FIGURE 4-Mean lag distribution for Connecticut Mental Center. (Calculated from .... distance telephone call frequency an
Recent Spread of Heroin Use in the United States LEON G. HUNT
New heroin use peaked in major U.S. cities around 1968, leading to a theory of a simultaneous national "epidemic". Analysis of treatment data does not support this theory. Instead, peak use is shown to have shifted from larger to smaller cities and is still occurring in places under 400,000 population.
Introduction and Discussion Is new heroin use spreading in the United States or is it declining from a single nationwide peak which occurred around 1968? The answer may be yes to both parts of the question, depending on how incidence data are viewed. In exploring the question, this study examines incidence estimates and finds that they are ambiguous. Aggregate treatment program data seem to show that the peak period of new heroin use- occurred everywhere in the U.S. about 1968, but when local data are corrected for addicts' delay in entering treatment, this synchronous national "epidemic" becomes a sequence of local peaks ranging from 1967 to the present. Further analysis shows that the sequence of local peak use is related to city size-large cities have generally preceded small ones. There is a definite limiting relationship, so that after a given time all cities of a certain size will have experienced peak use. This relationship implies that new heroin use may continue to appear in smaller cities in the future. Currently (1 974), rising heroin use incidence is limited to Standard Metropoliton Statistical Areas (SMSAs) of about 500,000 population or less. The shift from large to small is empirically similar to "hierarchical diffusion" observed in the spread of innovations (such as television). If this relationship is correct, it has important implications for drug abuse policy and planning. First, it leads to an estimate for future levels of heroin use in "new" cities. In the next five years, one might estimate that no more than Mr. Hunt is a consultant in applied mathematics who specializes in analysis of social problems. His address is 310 Park Road, Alexandria, VA 22301. This paper is based on research jointly sponsored by the Drug Abuse Council, Inc., Washington, D.C., and the Special Action Office for Drug Abuse Prevention, Executive Office of the President. The author is grateful to Mr. James DeLong, Program Director, DAC, and Dr. Robert L. DuPont, Director, SAODAP, for support and encouragement. A more extensive version of this work will be published by the Drug Abuse Council in 1974.
16 AJPH Supplement, Vol. 64, December, 1974
200,000 new users* are likely to appear in places where heroin use has not yet become widespread. These estimated results suggest the need for continuous reallocation of drug treatment funds to smaller and smaller cities as peak use shifts and treatment demands declines in areas of older heroin use. This urban sequence of peak use also defines those locales in which intervention is still possible. If there is to be any systematic attempt to prevent epidemic heroin use, it must be made in the middle-sized and small cities which may only now be approaching their peak phase. This paper begins with a discussion of incidence of first heroin use obtained from treatment program data, showing how crude incidence must be corrected to account for addicts' lag between onset of use and entry into treatment. The statistical characteristics of lag estimators are developed and applied to treatment program incidence data. The resulting patterns of peak heroin use are compared with city sizes to show the relationship between population and epidemic sequence.
Measures of Diffusion Incidence of First Use This study employs incidence of first use of heroin in a given locale as a unique measure of spreading. There are obvious difficulties in determining incidence: all cases are not known, and the definition of a "case" itself is uncertain, possibly ranging from casual occasional use to addicted daily use. In spite of these problems (which are also true of many diseases, such as syphilis and mental disorders that may be both stigmatized and hard to diagnose), incidence of first use retains a special significance, since it alone measures the ten*This is determined by applying empirical incidence rates to the population at greatest risk of drug abuse (individuals age 15-29 years) in cities with populations of less than 300,000.
dency of new individuals to become involved with heroin. Indirect indicators, such as overdose deaths, are probably more closely related to prevalence of total active use than to the actual spread of the drug. Widespread drug treatment facilities offer an unusual opportunity to sample incidence of first use geographically. These treatment-derived incidence data are sometimes criticized for their demographic bias. Since treatment units are located where highly visible heroin addicts are known to live-often in low income or ghetto areas-they may ignore certain groups, such as middle class or suburban users, or those who obtain private treatment. The criticism may be valid: little is known about the demography of total heroin prevalence. However, drug programs at least include incidence data for an important and treatable group of users and, more especially, the one which is responding to public programs. Treatment data therefore describe a significant class of users, and, while they do not measure absolute incidence, they are worth detailed study. This study attempts a systematic interpretation of incidence derived from treatment program data.
