Appendix A
How Did We Estimate the Number of Heavy Users?

Estimates of the number of heavy users rely principally on the Drug Use Forecasting data from 1989 through 1997. The National Institute of Justice collected these data on a quarterly basis in 24 sites. During each quarter, at each site, interviewers asked arrestees about recent and past drug use, and they requested a urine specimen. Analysis of the urine provides a reliable test of drug use within the last 72 hours.

We mapped DUF sites into counties and collapsed the data into years. Within each county and year, we separated the data by the arrestee's most serious offense at the time of booking (six offense categories) and gender. Define:

PIJKL

The proportion of arrestees in the Ith county, charged with the Jth offense category, and of the Kth gender, during the Lth year who said that he or she used drug X on more than 10 days during the month before the interview. The 10 day threshold was the criterion for being a heavy user. Drug X was heroin or another opiate, or else it was crack or cocaine. That is, we developed separate estimates for heroin/opiates and for cocaine/crack, but the methodology was the same for both. Because the data was not available for female arrestees for all sites for all years, we assumed that drug test rates for men also applied to women. Since females do not make up a large percentage of hardcore users, modest errors in this assumption should have no big effect

AIJKL

The number of arrestees in the Ith county, charged with the Jth offense, of the Kth gender, during the Lth year. The number of arrestees was taken from the Uniform Crime Report. We imputed arrest numbers when police failed to report for any one of the twelve months included in the UCR. When the police reported for more than six months, we simply prorated the reported total for the entire year. When they reported for fewer than seven months, we used a regression model (based on region and population served by the police force) to impute the total.

A preliminary estimate of the number of heavy (hardcore) drug users in the Ith county during the Jth year is written as:¹

This estimate is preliminary. It certainly underestimates the number of heavy drug users who are booked into jails in the Ith county during the Jth year, because many hardcore drug users deny their substance use. The degree of underreporting can be inferred from the DUF data. Of 13,759 arrestees who tested positive for opiates, 8,342 said they had used heroin during the 30 days before the interview.² This implies a truthful reporting rate of about 0.61 for heroin users. Of 73,504 arrestees who tested positive for cocaine, 41,346 said they had used cocaine or crack during the 30 days prior to the interview. This suggests a truthful reporting rate of 0.56.

These estimates of the rate of truthful reporting seem too low. There are three problems.³ The first problem is that the urine tests have a small but appreciable false positive rate. As an illustration, we observe that DUF sites with a low prevalence of heroin use (based on urine testing) have a lower than average rate of admissions of use (based on the above criterion).

Proportion of Arrestees Admitting Use as a Function of the Number Who Tested Positive

The pattern is clear: The larger the number of arrestees who tested positive for heroin, the larger the proportion of those who tested positive who also admitted recent use. The interpretation is less clear. Certainly we would expect false positive rates on the urine screen to be larger when the prevalence of heroin use is relatively low. Consistent with this explanation, 7 percent of arrestees who test positive for opiates in Omaha (only 116 positive urine tests) admitted 30-day use of heroin and 18 percent of those who tested positive in Fort Lauderdale (only 130 positive urine tests) admitted 30-day use. In contrast, we see reporting rates of 71 percent in New York (1493 positive urine tests) and 65 percent in San Diego (1069 positive urine tests). This same problem with truthful reporting does not seem to affect cocaine, whose prevalence is fairly high everywhere.

Another problem with self-reports for heroin is that the DUF interview asks about the use of methadone purchased on the street, but it does not ask about the use of methadone received from methadone clinics or physicians. According to SAMHSA=s Uniform Facilities Data Set, twenty of these twenty-four DUF sites have methadone clinics, and three more have methadone clinics in neighboring towns. Some of the negative responses to recent heroin use are likely to be truthful, then, despite evidence of a positive urine test. That is, some arrestees who denied recent heroin use despite positive urine tests were in methadone programs.

A third problem is that heroin and cocaine are sometimes mixed and administered together. Although users are generally aware that the drugs are mixed, it seems reasonable to assume that at least some users of heroin do not know they have used cocaine (or do not think of it as use of cocaine). Similarly, some users of cocaine do not know they have used heroin (or do not think of a mixture of heroin and cocaine as heroin use.)

