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Matthew J. Abdo, Maeve B. Mello, Francisco I. Thus, the authors empirically assessed a promising new method for estimating the sizes of most at-risk populations: the network scale-up method. Using 4 different data sources, 2 of which were from other researchers, the authors produced 5 estimates of the number of heavy drug users in Curitiba, Brazil. The authors found that the network scale-up and generalized network scale-up estimators produced estimates 5—10 times higher than estimates made using standard methods the multiplier method and the direct estimation method using data from and Given that equally plausible methods produced such a wide range of results, the authors recommend that additional studies be undertaken to compare estimates based on the scale-up method with those made using other methods. The resulting lack of accurate, timely, and comprehensive information makes evidence-based approaches to targeting prevention programs and monitoring effectiveness difficult. Consider one of the most basic questions one might ask: How large are the most at-risk populations around the world, and how are the sizes of these populations changing over time? Despite enormous amounts of work carried out using a variety of methods, much uncertainty remains 1. For example, in many countries where injecting drug use has been reported, no reliable estimate of the number of drug injectors exists 2. Even the estimates that do exist are difficult to interpret because of methodological differences between countries and over time within countries 3. Similar uncertainties exist about the numbers of female sex workers and men who have sex with men 4—7. One promising approach for estimating the sizes of groups most at risk of HIV infection is the network scale-up method, a technique that is new to epidemiology but has established roots in anthropology and social network analysis 8— Therefore, we empirically assessed the utility of the network scale-up method and the newer generalized network scale-up method in this context. Therefore, we conducted our study in a most-at-risk population whose size had been estimated previously: heavy drug users in Curitiba, Brazil. In addition to this previous estimate, we also estimated the number of heavy drug users in Curitiba using 2 standard methods: the multiplier method and the direct estimation method These 3 estimates provided a background that we could use to assess the scale-up and generalized scale-up estimates. Thus, while most studies of hard-to-count populations produce only a single estimate, our study produced 5 different estimates based on 4 distinct data sources, 2 of which were from other researchers. The target population in our study was heavy drug users, defined as people who had used illegal drugs other than marijuana more than 25 times in the past 6 months. Our study used 4 data sources to produce 5 estimates, as summarized in Figure 1. One source of data, which were collected by our research team, was a face-to-face survey administered to a household-based random sample of adult i. The second source of data, also collected by our research team, was a respondent-driven sample 13—17 of heavy drug users in Curitiba selected in 18 , Design of a study for estimating the number of heavy drug users in Curitiba, Brazil. Four distinct data sources, 2 of which were from other researchers, were used to produce 5 estimates. The network scale-up method estimates population sizes using information about the personal networks of survey respondents under the assumption that personal networks are, on average, representative of the general population. This estimate can be improved by averaging data over many respondents 9. The data needed for the network scale-up method come from interviews with a random sample of the general population. In this context, the 2 methods most appropriate for estimating the total number of people known by each respondent are the known population method and the summation method Because it was not clear a priori which method would produce more accurate estimates in this context, we used both methods in our study. Tests described in the Supplementary Data showed that in this study, the data from the known population method were preferable, and therefore those data will be presented throughout. The network scale-up method makes some strong implicit assumptions, and for that reason, we also collected the data needed for the generalized scale-up estimator. These data come from a sample of the target population—in this case, heavy drug users—and are then combined with the data from the general population to produce 2 correction factors: one for the lack of information flow and one for the differential network size between the target population and the general population. These correction factors and the procedures needed to estimate them are described in detail in the Supplementary Data. The results from all 5 estimates are presented in Figure 2 and described in detail below. Five estimates of the prevalence of heavy drug use in Curitiba, Brazil, and — Scale-up and generalized scale-up estimates were substantially higher than those obtained from standard methods direct estimation and the multiplier method. Estimates of the number of heavy drug users in Curitiba ranged from 4, to , We had 2 different sources of data for direct estimates. First, in , the Brazilian Ministry of Health conducted the PCAP survey, which included approximately 1, people in Curitiba, and asked directly about the use of powder cocaine and injected cocaine. From these data, we estimated a prevalence of heavy drug use within the Curitiba population of 0. In our survey of the general population, we produced a direct estimate of the prevalence of heavy drug use in the general population of 0. To produce our multiplier estimate, we learned from administrative records that heavy drug users were enrolled in the CAPS drug treatment program in August We also estimated from our sample of heavy drug users data collected in that 3. Thus, we see that these 2 commonly used methods produced similar estimates. While this is somewhat reassuring, there are reasons to suspect that direct estimation and the multiplier method both produce underestimates. Direct estimates of the prevalence of drug use can be plagued by nonsampling error 21 and are suspected to be underestimates for 2 reasons First, several studies that compared self-reported drug-use data with drug-testing data found that respondents underreport their drug use, in some cases substantially 23— Second, heavy drug users appear to be more difficult to reach in standard household surveys, which creates differential nonresponse 26 , However, the multiplier-based estimates are only as good as the data used to create them. Multiplier methods will