Correcting Treatment Program Data for Onset-to-entry Lag The most casual inspection of incidence of first use data from voluntary treatment programs reveals a characteristic
pattern: there are always relatively few heroin users admitted during their first year of heroin use (Figure 1). As time passes, more and more users originating in a given year will appear in such programs until, after about five or six years, the given onset cohort (i.e., all users who began heroin use during a given year) will produce few new entrants-it will be exhausted, from the treatment point of view. This delay between onset of heroin use for the members of a given onset cohort and their subsequent entry into treatment over a period of years is collectively referred to as "lag." Lag is responsible for many misinterpretations of the incidence of local heroin use, since it always results in the appearance of new use dying out, and causes apparent peaks of maximum use to migrate to later and later years. There are two basic approaches to correcting for lag, both involving the construction of lag distribution curves.* One method in common use is to take all users who entered treatment in a given year (an entry cohort) and to classify them into subsets of those who began use within the last year, within one to two years, within two or three years, etc. This produces a conditional distribution, the probability of lag, given the user entered treatment in the year under con-
*In mathematical terms, lag is a random variable, the interval of time between first use of heroin and entry into treatment, and a lag distribution curve is its probability distribution function.
(1)
(2)
CD
a,
a I I I
I
I
._
0~Lo
a,
I
I
I
I
I
m
Year
0
x I..
z
m
m+2
m+4
m
FIGURE 1-Development of a hypothetical Incidence curve as recorded by the intake of a treatment program. Sold line is cumulative Incidence for the year Indicated. The most recent year for which data are available is designated "m". (1) a is the incidence of new users from year (m-1) who had appeared by the end of the year m. (2) b more had appeared in year m+1, (3) entered the program in year m+2. (4) The final stable form of the curve.
Spread of Heroin Use 1 7
cohorts (Figure 2). The distribution often appears stable from year to year (i.e., the slope of each curve in this family of curves is similar), suggesting that there has been little change in addicts' disposition to volunteer for treatment (Figures 2,3). Of the programs examined to date, none have yielded onset cohort lag curves which showed progressive changes in slope which would indicate a changing lag disposition for entrants. If onset cohort lag curves are stable, percentages of each year's entrants may be averaged to yield a mean cumultative entry curve, which is a more accurate estimate of overall behavior than any single year. Mean cumulative entry curves are displayed in Figures 4 and 5. Curves from shorterduration programs also may be adjijsted for probable longerterm behavior, by assuming they will develop like known older programs. Having mean cumulative entry data, crude estimation of lag effects is a direct consequence. For example, if the cumulative curve for a program shows that 10 percent of users in a given onset cohort enter treatment during their first year of heroin use (a "10 percent one year lag"), then we might expect that 90 percent of the current year's cohort has not yet entered treatment, but will eventually do so. Suppose that 12 users who began use in the current year had actually entered treatment in that same year. Then the estimate of that year's total onset would be:
sideration. Alternatively, all the users originating in a given year (an onset cohort) may be classified into those who appeared for treatment within one year, one to two years, etc. In either case, the specific duration of lag cannot be measured beyond the program age. That is, if treatment has been available for five years, six years or greater lag cannot be distinguished. Apart from this common limitation, there is a fundamental distinction between the two methods. If incidence were constant, they would yield the same result, but, since it varies from year to year (and it is exactly this variation we are seeking to estimate), entry cohort-based lag contains a serious flaw. Consider a situation in which a large peak in incidence actually occurred. This peak will generate relatively larger groups of program entrants for each subsequent year, regardless of the shape of the lag curve. But these large groups of entrants from the peak year will occur at different intervals for each entry cohort. That is, as time passes, the peak year's input to an entry cohort will represent a longer and longer lag. Therefore, the lag distributions will migrate to the right (mean lag will increase) creating the illusion of unstable and lengthening lag time for program entrants. This misunderstanding is widespread. Proper estimation of lag is based on onset cohorts, which are homogeneous groups that may be compared from year to year to determine whether their distributions are similar or not. In principle, of course, any onset cohort is always incomplete-more entrants may appear in the future-but in practice some older programs exhibit exhaustion of onset
= 12 = 120 Observed Entrants for Onset Year 10 Cumulative % for Years of Delay from Onset Year
100
/ 1968 Onset Cohort /
75
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.