Thus, the rate of truthful reporting for heroin use would seem to be higher than 61 percent, and the rate for cocaine use would seem to be higher than 0.56, but we are uncertain how much higher. Another way to look at these data is to ask: Of those people who tested positive for opiates, what percentage of them were willing to admit to illicit use of any drug during the month before the survey. Unless there is some reason to expect people to deny heroin use but admit other use, this percentage would seem to be a reasonable measure of being truthful. For this purpose, we excluded marijuana, because its use is quasi-legal in many places, so there is no reason to deny its use. Of those who tested positive for opiates, 73 percent were willing to admit some illicit drug use other than marijuana. For those who tested positive for cocaine, 61 percent reported that they used some illicit drug other than marijuana during the month. As expected, given this alternative criterion for truthful reporting, truthfulness by heroin users is greater than truthfulness for cocaine users.

Thus, let TRUTH = 0.73 for heroin and 0.61 for cocaine. Then an adjusted estimate for the number of heavy users equals:

Although HC(2) provides an estimate of the number of heavy users among arrestees, we seek to estimate the number of hardcore users in the county. Suppose that heavy drug users are arrested and booked an average of AVG_BOOK per year. Then the number of hardcore drug users necessary to produce HC(2) heavy users among arrestees equals:

There are no national survey results to provide the average yearly arrest rate of hardcore users, but there are local studies. According to an ONDCP study, hardcore users in Cook County, Illinois, averaged 0.34 arrests per year.⁴ This compares with figures of 0.39 and 0.37 for arrestees who tested positive for cocaine and heroin, respectively, and 0.36 for intravenous drug users, in Los Angeles, California.⁵ Cohen reports yearly arrest rates of 0.36 for robbers and burglars who tested positive for drugs (exclusive of marijuana) in Washington, D.C.⁶ According to Abt Associate's tabulation of the 1993 National Household Survey on Drug Abuse, 39 percent of weekly cocaine users had been arrested during the year before the survey, so their arrest rate must have been greater than 0.39. These estimates are probably low, partly for study-specific methodological reasons (Cohen), partly because those who test positive for drugs are not necessarily hardcore users (some of the studies), and partly because the studies do not control for time spent in jail and prison (all the studies). On the latter point, Abt Associate=s analysis of responses from 12,000 male non-incarcerated intravenous drug users suggests they spent an average of 15 percent of the last five years in jail or prison, and 4,000 female IDUs spent an average of 10 percent of their time in jails and prisons. Using self-reports from DUF data, Hammett, Harmon and Rhodes find that heavy users of cocaine and heroin caused about an average of 0.38 arrests per year across five cities. Presuming that some interviewers would deny previous arrests, and given that some arrestees were not at liberty for the entire year, 0.38 probably understates the underlying arrest process.⁷ Analysis by Rhodes, Hyatt and Scheiman was used to estimate annual arrest rates of 0.44 for cocaine users across six cities and 0.51 for heroin users across five cities.⁸ These estimates, too, are probably too low. Although they pertain to time on the street, they are for individuals who tested positive, not necessarily those who are hardcore, and evidence is that hardcore users have higher arrest rates than more casual users.⁹

We adopted the estimates from Rhodes, Hyatt and Scheiman because they are conceptually the cleanest measure of arrest rates for people at liberty to be arrested. That is, we assumed that AVG_BOOK equals 0.44 for heavy cocaine users and 0.51 for heavy heroin users.

At this point HC(3)ij is an estimator of the number of heavy users in the counties represented by DUF. For reasons that will become clear, we seek to convert HC(3)ij into an estimate for the Metropolitan Statistical Area (MSA) that includes the DUF site. Define:

A_RATIOIJ

as the ratio of drug-related arrests in the MSA to drug-related arrests in the county. This is typically a number close to one, except in New York City, where it is close to five, and Washington D.C. and Philadelphia, where it is close to two.10

The number of heavy users in the MSA is estimated as:

The next step is to sum HC(4) over the DUF sites that have counterparts in the Drug Awareness Warning Network (DAWN). Call this summation:

