How much of the cocaine market are we missing? Insights from respondent-driven sampling in a mid-sized American city
Introduction
The size of an illegal drug market can be defined by the number of users, number of sellers, total consumption, or total expenditures. The measure of greatest interest depends on the question being asked. For example, the number of users is important for treatment planning, while expenditures can be more useful when studying drug-related crime, since most crime related to illegal drugs is economic-compulsive and systemic, not psychopharmacological (Pacula et al., 2013).
It is difficult to estimate any of these market measures since drug users are a hidden population and random sampling is not feasible. General population and school-based surveys may produce reasonable estimates for common and less stigmatized aspects of drug use (e.g., number of marijuana users; Kilmer et al., 2013, Kilmer et al., 2011, Office of National Drug Control Policy, 2001), but their limitations for measuring heavy use of less common substances are well known (Office of National Drug Control Policy, 2012, Office of National Drug Control Policy, 2014). As an extreme example, the National Survey on Drug Use and Health (NSDUH) suggests there were 60,000 daily/near-daily heroin users in the U.S. in 2010, but rigorous estimates rooted in other datasets put that figure at closer to 1 million (Caulkins et al., 2014).
There are various approaches for obtaining information about heavy users, such as multiplier and capture-recapture methods. Multiplier methods pick one “lens” that is thought to encompass an important share of the activity and then extrapolate to what falls outside that lens. For example, Archibald et al. (2001) estimate the number of injection drug users (IDUs) by dividing the number who appear in an HIV serodiagnostic database by the proportion who report being tested each year. Likewise Holmberg (1996) estimated the number of IDU in the U.S. as 11.3 times the number of IDUs in treatment on the grounds that 10–20% of IDUs are in treatment at any given time. (11.3 is the (rounded) simple average of half the smallest multiplier (0.5 * (1/20%)) and twice the largest multiplier (2 * (1/10%)) suggested by the 10–20% range.) However, multiplier methods are only as good as their often frail multipliers, and can perform poorly compared to other approaches, such as capture-recapture methods (Hickman et al., 2006).
A related approach uses two or more complementary “lenses” that together are thought to cover the bulk of the activity to be estimated. This requires the analyst to add what is seen through each lens separately, subtract the overlap to avoid double-counting, and possibly use a multiplier to adjust for the (hopefully small) amount of activity that is not captured by either lens. This is essentially an application of elementary probability rules. If two lenses see subsets A and B of the hidden population, then N[A ∪ B] = N[A] + N[B] − N[A ∩ B], where the operator N[] computes some outcome of interest, such as the quantity consumed or the amount of money spent on drugs. The estimate mentioned in the second paragraph—that there were about 1 million daily/near-daily users of heroin—was generated using this method.
In the United States, it is commonly believed that many frequent users of cocaine, heroin, or methamphetamine will encounter the arrest and/or treatment lenses in any given year. For example, Mark Kleiman has argued that the majority of cocaine and heroin consumption is attributable to people under criminal justice supervision—meaning those on pretrial release, probation, or parole (Kleiman, 2001).
In other areas of study involving hidden populations, there are occasional census opportunities that can be used to calibrate methods for estimating parameters. For example, counts obtained following the draining of a reservoir can help refine methods for estimating fish populations. Few such census opportunities exist for drug market aggregates; as a result there is no “gold standard” which can be used to estimate the proportions of total market activity that are actually covered by the different lenses.
In this paper, we assess the extent and quality of coverage provided by three lenses commonly used to estimate drug market attributes: (a) past-year arrestees, (b) people who received treatment in the past-year, and (c) the household population. We do this by comparing estimates derived from various combinations of these lenses with estimates from a “silver standard:” respondent-driven sampling (RDS; Heckathorn, 1997, Heckathorn, 2002). We refer to RDS as a silver, not a gold, standard to acknowledge its limitations. However, to the extent that the RDS-based estimates are more accurate than other available alternatives, the exercise can generate insights into the relative strengths and limitations of the various lenses commonly used to understand drug markets. RDS estimates have been shown to be asymptotically unbiased for true population parameters provided that certain assumptions are met (Salganik and Heckathorn, 2004), and have been used to study drug-using populations in mid-sized (Heckathorn et al., 2002) and large urban areas (Iguchi et al., 2009).
Section snippets
Location
The analysis focuses on drug users in Roanoke, Virginia, a medium size city (population 97,000; 68% White and 29% Black) that is the principal municipality within a Metropolitan Statistical Area of 309,000 people. 22% of the city's residents live below the poverty level, compared to 11% for the state (U.S. Census). In 2011, Roanoke participated in a U.S. Department of Justice program—the Drug Market Intervention, or DMI—to reduce drug selling and associated crime in its Hurt Park neighborhood.
Results
Both the crude and adjusted estimates of sample characteristics (Table 2) describe a group in which approximately 2/3 of respondents are male and approximately 2/3 of respondents report an education level of high school degree or lower. A majority of the sample is unemployed; the overwhelming majority of respondents report cocaine usage (either powder or crack) within the last 30 days; and high levels of use of marijuana, Percocet and other prescription painkillers, and benzodiazepines are also
Discussion
There are three important limitations of this analysis: (1) RDS-based estimates are only a silver, not a gold standard for understanding true market aggregates, (2) the Drug Market Intervention could have affected the cocaine market in ways that influence responses; and (3) results could be different in other locations. In particular, these samples may be more representative of an urban place-based market than of suburban social-network based distribution. If participants in an urban
Role of funding source
This work was funded in part by a National Institute of Justice (NIJ) grant (#2010-DJ-BX-1672) to the RAND Corporation, as part of a multi-site, multi-armed evaluation of the Drug Market Intervention (DMI). The NIJ had no role in any of the following: study design; collection, analysis, and interpretation of data; the writing of this manuscript; the decision of whether and where to submit the manuscript for publication.
Contributors
Jonathan Caulkins conceived of the underlying analytical approach (exploiting RDS to assess the coverage proportions of different methods for estimating drug market aggregates). He was also the primary author of the manuscript. Jesse Sussell was the secondary author of the manuscript and the primary analyst. He conducted the technical analyses in the paper, including RDS weight generation and statistical analysis. Beau Kilmer was the primary investigator of the evaluation within which the RDS
Conflict of interest
No conflict declared.
Acknowledgements
We are grateful to Susan Everingham, Greg Midgette, and Peter Reuter for their comments on earlier drafts of this paper. The views presented here are solely those of the authors.
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