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Years from first use of heroin to entry into treatment FIGURE 2-Distribution of lag for addicts entering treatment at the Connecticut Mental Health Center, New Haven. Onset cohorts 1960-68 are shown. (Calculated from data In the Institute for Behavioral Research, Texas Christian University, sample. 1972 data Incomplete).
18 AJPH Supplement, Vol. 64, December, 1974
13
100
75 4.'
c
0~a)a, Cu
50
E 0
25-
0
1
2
3
4
5
6
7
8
9
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Years from first use of heroin to entry into treatment FIGURE 3-Distribution of lag for addicts entering treatment at LaUave Inc., Albuquerque, New Mexico. Onset cohorts 1962-68 are shown. (Calculated from data In the IBR, TCU, sample. 1972 data Incomplete).
Accuracy of Lag Estimates: Mathematical Considerations Assuming lag to be stable (which can be determined empirically by comparing successive onset cohorts for a given program), the variation from year to year in pi, the proportion of entrants showing a lag of duration years, is due solely to sampling effects. By averaging the series of onset cohort curves, we determine pi, and then assume that in any calendar year where we wish to estimate lag effects, that p5, is the actual percentage which the observed number of program entrants represents. For instance, in the preceding example, pi = 10% and the 12 observed entrants with current year onset are assumed to be 10% of that-year's total onset cohort. Any year's estimate of pi will have a hypergeometric distribution (as a result of sampling without replacement from a finite population-the total local population of users who began use in the year in question), and will therefore differ from P. The effect is that the chosen confidence limits on p will become two alternative denominators, one larger and one smaller than pi, which will increase or decrease the estimate of the true incidence for that year. Note that the resulting larger and smaller estimates of the size of the onset cohort (which produced the observed program entrants) are not confidence limits, but are simply estimators corresponding to the confidence limits on P. The actual distribution of the size of the onset cohort is unknown (to this author). The error in the onset cohort is probably largest in the current year, where the numerator of the estimator (observed onset for current year) is a small integer which is divided by p,
a small proportion. However, the absolute size of the current year's incidence is of little concern: we are primarily interested in the relative shape of the curve-whether it is rising or falling, and less in its steepness.
Other Considerations* The apparent constancy of lag is difficult to explain, considering all the changing conditions which may influence an addict's attitude toward treatment. Program capacities, treatment modalities, drug laws and the rigor of their enforcement, the availability of heroin and other drugs, and other circumstances alter radically from year to year but, in spite of these differences, empirical data show lag to be fairly consistent. Any explanation for lag is pure speculation. It cannot be tested by asking addicts, since lag is a description of aggregate behavior. (Just as the data in mortality tables are outside individual experience.) One possibility is that lag measures a fundamental characteristic of heroin addiction-its "involuntary" duration. That is, the lag curves shown above may actually record the distribution of time before addicts become treatable. (Note that we are considering only those who ultimately present themselves for treatment.) If such an "untreatable" period actually existed, it might be little affected by externals such as program characteristics, etc. *The author is grateful to the reviewers of this manuscript for raising some of the issues discussed in this section.
