MSM face a devastating HIV epidemic globally . Odds ratios for HIV infection among MSM, as compared to the general population, are estimated at 7.8 and 23.4 in low and middle-income countries, respectively . Forty-two percent of new HIV infections in Asia have been forecast to occur among MSM in 2020 .
HIV-related forecasts should rely on unbiased estimates of core epidemiological indicators, for example HIV prevalence and risk behavior. There are, however, major challenges inherent in performing probability sampling among hard-to-reach populations like MSM. The development of a chain-referral method, named respondent-driven sampling (RDS) in 1994, marked an important methodological achievement . By 2007, more than 120 HIV-related RDS studies in at least 28 countries had been performed among hard-to-reach populations [5,6]. As a result of the method's appeal, the global epidemiological evidence base for HIV-related surveillance and research among MSM is increasingly reliant upon the RDS method.
Whereas we consider the RDS method to be a promising sampling methodology for HIV-related MSM research in many settings, we here present a hypothesis that questions the validity of important RDS study outcomes in the MSM population.
Implementation of a respondent-driven sampling study
At the start of an RDS study researchers recruit a few study participants (seeds) belonging to the risk population of interest. The participants are, after completion of, for example, an HIV test and a questionnaire, given invitation coupons (usually three) to give to friends within the population under study. These friends in turn invite other friends and long recruitment chains are created. Analytical proofs and simulations have shown that the RDS method, under a limited number of assumptions, allows calculations of unbiased estimates of population proportions and that the final composition of the sample is independent from the characteristics of the seeds [7,8]. For methodological discussions, please see selected references [9–12].
Adjusting for different inclusion probabilities
A major difference between analysis of data from an RDS sample and a standard sample is that the sample proportion of a characteristic (e.g. the proportion of the population reporting sexual risk behavior) is adjusted by the possibilities the group members have for being invited into the study by other persons in the population. To formalize and measure inclusion probabilities, each participant is asked about the size of his/her social network. For MSM this usually includes a question equivalent to: ‘How many MSM do you know, who also know you and whom you have met during the last month/last six months?’. The underlying assumption is that a person who only knows one other person within the population under study has merely one chance of being invited to participate, whereas a person with 100 contacts has 100 chances of being invited.
The proportion of persons with characteristic A in the population can be estimated by the RDSII estimator:
where di is the personal network size (degree) of individual i and S is the set of all individuals in the sample. The RDSII estimator gives point estimates equivalent to the earlier RDS/DS estimator but has analytical advantages .
Are HIV indicators underestimated?
Imagine a gay man (MSM) maintaining a large network for dating and sex. In addition, he has a smaller set of close MSM friends. We hypothesize that his chances of being invited to a study about HIV is largely dependent on his number of close friends rather than on his number of casual sexual and dating partners (past, current or potential), as fear of being associated with HIV is well documented in numerous settings . Studies have shown that HIV-positive MSM less frequently disclose their HIV status to casual sexual partners than to a stable partner . Such data possibly support the common sense notion that sensitive issues such as those related to HIV and sexual behavior are more difficult to communicate about with casual sexual partners than with close friends.
Unfortunately little empirical evidence that could illuminate this issue has been reported from RDS studies among MSM. One Brazilian study  published details on the proportion of participants who were recruited by a sexual, as opposed nonsexual contact and specifically if the sexual contact was a casual or stable partner. In this study, which included 626 participants, 11% reported being recruited by a ‘boyfriend or spouse’, but only 2% said that they were recruited by an ‘occasional sexual partner’.
On the basis of data from Shanghai, China , let us assume that the gay man in our example above has a network of 12 male sexual contacts and five close MSM friends, and that he counts his sexual contacts as men that he knows and who knows him and whom he has met during the last 6 months. The data referred to in the example describe 15% of the sample reporting 6–20 male anal sex partners during the last 6 months. Non-anal sex partners were not reported. Although the current RDS methodology assumes that any of these (12 + 5) = 17 members of his network may invite him into the study, he would, given our hypothesis, really only stand a chance of getting invited by one of his five close friends. Thus, his chances of being recruited to the study are less than a third of what would be predicted by network size alone.
If we assume, based on the Chinese data, that 15% of the men in the sample share the characteristics of this man, while actually standing similar chances to be invited into the study as the rest of the sample, that is by five close friends, the network-adjusted estimated population proportion of this group with most partners would then only be half of the true value (7.4% instead of the correct figure 15%).
The overwhelming number of RDS studies among MSM report only network size-adjusted proportions of MSM. The few that report both crude and adjusted proportions for the group with the highest number of sexual partners show adjusted proportions that are as low as a third of the crude, unadjusted proportions [17–19].
Thus, adjusting sample proportions by a reported social network size that includes sexual contacts, which in itself is a study outcome, can potentially introduce a considerable bias. Such bias is from a surveillance point of view very troubling in a population in which anal sex is not practised safely. Hence, it seems warranted to show that any adjustment by network size is based on good empirical evidence. Such evidence is not available today.
During the past decade, it has become increasingly clear that concurrent sexual relations are very important for the sexual spread of HIV . Hence, biases in indicators that relate to multiple partnerships are especially serious as they may obscure a correct understanding of the major drivers of the HIV epidemic among MSM. If our hypothesis holds true, it may also be particularly relevant to the high-risk group of male sex workers. Along the same line of reasoning, we hypothesize that many of these men will know a large number of regular clients, who may be included in their reported social network, whereas they would rarely be recruited into an HIV study by these clients. Consequently, the proportion of men selling sex could be severely underestimated, as could the sex workers' relatively large contribution to the average level of risk behavior and HIV prevalence within the global MSM population.
Current adjustment of sample proportions by network size may introduce considerable bias in HIV-related RDS studies among MSM, resulting in an underestimation of the proportion of the population with high partner numbers. As HIV prevalence is correlated with having casual or concurrent sexual partners, HIV prevalence could likewise be underestimated.
We recommend future RDS studies among MSM to ask participants for the composition of their MSM network (number and types of contacts). Together with participants' reports of whom they were actually recruited by, this would enable an evaluation of the presented hypothesis and consequently a rephrasing of the social network question in a way that reflect true inclusion probabilities.
In conclusion, RDS constitutes an important leap forward in the provision of evidence-based information to curb the spread of HIV among millions of stigmatized and at-risk men. We therefore urge funders and the research community to increase their efforts in support of methodological research in MSM sampling methodologies with a particular emphasis on the stated hypothesis.
L.B. conceived of the idea and made the literature search. A.T. contributed with additional ideas and L.B. and A.T. wrote the manuscript together. The authors wish to thank Xin Lu, Karolinska Institutet, for valuable discussions. We are grateful to Sida who has supported the project financially.
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