tend to produce underestimates if the members of the target population that appear in administrative data are overrepresented in the sample of the target population—akin to problems with capture-recapture when capture probabilities are correlated For example, we suspect that participants in the CAPS treatment programs were overrepresented in our sample of heavy drug users, because middle- and upper-class heavy drug users were less likely to participate in CAPS because it is a free government program and less likely to participate in our respondent-driven sampling study because the financial incentives for participation were less attractive for middle- and upper-class drug users. If this pattern did occur, these middle- and upper-class heavy drug users would be essentially invisible to the multiplier method. Given these sources of concern about the commonly used methods, we now turn to another indirect method, the network scale-up method. Respondents in our general population survey reported knowing a total of 3, heavy drug users in Curitiba. Further, we estimated that our respondents knew a total of 92, people in Curitiba. Therefore, the scale-up estimator produced an estimated proportion of heavy drug users of 3. The generalized network scale-up estimator relaxes 2 assumptions of the network scale-up estimator. It relaxes both the assumption that people are aware of everything about the people they are connected to and the assumption that the target population has the same average personal network size as the population as a whole. As we describe in more detail in the Supplementary Data , we estimated the 2 necessary correction factors using data from our sample of heavy drug users and produced a generalized scale-up estimate of the proportion of heavy drug users of 6. The estimates derived from the network scale-up method and the generalized network scale-up method were substantially higher than those from standard methods Figure 2. However, our scale-up-based estimates of drug use are roughly comparable to those of previous national-level studies in Brazil and international benchmarks see Supplementary Data. Further, because the scale-up method allows researchers to estimate the sizes of multiple target populations, our study also estimated the number of female sex workers and men who have sex with men in Curitiba. We find that these estimates too are roughly comparable with those of other studies from Brazil and international meta-analysis see Supplementary Data. We caution, however, that all of these comparisons have a large degree of uncertainty because of differences between the studies and ambiguities in the definitions of the target populations. Although these consistency checks are somewhat encouraging, they cannot assess the accuracy of the estimates. Therefore, as a final check, we note that we also asked respondents how many people they knew in 20 populations of known size—for example, women who have given birth in the last 12 months, students enrolled in public universities, and employees of the city of Curitiba see the Supplementary Data for a list of the 20 populations. Therefore, to assess the network scale-up method, we estimated the size of each of these populations using our sample and the scale-up estimator equation 1. Figure 3 reveals that for most of the 20 populations, the size estimates, while not perfect, were quite reasonable. However, Figure 3 also reveals a tendency to overestimate the sizes of smaller populations and underestimate the sizes of larger populations, a finding that is consistent with previous studies 29 , The fact that this exact estimator in this exact sample can produce reasonable estimates for quantities we can check gives us some additional confidence about the estimates for quantities we cannot check. Validation of network scale-up estimates for 20 populations of known size in Curitiba, Brazil, A list of the 20 populations is presented in the Supplementary Data. The estimates were generally similar to the true values, but there was a tendency to overestimate the sizes of small groups and underestimate the sizes of large groups, a pattern that has been observed in other scale-up studies as well 29 , While this is somewhat discouraging, it is also exciting that we can actually detect this problem we suspect that the confidence intervals for many comparable methods are also too small, but this problem is largely invisible. Therefore, we suggest that in future research, investigators also address nonsampling sources of uncertainty, such as those introduced by response bias or recall errors. Because the scale-up-based estimates were so much higher than those obtained with existing methods, we considered many possible sources of error that might have inflated our estimates of course, as explained above, there are reasons to suspect that the standard estimates are too low. One possible source of overestimation could be the order of the questions in our survey: Heavy drug users were the first group asked about, and this might have led to inflated responses. However, no effects of question order were found in a previous telephone-based network scale-up survey in Italy Unfortunately, we were unable to randomize the order of our questions for logistical reasons, so we cannot address this possibility directly with our data. We recommend that future researchers randomize the order of the questions if possible. An alternative explanation for these apparently high estimates is that some interviewers may not have followed the study protocol. This shorter question could have produced much higher responses that would have led to a higher estimated population size. Although we had no reason to believe that this occurred, we assessed the robustness of our estimates to data from a single interviewer by systematically dropping the data collected by each of our 9 interviewers. This analysis showed that no particular interviewer had a large effect on the estimate see Supplementary Data. For example, if a respondent knew someone who drank alcohol every day, the respondent might have included this person in his or her count even though that person did not match our study criteria. A further possible source of error in the scale-up estimates is problems with the sampling frame. If residents of Curitiba differ in their propensity to know heavy drug users 30 and if the sampling frame was less likely to include persons with higher propensities to know heavy drug users possibly the homeless , then our scale-up estimates could be too low. Conversely, if the sampling frame systematically excluded persons who have a lower propensity to know heavy drug users possibly those living in gated communities , then our scale-up estimates could be too high. The relative magnitude of these problems is difficult to assess empirically, and the