HC(5) estimates the number of heavy users in the MSAs that include a DUF site and also are part of the DAWN system. We observe that over ten years of DAWN data—1988 through 1997—this subset of DAWN sites accounted for 57 percent of all the emergency room mentions for cocaine and 50 percent of all emergency room mentions for heroin. If we adopt these figures as adjustment ratios, so that ADJ=0.57 for cocaine and ADJ=0.50 for heroin, then the final national estimate for heavy users is:

HC(6) is reported in the text.¹¹

To this point, we have estimates of the number of hardcore heroin users and cocaine users. At any time, a significant proportion of those hardcore users will be in jail or prison. The Bureau of Justice Statistics reports that 744,000 people were held in Federal or State custody in 1985 and 1.1 million were held in 1990. This suggests that about 1.0 million were held in custody in 1988, the beginning of the data series reported here. By 1998 the number had grown to 1.8 million.¹² According to BJS¹³, the percentage of inmates on a 1991 survey who reported ever using drugs during the month before the survey were 25 percent of inmates for cocaine, 9 percent for opiates, and 7 percent for stimulants. Comparable figures on a 1997 survey were 25, 9 and 9 percent, respectively, so estimates of prior drug use have not changed appreciably over time. Multiplying the number of inmates by 0.25 (for cocaine) and 0.09 (for heroin) provides yearly estimates of the number of hardcore users incarcerated during each year. We subtract the number of incarcerated hardcore users, INCAR, to estimate hardcore users on the street:

Estimation requires two more final steps. The DUF data were provided by special request from the National Institute of Justice, whose contractor created a uniform file for DUF data from 1989 through 1998. This meant that we could not estimate hardcore drug use for 1988, and instead, for the 1988 estimate, we just used the figure reported previously in What America's Users Spend on Illegal Drugs: 1988–1995. The FBI data were only available through 1997, so we could not use the methodology described above to estimate 1998. Furthermore, given that these calculations were being made in late 1999, the UCR data had not been collected for 1999 or 2000.

To project hardcore heroin and cocaine use for 1998–2000, we used a simple methodology: The 1998 estimate is a linear projection based on observations from 1995–1997. The 1999 and 2000 estimates were set equal to the 1998 estimate. As a final step, we used a three year moving average (centered on the reported year) to smooth the estimates. The end year (1988 and 2000) are based on a two-year moving average. The smoothed estimates are reported in the text.

We had to modify this approach for methamphetamine.

Methamphetamine users seemed to have an unusually high rate of truthful reporting, at least when compared with the rate for cocaine and heroin users. About 69 percent of those who tested positive said they used during the last month.

• We did not have separate arrest rates for methamphetamine users.
• We used the same rate as was used for cocaine users: 0.44 arrests per year.
• The DUF MSAs accounted for only 23 percent of emergency room mentions for methamphetamines. Thus, to adjust data from DUF sites to represent the nation, we used an adjustment factor based on 1/0.23.
• We assumed that the proportion of hardcore methamphetamine users in the prison population grew linearly so as to achieve 7 percent of arrests in 1991 and 9 percent in 1997.

Given the high year by year variance in the resulting estimates, we did not project a trend into 1998. Instead, we set the estimates for 1998 through 2000 equal to the estimate for 1997. Three-year moving averages were then used to smooth the data.

Endnotes

¹ DUF is not a probability sample, and in some places, the DUF sample looks unlike the larger population of bookings. (J. Chaiken and M. Chaiken, Understanding the Drug Use Forecasting [DUF] Sample of Adult Arrestees. Lincoln, MA: LINC, 1993.) To deal with the fact that DUF is not a probability sample, we weighted the data by FBI arrests and by gender. Provided that DUF can be treated as random conditional on the booking charge and the arrestee's gender, this approach should provide estimates that approximate that of a true random sample.

This assumes, however, that we know the number of bookings by charge and gender. There are no booking data, so we had to used arrest data to approximate booking data. We assumed that all arrests for crimes of violence, property crime, robbery, drug-law violations and sex-related crimes resulted in bookings. We assumed that all other offenses resulted in bookings for half the arrests.

