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LETTER |
Jon Mark Hirshon and P. David Wilson are with the Department of Epidemiology and Preventive Medicine, University of Maryland School of Medicine, Baltimore.
Correspondence: Requests for reprints should be sent to Jon Mark Hirshon, MD, MPH, The Charles McC. Mathias Jr National Study Center for Trauma and EMS, 701 W Pratt St, Room 548, Baltimore, MD 21201 (e-mail: jhirs001{at}umaryland.edu).
It was a pleasure to read the article by Hammett et al. in the November 2002 issue of the Journal, in which the authors tried to quantify the burden of specific infectious diseases among incarcerated and recently incarcerated individuals.1 As they stated, this population is generally marginalized and disenfranchised, and further efforts are required to quantify its burden of disease and to develop appropriate and efficacious interventions. Thus, we are very interested in understanding how arrests of frequent drug users fit into a negative binomial process.
A negative binomial process is based on an unlimited number of independent "trials" occurring over time, with only 2 discrete events as possible outcomes for any trial. These events are usually labeled "success" and "failure," and the probability of a success (and hence the complementary probability of a failure) is assumed to remain constant over time. The negative binomial process is used to study the distribution of the number of trials before the occurrence of a specified number of successes.2
The authors should justify the assumption that the negative binomial process generates arrests. To do this they should begin by defining a trial and a success in the context of the arrests they discuss. They should then explain how the assumption of independence of trials and the assumption of constant probability of success are met in applying the process to these arrests. We doubt that these assumptions are met, even to a reasonable approximation, considering that previous interactions with law enforcement may or may not affect the probability of arrest. (Of course these assumptions can be relaxed to obtain a nonstationary negative binomial process with time-lagged dependence of trials, and it is likely that such a process would indeed generate arrests, but the specification of the parameters of the process and the demonstration that it generates arrests would be a project worthy of publication in its own right.) Furthermore, the authors should explain the derivation of the expression that, out of N weekly drug users, N/1.38 are arrested per year. If the authors can justify the use of a negative binomial process in generating arrests it could be a significant development.
We are concerned that the use of a potentially inappropriate probabilistic model may have an adverse effect on the authors’ important perspective. We applaud and encourage their efforts and offer these comments in the spirit of collegial scientific dialogue.
References
1. Hammett TM, Harmon MP, Rhodes W. The burden of infectious disease among inmates of and releasees from US correctional facilities, 1997. Am J Public Health. 2002;92:1789–1794.
2. Feller W. An Introduction to Probability Theory and Its Applications, Vol. 1. 3rd ed. New York, NY: John Wiley & Sons Inc; 1957:164–167.
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