2. Robins, L. N., and Murphy, G. E. Drug Use in a Normal Population of Young Negro Men. Am. J. Public Health 57:1580-1596, 1967. 3. Robins, L. N. A Follow-up of Vietnam Drug Users. Special Action Office, Washington, DC, 1973.
Leroy C. Gould, PhD W. Douglas Thompson, BA Rosalie M. Berberian, MPH Department of Psychiatry Yale University School of Medicine
P(A V)i = P(A V)_1 -P(ET)j_j -
R[P(A V)j_j- P(ET)j_j
reduces to
P(AV)i = (l-R-W + RW) P(AV)j_1 Since R, W < 1, then (1 - R - W + RW) < 1 and because P(A V)i = 1, i = 1 (by assumption), then
P(A V)i = Ki-1, i > 1,
HUNT'S RESPONSE Professor Gould and his associates raise important issues for drug incidence analysis. We are, of course, aware that treatment-derived incidence data are imperfect: that the early onset cohorts are underrepresented through removals and late ones through lag. These flaws are generally recognized; the question is whether we can even use treatment data (which are our richest source of unequivocally identified users) to study the spreading of new use in a community. Our critics' arguments conclude that treatment-derived incidence is so poorly understood that the basic shape of the NTA curve (and presumably others) is incorrect: "the apparent epidemic . .. is in reality an artifact." They construct a difference equation which produces a false peak from constant incidence as an illustration. The literature is now replete with examples-both empirical and theoretical-of incidence of first use curves which behave like NTA and New Haven,112 but which were obtained by different means than from voluntary treatment data. Their properties are consistent: epidemic-to-endemic ratio, width of peak period, etc., are similar in most places. We therefore have no reason to doubt the basic "epidemic" forns of such curves, and indeed, every reason (including mathematical arguments from stochastic diffusion theory) to believe that they are cor-
rect.' In contrast, why should we be persuaded by Professor Gould's difference equation? Its assumptions are certainlv peculiar. For any year after a treatment program opens, the equation
where K = (1-R-W + RW). In other words P(A V)i is simply a geometric series which declines at a constant rate K. This assumption may be justified for removals, but it is not for lag. However little we know about lag, we are sure that it is not constant for each year after onset. The consequence of this assumption is that the incidence curve generated by the difference equation will always peak in the year the programs opens (under the given conditions). Thus the similarity between the two curves is adventitious, resulting from NTA's origin in 1970 and the simplistic mathematical structure of the model. In attempting to correct for lag, I have used the observed behavior of addicts entering treatment, rather than any theoretical imputation. Professor Gould errs when he says the method is based on "the assumption of similar lag distributions." Constant lag from year to year is not an assumption but an empirical property of the 20 or more sets of program data which I have analyzed.3 I agree that it is hard to explain (cf. p. 19 of my article), but it is a fact and not a speculation. I am grateful to Professor Gould for pointing out that the New Haven data are incomplete (which I did not know), but he misunderstands the effect of the omissions. In using any treatment-derived sample of incidence data we are certain that these data will be both incomplete and biased.3 Our intention is only to obtain a sample, from which relative comparison of successive onset cohorts can be made: is incidence rising or falling? Unless this sample is biased against particular
onset cohorts, its incompleteness is no more important than in any other sample. Thus, unless Professor Gould is prepared to argue that 1968 and 1969 entrants to New Haven, who were still in treatment in 1970, systematically excluded some onset cohorts, I cannot see the force of his argument. The same explanation applies to all of the onset cohorts originating prior to the availability of treatment. What is being averaged in their lag curves is not their numbers, but their distributions of the random variable, years from onset of use to entry into treatment minus years when no treatment was available. A final comment: Longitudinal studies of complete onset cohorts would represent a splendid solution to these complexities, but no one has yet discovered how to identify heroin users. When that problem is solved, incidence analysis will be reduced to counting. Perhaps we shall all be able to agree on that method.
References 1. Hunt, L. G. Heroin Epidemics: A Quantitative Study of Current Empirical Data. Drug Abuse Council, Inc., Monograph MS-3, Washington, DC, May, 1973. 2. Hughes, P. H., Senay, E. C., and Parker, R. The Medical Management of a Heroin Epidemic. Arch. Gen. Psychiatry 27:585-591, 1972. 3. Hunt, L. G. Recent Spread of Heroin Use in the United States: Unanswered Questions. Drug Abuse Council, Inc., Monograph MS-10, Washington, DC, July, 1974.
