Are users’ most recent drug purchases representative?

Abstract

Background

Various surveys now ask respondents to describe their most recent purchase of illicit drugs, as one mechanism through which market size can be estimated. This raises the question of whether issues surrounding the timing of survey administration might make a sample of most recent purchases differ from a random sample of all purchases. We investigate these issues through a series of questions which ask about the three most recent purchases, and about drug use.

Methods

Data were drawn from 688 respondents in the Melbourne Injecting Drug User Cohort Study across the period 2008–2013 and 2782 respondents to the Washington Cannabis Consumption Study in 2013. Responses to questions about the most recent purchases were compared to larger subsets of all recent purchases.

Results

For heroin, methamphetamine and cannabis no differences were found between the amount spent by participants on their most recent purchase and the average amount spent on three or more recent purchases. There were also no differences concerning the locations and types of deals, and the duration between consecutive cannabis purchases was the same for first and second most recent, and second and third most recent.

Conclusions

Asking about the most recent purchase appears to be an economical way to learn about purchases more generally, with little evidence of substantial variation between the most recent purchase and other recent purchases reported by participants. In spite of consistent findings across our two surveys, further replication of the work reported in this paper involving other populations of users is warranted.

Introduction

The harms associated with illicit drugs include those created by their distribution and sale (UNODC, 2013), so understanding the size and character of illegal markets is important (Kilmer and Pacula, 2009).

Illicit drug markets have been studied in various ways, including analyses of court documents (e.g., Mason and Bjerk, 2011, Bright et al., 2012), ethnography (e.g., Fuentes and Kelly, 1999, Johnson, 2003), analysis of seizures and undercover buys (e.g., Reuter and Caulkins, 2004, Coomber, 2006, Burgdorf et al., 2011), analysis of surveillance videos (e.g., Moeller, 2012), and surveys of drug users. Surveys can ask users how much they spent; what they bought, from whom, when, and where; how easy it was to locate a dealer and whether law enforcement complicated that search, among other topics. Market-oriented questions have been analyzed in surveys of users in the household population (e.g., Caulkins and Pacula, 2006), street users (e.g., Hando et al., 1998), arrestees (e.g., ONDCP, 2012), web-survey respondents (e.g., van Laar et al., 2013), and high-school students (e.g., Johnston et al., 2012).

Estimating the markets’ size, in terms of revenue, is of particular interest since users’ spending drives economic-compulsive crime, systemic crime, impoverishment of some users, and incentives for corruption. Kilmer et al. (2011) describe four strategies for estimating markets’ size; the most direct multiplies prevalence of use by population and average spending per user, meaning that accurate estimates of average spending are needed.

Some analyses (e.g., ONDCP, 2012) estimate monthly spending by multiplying the size of most recent purchase by the number of purchases made in the past-month. This raises the question of whether the most recent purchase is representative and so whether extrapolating from descriptions of most recent purchases gives an accurate understanding of purchases overall and, hence, of markets. After all, even when surveys sample users at random, they do not sample purchases randomly. If because of the vagaries of sampling the most recent purchases tended to be larger than average, then the multiplication just described would over-estimate user’ spending and, hence, the size of the markets. This possibility is illustrated by the following hypothetical example from ONDCP (2014):

Suppose there were a population of users who consume one gram of cannabis each day (so 30 grams per month). Suppose further that they buy an ounce once each month, and also make two additional purchases of one gram each, perhaps because they shop around before making their main purchase. An ounce is roughly 28 grams, so these three purchases add up to 1 + 1 + 28 = 30 grams per month. If this population were surveyed about their most recent purchase and each respondent's survey date was random there would be one chance in thirty that the survey would be administered in the 24 hours following the first one-gram purchase, one chance in thirty it would be administered after the second one-gram purchase, and 28 chances in 30 that it would be administered after the one-ounce purchase and before those 28 grams run out, occasioning a new purchase. At the population level, 2 out of every 30 survey respondents would report their most recent purchase as one gram, and 28 out of 30 would report their most recent purchase as 28 grams. So the average size of the most recent purchase reported would be (2/30) * 1 + (28/30) * 28 = 26.2 grams. Since all respondents report making 3 purchases per month, the naïve estimate of 26.2 * 3 = 78.6 grams purchased per person per month would be two-and-a-half times the true value of 30 grams per person per month. This phenomenon of most recent purchases being larger than typical purchases if big purchases are followed by long inter-purchase times is known as random incidence (Larson and Odoni, 1981).

There are other potential sources of bias when using only most-recent purchase data. For example, if weekend purchases tend to be larger and survey staff work Monday to Friday, then the survey may under-estimate the average purchase size. Likewise if data are collected around mid-day and drug users purchase both small “wake-up” doses and larger amounts in the evening, then most recent purchases may be smaller than average purchases. There might even be Hawthorne effects if payments made to compensate respondents for participating in the survey are large enough to influence purchasing decisions (Landsberger, 1958).

In short, assuming that the most recent purchase is representative amounts to making a strong untested assumption, yet this is a feature of some studies of drug markets. We investigate the assumption by asking respondents in two different surveys to describe a larger number of past purchases, and then comparing the most recent purchases nominated to that larger set with respect to price paid, location, and time between purchases. If biases of the sort just described are commonplace, then we would expect to observe significant differences.

Estimates of market size combine estimates of purchase size with estimates of purchase frequency. We also investigate whether the intervals between the two most recent purchases are similar to gaps between the 2nd and 3rd most recent purchase and, more generally, whether asking about multiple recent purchases offers greater insight into purchase frequency than does simply asking directly how many purchases were made within a specified period of time.