Another problem with DUF is that the survey is generally based on a single jail in each county. This is often little or no problem, because one jail served the entire county. At some other places it is a minor problem, because there is one dominant jails and a few small ones. But at a few other placesB such as in New York and Los Angeles B one jail (Manhattan and Los Angeles City) must represent bookings in the rest of the county. Until ADAM implements its new sampling plan, we cannot estimate the bias, if any, imparted by assuming that, say, Manhattan (New York County) represents the other four New York boroughs.

² Someone who tested positive for opiates must have used an opiate within about three days of their interview. This three-day period is included within the last thirty days, so anyone who tested positive would be lying if they said they had not used in the last thirty days. Of course, people could have used in the last thirty days and still tested negative at the time of the interview, but that fact is irrelevant to a judgement about the rate of truth telling.

³ There may be a fourth problem not discussed in the text. The DUF survey is being replaced by the Arrestee Drug Abuse Monitoring (ADAM) survey. When pretesting the ADAM instrument, the ADAM team found that many people who tested positive for a drug denied use during the last three days but admitted use during 27 or 28 days during the last month. Apparently they simply wanted to avoid an admission of the drug use episode most associated with their arrest, but they were willing to report about other use. This phenomena would cause hardcore drug users to be more truthful than occasional drug users, so estimates of truthfulness may be understudied for hardcore users.

⁴ R. Simeone, W. Rhodes and D. Hunt, "Methodology for Estimating the Number of Hardcore Drug Users," report submitted to the Office of National Drug Control policy, March 1997.

⁵ Y. Hser, "Population Estimation of Illicit Drug Users in Los Angeles County," Journal of Drug Issues 23(2), 1993: 323-334.

⁶ J. Cohen, "Incapacitation Effects of Incarcerating Drug Offenders," Final Report Submitted to the National Institute of Justice, May 4, 1992, figures interpolated from figure 4.

⁷ T. Hammett, P. Harmon and W. Rhodes, paper prepared for the National Commission on Correctional Health Care, Abt Associates Inc., October 14, 1999.

⁸ Calculations based on W. Rhodes, R. Hyatt and P. Scheiman, "Predicting Pretrial Misconduct with Drug Tests of Arrestees: Evidence from Eight Settings," Journal of Quantitative Criminology, 12(3): 315-348.

⁹ E. Wish, M. Cuadrado, and J. Martorana, "Drug Abuse as a Predictor of Pretrial Failure-to-Appear in Arrestees in Manhattan," unpublished paper prepared under Grant 83-IJ-CX-K048 to Narcotic and Drug Research Inc.

¹⁰ Using drug arrest ratios across an MSA poses some problems. We would like to prorate based on arrests for cocaine and for heroin, as appropriate, but this is not possible. The FBI lumps all drug-law violations together. We cannot distinguish heroin arrests from cocaine arrests.

¹¹ Using DAWN to prorate estimates from DUF sites to other locations poses potential problems. It is difficult to know just what DAWN represents especially given trends that contrast sharply with trends reported in other sources. Because trends are so difficult to interpret, we employ the average ratio of ER mentions over the entire ten years in our calculations.

Although trends are difficult to interpret, DAWN clearly reflects the behavior of hardcore drug users, so DAWN is helpful for our purposes. Of course, DAWN reports vary from year to year for reasons that have little to do with long term trends in drug use. About 32 percent of the time heroin users go to the emergency room because of unexpected reactions or overdose. The figure is 38 percent for cocaine users. Such visits are likely to result from idiosyncrasies in the drug markets across cities. Assuming that the ratio of ER mentions in city A to city B reflects the ratio of hardcore heroin users in city A to city B is unjustified in part because of those idiosyncrasies. But when we adopt a longer time-frame, and when we base the ratio on larger groups of MSAs, the assumption that ER mentions is proportional to the number of heavy drug users seems supportable.

¹² D. Gilliard, Prisoners and Jail Inmates at Midyear 1998, Bureau of Justice Statistics Bulletin, U.S. Department of Justice, March 1999.

¹³ C. Mumola, Substance Abuse and Treatment, State and Federal Prisoners, 1997, Bureau of Justice Statistics Special Report, U.S. Department of Justice, January 1999.