Leon G. Hunt
ON IMMUNIZATION RECORD KEEPING My 12-year-old son was recently diagnosed as having measles. His medical records indicate that he received "measles vaccine" in 1963. His current pediatrician mentioned that he and his colleagues have seen several cases of measles in persons who supposedly were vaccinated. Some of these cases even had booster immunizations. This raises some very interesting epidemiological questions. (1) Is the LETTERS TO TH E EDITOR
983
current forn of measles caused by a single newly mutated viral strain, or are there several new strains which produce similar phenotypic manifestations? (2) Do the current measles cases indicate that the patients received an ineffective vaccine? If this is the situation, how widely distributed was the ineffective batch(es)? To facilitate future epidemiologi-
cal studies, it would be extremely helpful if physicians would record the following information in the patient's medical record: (1) name of vaccine; (2) company producing the vaccine; (3) date of production; (4) lot or batch number used. Similar infornation might also be recorded for all prescribed medications. This valuable information will
take only a few seconds to record and will enable a patient's new physician to know exactly which vaccines have been administered. This is critical in our highly mobile society. Arlene L. Fraikor, PhD Assistant Professor Biological Anthropology Wichita State University Wichita, KS 67208
Keep your copies of The American Journal of Public Health in an attractive volume file Specially designed to protect your back issues of AJPH, help you locate needed ones instantly, these custom-made journal volume files are an attractive permanent addition to your professional library. These durable files come in two sizes to accommodate both the old size and the new size of the American Journal of Public Health. Be sure to specify which size when ordering. File cases are made of heavy bookbinder's board, covered with kid grain leatherette and embossed in gold leaf. Each volume file for journals published prior to 1972 holds 8 or 9 issues of AJPH. Each volume file for the new journal size, adopted in 1972, will hold 12 issues of AJPH. Shipped postpaid, volume files cost only $4.25 each, three for $12, or six for $22. U.S.A. orders
r---------------- ----
Make checks payable to: Jesse Jones Box Corp.
Complete order blank and mail to: JESSE JONES BOX CORP.
Philadelphia, Pa. 19141 green volume files for AJPH pub| Please send meI lished prior to 1972 ($4.25 each, three for $12, six for $22.) Please send me
984 AJPH SEPTEMBER, 1975, Vol. 65, No. 9
black volume files for the new size
AJPH. ($4.25 each, three for $12, six for $22.) I
________________________________________________________________ .1 only-no foreign shipments accepted.
I
Your money will be refunded if, for any reason, you are not fully satisfied.
My check or money order for $
-
is enclosed.
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Address City
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Zip Code
Leroy C. Gould, PhD W. Douglas Thompson, BA Rosalie M. Berberian, MPH Department of Psychiatry Yale University School of Medicine
P(A V)i = P(A V)_1 -P(ET)j_j -
R[P(A V)j_j- P(ET)j_j
reduces to
P(AV)i = (l-R-W + RW) P(AV)j_1 Since R, W < 1, then (1 - R - W + RW) < 1 and because P(A V)i = 1, i = 1 (by assumption), then
P(A V)i = Ki-1, i > 1,
HUNT'S RESPONSE Professor Gould and his associates raise important issues for drug incidence analysis. We are, of course, aware that treatment-derived incidence data are imperfect: that the early onset cohorts are underrepresented through removals and late ones through lag. These flaws are generally recognized; the question is whether we can even use treatment data (which are our richest source of unequivocally identified users) to study the spreading of new use in a community. Our critics' arguments conclude that treatment-derived incidence is so poorly understood that the basic shape of the NTA curve (and presumably others) is incorrect: "the apparent epidemic . .. is in reality an artifact." They construct a difference equation which produces a false peak from constant incidence as an illustration. The literature is now replete with examples-both empirical and theoretical-of incidence of first use curves which behave like NTA and New Haven,112 but which were obtained by different means than from voluntary treatment data. Their properties are consistent: epidemic-to-endemic ratio, width of peak period, etc., are similar in most places. We therefore have no reason to doubt the basic "epidemic" forns of such curves, and indeed, every reason (including mathematical arguments from stochastic diffusion theory) to believe that they are cor-
rect.' In contrast, why should we be persuaded by Professor Gould's difference equation? Its assumptions are certainlv peculiar. For any year after a treatment program opens, the equation
