Table 3.

Testing RDS assumptions for population estimation, New York City (2006-2009)

Assumption	Test of Assumption	Conclusions
1) Respondents know one another as members of the target population and recruitment ties are reciprocal(29).	Participants were asked to describe their relationship with the person who recruited him/her.	Most participants described their recruiter as a friend or acquaintance (83%); 6% as a relative, 7% as a stranger, and 4% as other.
2) There is sufficient cross-over between subgroups and networks are dense enough to sustain a chain referral process(30).	This assumption could not be tested because peer recruitment did not terminate naturally, however we did evaluate cross-over recruitment.	There was a tendency to recruit within-group for all variables considered, but cross-group recruitment was substantial for gender (36%), race (39%), income (22%), education (43%), and homelessness (36%), so chains did not become trapped within a single group. Cross-group recruitment was low for injection status (11%) and HIV status (8%). HIV positives comprised 10% of the sample and recruited other HIV positives 59% of the time. HIV negatives comprised 90% of the population and recruited other HIV negatives 97% of the time.
3) Sampling occurs with replacement(29).		This is not a reasonable assumption for well-connected networks because many people share the same networks. Thus as recruitment waves extend, the proportion of networks available for recruitment (not enrolled or previously screened for eligibility) decreases, and this assumption is less likely to be valid.
4) Respondents are recruited from one’s network at random(29).	T-tests and Chi-square tests were used to compare peer-recruit characteristics with the characteristics that individuals reported that their networks possessed.	Networks and recruits were not significantly different with respect to race and injection status. There were significant differences with respect to gender, age, education, crack smoking, and heroin snorting. Relative to what would be expected if recruitment reflected the composition of the self-reported personal networks, males were over-recruited by 20%, high school educated individuals were underrepresented by 56%, crack smokers were overrepresented by 11%, and heroin snorters were overrepresented by 101%. The sample was also younger than what would have been expected had the sample’s age distribution reflected the composition of self-reported drug- using network members.
5) Respondents can accurately report their personal drug-using network size, defined as the number of relatives, friends, and acquaintances who can be considered members of the target population(29).	Compare degree estimates to the number of drug-using network members reported in comparable studies.	Degree estimates, which were based on the number of drug users that each respondent reported in his/her network are also likely to be inaccurate. As only 59% of those recruited by their peers were eligible, the number of self-reported drug-using network members may be an overestimate. However fewer drug-using network members were reported in this study than in other studies among NIDUs(28) and IDUs(31, 32). For example, Weeks and colleagues (2002) reported an average of 4.5 drug using peers(33) and Latkin and colleagues (1995) reported an average of 5.22 drug-using network members(32), both of which are larger than the 1.52 drug-using network members reported here. Each of these studies also reported more total network members (including non-drug network members; means: 5.6(33) and 10.3(32)) than what is reported here (mean=3.33).
6) Each respondent recruits a single peer(29).	To prevent recruitment chains from terminating early, most studies break this assumption. Instead of allowing each participant to recruit only one peer, most RDS studies allow 3 peer recruits.	Of the 390 RDS participants (including seeds) who were given peer recruitment coupons (13 participants were not given coupons), 87 recruited 1 eligible peer (22%), 47 (12%) recruited 2 eligible peers, 61 (16%) recruited 3 eligible peers, and the remaining did not refer any eligible peers.
7) The composition of those in the final sample is independent of those selected as seeds at equilibrium.	While an ideal test of this assumption would evaluate the independence of each seed and the respondents comprising its referral chain, this was not possible. Instead, t-tests and chi- square tests were used to assess the independence of seeds and peer recruits.	Seeds and peer recruits were independent with respect to gender, age, education, crack smoking and heroin snorting. Compared with recruits, seeds were more likely to be Hispanic and Black and to inject drugs