Appendix A. Alternate approaches to measurement
We considered several alternate approaches to measuring connected triplets based on the available data because reports of co-injection may be susceptible to bias. All yield results in the same direction as those presented in the main text, such that Cebu had higher clustering than Mandaue, but the alternate approaches we considered exhibited different levels of clustering with variable magnitudes of difference between the two cities.
In the main text, for each recruiter-recruit-recruitee triplet, we measured the existence of a) recruiter-recruit and b) recruit-recruitee co-injection based on reports from the follow-up survey where a) recruiters reported on co-injection with their recruits and b) recruits reported on co-injection with their recruitees. This analysis, therefore, mixed reporting sources across multiple people but used the same question wording for each person.
We first consider an alternate set of estimates where the same person, the recruit, reports on co-injection with his recruiter and his recruitee. In the primary interview, respondents were asked: “In the past 30 days, how many times have you injected drugs with the person who gave you your coupon?” We code all non-zero responses to this question as cases where co-injection occurred between the recruit and his recruiter. Using the definition in the main text of co- injection between the recruit and his recruitee, from the follow-up survey, this allows us to measure based on the same respondent’s reports the existence of co-injection between recruiter and recruit and between recruit and recruitee. Only 1 triplet, from Cebu, contained missing data when we measured triplets in this way. Table A1 provides the estimates comparable to Table 3 in the main text using this approach. As in the main text, Cebu has higher local and global
clustering coefficients under all three definitions, although the magnitude of the difference is much smaller because the Mandaue numbers are substantially higher.
Table A1. Alternate definition of ties, test 1.
Local clustering coefficient
Global clustering coefficient Missing data assumption Cebu Mandaue Cebu Mandaue Triplet is open if missing 0.393 0.203 0.311 0.209 Triplet is closed if missing 0.405 0.203 0.311 0.209
Drop missing triplets 0.397 0.203 0.311 0.209
Average 0.398 0.203 0.311 0.209
We next consider an alternative that uses responses to “In the past 30 days, how many times have you injected drugs with the person who gave you your coupon” for both the recruiter- recruit pair (based on the recruit’s primary interview) and the recruit-recruitee pair (based on the recruitee’s primary interview). Under this coding scheme, there were 4 missing triplets, all in Cebu. Table A2 provides estimates obtained via this approach that are broadly comparable to those seen in Table A1, with the same direction of differences presented in the main text.
Table A2. Alternate definition of ties, test 2.
Local clustering coefficient
Global clustering coefficient Missing data assumption Cebu Mandaue Cebu Mandaue Triplet is open if missing 0.320 0.224 0.311 0.220 Triplet is closed if missing 0.332 0.224 0.317 0.220
Drop missing triplets 0.324 0.224 0.313 0.220
Average 0.325 0.224 0.314 0.220
Finally, we consider a case where we restrict the definition of open triplets to those that have definite i, j and i, k co-injecting ties but no j , k co-injecting tie. Because the volume of data, we focus on the “inject with” question used to define clustering in Table A2. As with above, 4 triplets in Cebu have missing data. Table A3 presents these results. As with all of our other definitions, we find that Cebu has higher clustering than Mandaue; the magnitude of this difference is similar to that seen in the main text, driven here by higher clustering in Cebu.
Table A3. Alternate definition of ties, test 3.
Local clustering coefficient
Global clustering coefficient Missing data assumption Cebu Mandaue Cebu Mandaue Triplet is open if missing 0.534 0.298 0.591 0.320 Triplet is closed if missing 0.553 0.298 0.603 0.320
Drop missing triplets 0.544 0.298 0.598 0.320
Average 0.544 0.298 0.598 0.320
Appendix B. Sample Size and Missing Data Breakdown.
There were 767 participants in the two surveys, 457 from Cebu and 310 from Mandaue.
In both cities, we exclude 7 seeds from analysis (including one in each city that did not recruit anyone). The remaining individuals in each city, shown in light grey boxes, are included in the analyses presented in Table 2. Approximately half of the respondents in each city are excluded from the subsequent clustering analysis in Table 3, because they did not recruit anyone or return to collect a follow-up incentive. The individuals for whom we can analyze clustering
(“remaining”), are involved in 374 measured triplets in Cebu and 282 measured triplets in Mandaue, reflecting approximately 1.8 recruitments per person. Of the analyzable triplets, 27 in Cebu and 6 in Mandaue did not report on clustering, which necessitates the high and low bound analyses we employed in Table 3.
Figure B1. Sample Size and Missing Data Chart.