where K = (1-R-W + RW). In other words P(A V)i is simply a geometric series which declines at a constant rate K. This assumption may be justified for removals, but it is not for lag. However little we know about lag, we are sure that it is not constant for each year after onset. The consequence of this assumption is that the incidence curve generated by the difference equation will always peak in the year the programs opens (under the given conditions). Thus the similarity between the two curves is adventitious, resulting from NTA's origin in 1970 and the simplistic mathematical structure of the model. In attempting to correct for lag, I have used the observed behavior of addicts entering treatment, rather than any theoretical imputation. Professor Gould errs when he says the method is based on "the assumption of similar lag distributions." Constant lag from year to year is not an assumption but an empirical property of the 20 or more sets of program data which I have analyzed.3 I agree that it is hard to explain (cf. p. 19 of my article), but it is a fact and not a speculation. I am grateful to Professor Gould for pointing out that the New Haven data are incomplete (which I did not know), but he misunderstands the effect of the omissions. In using any treatment-derived sample of incidence data we are certain that these data will be both incomplete and biased.3 Our intention is only to obtain a sample, from which relative comparison of successive onset cohorts can be made: is incidence rising or falling? Unless this sample is biased against particular
onset cohorts, its incompleteness is no more important than in any other sample. Thus, unless Professor Gould is prepared to argue that 1968 and 1969 entrants to New Haven, who were still in treatment in 1970, systematically excluded some onset cohorts, I cannot see the force of his argument. The same explanation applies to all of the onset cohorts originating prior to the availability of treatment. What is being averaged in their lag curves is not their numbers, but their distributions of the random variable, years from onset of use to entry into treatment minus years when no treatment was available. A final comment: Longitudinal studies of complete onset cohorts would represent a splendid solution to these complexities, but no one has yet discovered how to identify heroin users. When that problem is solved, incidence analysis will be reduced to counting. Perhaps we shall all be able to agree on that method.
References 1. Hunt, L. G. Heroin Epidemics: A Quantitative Study of Current Empirical Data. Drug Abuse Council, Inc., Monograph MS-3, Washington, DC, May, 1973. 2. Hughes, P. H., Senay, E. C., and Parker, R. The Medical Management of a Heroin Epidemic. Arch. Gen. Psychiatry 27:585-591, 1972. 3. Hunt, L. G. Recent Spread of Heroin Use in the United States: Unanswered Questions. Drug Abuse Council, Inc., Monograph MS-10, Washington, DC, July, 1974.
Leon G. Hunt
ON IMMUNIZATION RECORD KEEPING My 12-year-old son was recently diagnosed as having measles. His medical records indicate that he received "measles vaccine" in 1963. His current pediatrician mentioned that he and his colleagues have seen several cases of measles in persons who supposedly were vaccinated. Some of these cases even had booster immunizations. This raises some very interesting epidemiological questions. (1) Is the LETTERS TO TH E EDITOR
983
current forn of measles caused by a single newly mutated viral strain, or are there several new strains which produce similar phenotypic manifestations? (2) Do the current measles cases indicate that the patients received an ineffective vaccine? If this is the situation, how widely distributed was the ineffective batch(es)? To facilitate future epidemiologi-
cal studies, it would be extremely helpful if physicians would record the following information in the patient's medical record: (1) name of vaccine; (2) company producing the vaccine; (3) date of production; (4) lot or batch number used. Similar infornation might also be recorded for all prescribed medications. This valuable information will
take only a few seconds to record and will enable a patient's new physician to know exactly which vaccines have been administered. This is critical in our highly mobile society. Arlene L. Fraikor, PhD Assistant Professor Biological Anthropology Wichita State University Wichita, KS 67208
Keep your copies of The American Journal of Public Health in an attractive volume file Specially designed to protect your back issues of AJPH, help you locate needed ones instantly, these custom-made journal volume files are an attractive permanent addition to your professional library. These durable files come in two sizes to accommodate both the old size and the new size of the American Journal of Public Health. Be sure to specify which size when ordering. File cases are made of heavy bookbinder's board, covered with kid grain leatherette and embossed in gold leaf. Each volume file for journals published prior to 1972 holds 8 or 9 issues of AJPH. Each volume file for the new journal size, adopted in 1972, will hold 12 issues of AJPH. Shipped postpaid, volume files cost only $4.25 each, three for $12, or six for $22. U.S.A. orders
r---------------- ----
Make checks payable to: Jesse Jones Box Corp.
Complete order blank and mail to: JESSE JONES BOX CORP.
Philadelphia, Pa. 19141 green volume files for AJPH pub| Please send meI lished prior to 1972 ($4.25 each, three for $12, six for $22.) Please send me
984 AJPH SEPTEMBER, 1975, Vol. 65, No. 9
black volume files for the new size
AJPH. ($4.25 each, three for $12, six for $22.) I
________________________________________________________________ .1 only-no foreign shipments accepted.
I
Your money will be refunded if, for any reason, you are not fully satisfied.
My check or money order for $
-
is enclosed.
Name
Address City
State
Zip Code
