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HUNT'S RESPONSE

HUNT'S RESPONSE 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 Leroy C. Gould, PhD W. Douglas Thompson, BA Rosalie M. Berberian, MPH Department of Psychiatry Yale University School of Medicine P(A V)i = Ki-1, i > 1, 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- 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png American Journal of Public Health American Public Health Association

HUNT'S RESPONSE

American Journal of Public Health , Volume 65 (9) – Sep 1, 1975

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Publisher
American Public Health Association
Copyright
Copyright © by the American Public Health Association
ISSN
0090-0036
eISSN
1541-0048
Publisher site
See Article on Publisher Site

Abstract

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 Leroy C. Gould, PhD W. Douglas Thompson, BA Rosalie M. Berberian, MPH Department of Psychiatry Yale University School of Medicine P(A V)i = Ki-1, i > 1, 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- 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.

Journal

American Journal of Public HealthAmerican Public Health Association

Published: Sep 1, 1975

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