Spread of Heroin Use 19
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Years from onset of use to entry into treatment FIGURE 4-Mean lag distribution for Connecticut Mental Center. (Calculated from Figure 2).
FIGURE 5-Mean lag distribution for LaLlave, Albuquerque, N.M. (Calculated from Figure 3).
The precise definition of lag-either its rate or its stability-is immaterial to the following results. Our purpose is to use lag data to identify approximately the peak period of heroin use in a given locale.
occurred. A distinct limiting relationship is shown (indicated by the broken line). Note that this is not a correlation: there is no one-to-one relationship between SMSA size and peak year, but rather, the peak year is limited or constrained by SMSA size. In other words, peak use occurred early in cities of various sizes-in 1967 in the New York City SMSA (11.6 million) and also in smaller cities-but as time passed the peak became limited to smaller and smaller cities. Evidently the largest cities all had early peaks (along with some smaller ones) and no peaks ever appeared in cities of a given size after a certain time. E.g., by 1971 all SMSAs of a million or more had already experienced peak use (so far as existing data
Results Diffusion Patterns When lag corrections are applied to local treatmentderived incidence data, two changes may occur. Apparent peaks increase in height, and peak use shifts to later years. Not all curves change: incidence from older areas of heroin use remains much the same (e.g., New Haven, Connecticut, Figure 6), but newer locales of use change significantly (Figures 7 and 8). These results are fairly insensitive to the exact shape of the lag curve, i.e., even appreciable differences in the curves would usually rot affect the year in which the peak occurs. When corrected incidence is determined for cities of different sizes, an interesting pattern emerges. Figure 9 plots the year of peak use against the size of the Standard Metropolitan Statistical Area (SMSA) in which the epidemic
very
20 AJPH Supplement, Vol. 64, December, 1974
show).
This time shift from larger to smaller cities is similar to the phenomenon of "hierarchical diffusion" observed by geographers in studies of spreading innovations. For example, the introduction of television, as measured by the date of opening of TV stations in cities of various sizes, displays a pattern like peak heroin use, though interrupted by halts during World War II and the Korean War.* Figure 9 compares *See Brian Berry, "Hierarchical Diffusion: The Basis of Developmental Filtering and Spread in a System of Growth Center," in N.M. Hansen, ed., Growth Centers in Regional Economic Development (New York: Free Press, 1972), pp. 108-138, especially 1 18-123.
)
150
I Ratio of Peak to Background ]Incidence Approximately 9:1
0-
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100
Estimated Incidence
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o
\
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0 1960
61
-.01 62
-
-
63
-Mean Endemic Incidence
64
66 68 67 Calendar Years
65
70
69
71
72
73
74
FIGURE 6-Reported and estimated Incidence of new heroin use, Connecticut Mental Health Center, New Haven (from data In Figure 2).
300r0n
9 200
Estimated Incidence Allowing for Lag
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0 z 10 Apparent Peak Incidence .0 m-m m m z Ratio of Apparent 0 Peak to Mean = 3:1 n1-
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1960
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72
73
Calendar Years FIGURE 7-Reported and estimated Incidence of new heroin use, Lave Inc., Albuquerque, N.M. (from dab In Figure 3).
Spread of Heroin Use 21
20
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Calendar Years FIGURE 8-Reported and estimated incidence of new heroin use, Crossroads Services, Inc., Jackson, Mississippi. (Data from Crossroads,
TV data from Berry to almost identical data for peak heroin use.
