically to a 2006 probability sample of King County bathhouse and sex club patrons with a 61% participation rate, and no evidence of selection bias was evident.10
A key assumption, of course, is that no large differences in methods of finding sex partners would develop if commercial sex venues no longer existed. It is entirely possible (as some critics of bathhouse closure have stated) that certain venues of only marginal interest now—such as private sex parties and public sex in parks and restrooms—could take on a different character and substantial importance in HIV transmission if bathhouses and sex clubs were no longer an option.16 There is some evidence that, in recent years, frequency of HIV risks in commercial sex venues may be declining, while frequency of risks from Internet partnerships increasing.38 We expect that the attributable number of HIV infections due to commercial sex venues would, in this case, be lower than we project. This evidence also serves to highlight the context-dependent nature of our findings: every combination of time and place offers its own set of sexual opportunities and restrictions, and behavioral patterns are likely responsive to these structural forces. Our findings should therefore be generalized only to those communities in which it is likely that men have similar levels of usage, and behaviors while using venues other than bathhouses and sex clubs for meeting sex partners.
Nevertheless, these findings are striking in that they suggest that bathhouses and sex clubs may not be among the primary facilitators of HIV transmission among men who have sex with men. It is possible that, in another era—with different patterns of unprotected anal intercourse and condom use and before the widespread use of the Internet to find sex partners—commercial sex venues played a central role in the epidemic. However, our findings suggest that public health officials cannot rely on the elimination of gay bathhouses and sex clubs to achieve large reductions in HIV transmission among men who have sex with men.
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