sensitivity of the network scale-up method to sampling frame problems is an important question for future research. Prior to data collection, we expected that the scale-up-based estimates might be higher than those made with other methods, but we did not expect them to be so much higher. As was described above, we suspect that direct estimates and multiplier estimates will be too low in our setting and possibly in many other settings. However, the generalized scale-up method, which we believe is more statistically appropriate than the scale-up method, produced estimates that were much higher than expected. Since these equally plausible methods produced such different results, we recommend that in additional studies investigators compare scale-up-based estimates with those made using other methods; conducting additional scale-up studies without having results from other methods for comparison will not address this challenge. Fortunately, our research design Figure 1 can be easily replicated in other settings. In this case, by adding a few additional questions to each data collection effort, investigators can replicate our study at virtually no cost. Further, our research design could be enriched with additional sources of data and additional estimation methods. For example, distributing a unique object to members of the target population before sampling from the target population could produce a capture-recapture estimate 33 , although some features of the target population sampling—in this case, respondent-driven sampling—may complicate this approach 17 , 33— Other sources of administrative data, such as HIV registry data, could be used to produce additional multiplier method estimates 37 , but the accuracy of these estimates will depend on the availability of administrative data and possible statistical dependencies between data sources. An additional variation in design would be to use alternative sampling methods to reach the target population e. Alternatively, it may be the case that existing methods have been systematically underestimating the sizes of these populations. At this point, we do not have enough evidence to definitively address this important possibility. However, Brazil is an emergent country with a growing population and competing health priorities Human and material resources in Brazil and in other countries should be mobilized in the most equitable way possible, on the basis of sound empirical evidence. The present study shows that scale-up-based estimators are a promising alternative to commonly used approaches, but more research is needed. The authors thank Dr. Mahy, Dr. Lyerla, Dr. Bernard, Dr. McCarty, Dr. Zheng, Dr. McCormick, K. Levy, and D. Feehan for helpful comments. They also thank Dr. Pascom, M. Vettorazzi, Dr. Moyses, D. Blitzkow, C. Venetikides, and M. Thomaz for assistance. The opinions expressed here represent the views of the authors and not the funding agencies. Google Scholar. Google Preview. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account. Sign in through your institution. Advanced Search. Search Menu. Article Navigation. Close mobile search navigation Article Navigation. Volume Article Contents Abstract. Journal Article. Salganik , Matthew J. Oxford Academic. Dimitri Fazito. Neilane Bertoni. Alexandre H. Maeve B. Francisco I. Cite Cite Matthew J. Select Format Select format. Permissions Icon Permissions. Figure 1. Open in new tab Download slide. From these survey data, one can estimate the size of the target population as. For comparison with the scale-up and generalized scale-up estimates, we estimated the number of heavy drug users using 2 common methods: direct estimation and the multiplier method Direct estimation involves asking a sample of the general population whether they are heavy drug users. The multiplier method estimates the size of the target population based on 2 pieces of information: 1 the number of people in the target population with some specific characteristic e. This information is combined as follows:. Figure 2. Figure 3. Google Scholar Crossref. Search ADS. Global epidemiology of injecting drug use and HIV among people who inject drugs: a systematic review. Improving the data to strengthen the global response to HIV among people who inject drugs. Elevated risk for HIV infection among men who have sex with men in low- and middle-income countries — a systematic review. Estimating the number of men who have sex with men in low and middle income countries. Epidemiology of male same-sex behaviour and associated sexual health indicators in low- and middle-income countries: — estimates. Estimates of the number of female sex workers in different regions of the world. Estimating the size of an average personal network and of an event subpopulation: some empirical results. Estimation of seroprevalence, rape, and homelessness in the United States using a social network approach. Counting hard-to-count populations: the network scale-up method for public health. HIV prevalence among female sex workers, drug users and men who have sex with men in Brazil: a systematic review and meta-analysis. Respondent-driven sampling II: deriving valid population estimates from chain-referral samples of hidden populations. Respondent-driven sampling: a new approach to the study of hidden populations. Sampling and estimation in hidden populations using respondent-driven sampling. Knowledge, practices and behaviours related to HIV transmission among the Brazilian population in the 15—54 years age group, Validity of drug use reporting in a high-risk community sample: a comparison of cocaine and heroin survey reports with hair tests. The validity of drug use responses in a household survey in Puerto Rico: comparison of survey responses of cocaine and heroin use with hair tests. How many people do you know in prison? How many men who have sex with men and female sex workers live in El Salvador? Using respondent-driven sampling and capture-recapture to estimate population sizes. Capture-recapture methods and respondent-driven sampling: their potential and limitations. Estimation of the number of injection drug users in St. Petersburg, Russia. Health conditions and health-policy innovations in Brazil: the way forward. Issue Section:. Download all slides. Supplementary data. Supplementary Data - zip file. Views 2, More metrics information. Total Views 2, Email alerts Article activity alert. Advance article alerts. New issue alert. Receive exclusive offers and updates from Oxford Academic. Citing articles via Web of Science Associations between pre-diagnostic plasma metabolites and biliary tract cancer risk in the prospective UK Biobank cohort. Effect of disability, homelessness, and neighborhood marginalization on risk-adjustment for hospital performance measurement. 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