The mechanism of hierarchical diffusion is not fully understood, although a number of mathematical rationalizations are capable of accounting for it.* * What is important is the fact that innovations do spread in this way from larger to smaller places, and peak heroin use-itself a period of intense social "innovation"-is empirically similar. Thus, there seems little justification for the assertion that all heroin epidemics have grown out of indigenous sources. If this were true, there would be no way to account for the limiting relation between city size and sequence shown in Figure 9. Instead it seems more likely that peak use has followed something like Most of these are gravity type models in which the diffusion potential between two cities is a direct function of their "masses" and an inverse function of their "distance" apart, by analogy to physical gravity. Mass and distance are variously defined and may be simply population and geographical separation, or they may be more abstract analogues. It has been observed that various processes such as long distance telephone call frequency and inter-city freight shipments are approximately described by such models. * *
22
AJPH Supplement, Vol. 64, December, 1974
Inc.)
typical diffusion paths-for whatever reasons.t If this is true, the implications are critical to treatment planning and epidemic intervention. For example, Figure 9 suggests that future peak use will be limited to SMSAs of about 500,000 population or less. Evidently these locales offer the best opportunities for intervening to prevent epidemic use and likewise they represent the locus of future treatment demand.
Estimates of Future Addiction If diffusion trends described above are accurate, they provide a basis for estimating future addicts. Assuming that local epidemic use will be limited to population concentrations of 500,000 and less, the following susceptible group was defined by the 1970 Census (Table 1). tNote that the sequence of peak use, here attributed to inter-city diffusion, cannot be related to the establishment or treatment programs themselves. Programs offer a means of observing or sampling some part of local incidence, but they cannot affect the past occurrence of new drug use. Neither is there any reason to suppose that they sample different onset years unequally (except due to lag).
10,000,000 r-
10,000,000 WORLD
.\ WAR II
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. \|S
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1,000,000
1,000,000
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1940
.
Date of TV Opening
10,000 19(65
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i
70
75
80
Year of Peak Heroin Use
FIGURE 9-Diffusion of TV and peak heroin use. (TV data modified from Berry, in Growth Centers in Regional Economic Development. Heroin data from treatment programs, corrected for lag).
There were about 28 million individuals in the susceptible age zone in 1970, and this number will not change greatly over the next few years. Ignoring those who both leave and enter the susceptible zone, we can make crude estimates of the maximum number of addicts that could occur in these smaller cities. Even at a gross addiction rate of one percent (which is far too high by current estimates), the remaining susceptible group would yield only 280,000 addicts,4t i.e., about one-third to one-half as many as are currently thought to exist. A more realistic estimate might be based on the assumed rate of 3 per 1,000, a common estimate of the frequency of addiction in the general population (i.e., 750,000 in 220,000,000). This leads to a total of 85,000. Still another estimate follows from the fact that current addicts in treatment are predominantly black males (about 80 percent male and 80 percent blacks). Attack rates of this highly susceptible group are reported to be as great as 15 percent. Considering only black males at a rate of 15 percent would yield about 225,000 additional users, within the range of the other two estimates, although all of these might not represent treatable users. Note, however, that all estimates assume that epidemic use would eventually occur everywhere in places under
500,000 population. There is currently no way of telling which cities have already experienced peak use and which have not. Therefore, if some cities were bypassed, or if others had already experienced their peaks, then future addicts would be proportionately lower. The conclusion is that something less than 200,000 more individuals could become treatable heroin users in the next few years in U.S. population centers of 500,000 or less. To this figure must be added the continuing endemic incidence from the larger cities which, however, may be quite low because recent epidemic use has depleted the susceptible populations. Whether any of these addicts appear depends-if nothing else-on the availability of heroin. TABLE 1-HeroIn-Susceptible Population in SMSAs, of 500,000 and Less, Smaller Cities and Non-Metropolitan Areas 1970 data (thousands) Total Black White Age Female Male Female Male Female (years) Male 602 609 5,141 5,371 10-14 4,762 4,539 537 554 4,863 5,077 4,326 15-19 4,523 356 345 3,998 3,937 20-24 3,592 3,642 14,385 14,002 Total 12,877 1,495 1,508 12,507 Data from U.S. Census of Population: 1970, "Mobility for Metropolitan Areas," PC(2)-2C, March 1973
t4Here, the term "addict" is operationally defined as a heroin user who will volunteer for treatment. Spread of Heroin Use 23
