Model phobia: looking past the curves

I must freely admit that when new mathematical models of HIV cross my desk, I grow discomforted. My heart rate and salivation are increased, a combination elicited by unrelieved stress. This formula phobia is my initial response since I am neither mathematician nor statistician. Once calmed, I begin to approach such documents in the hopes that the models will reveal new ways of investigating a thorny problem, identify variables where additional data will determine the shape of the epidemic, or suggest a natural course for meaningful interventions. And, of course, I hope that I will understand the model well enough for any of the above to occur. So, when I was asked to comment on the three modeling articles which appear in this issue of the International Journal of Drug Policy , I felt formula phobia mixed liberally with the queasiness that comes with responsibility. These feelings have slowly been replaced by respect for the hard work of the authors in creating understandable reports and by the discomfort that comes from being unable to retain my natural optimism in the face of impending disaster predicted by these models. The most easily approachable of the three modeling papers is that by Lowndes et al. It presents a plausible scenario for a transition of the Russian HIV epidemic from one concentrated almost exclusively within injector populations to a generalised heterosexual one. And it does so without a single equation in the text. The authors recognise the paucity of data from Russia, which means that they often argue by analogy. My first reading led me to think that many of the details of the analogies were extraneous. But reading it again, I was forced to reconsider. Remembering that the devil is in the details, I began to understand that the subtleties encountered in compiling and analysing epidemiological data elsewhere also apply to Russia. The authors are explicitly drawing our attention to the need to collect comprehensive and coordinated data. Without proper data the purposes of surveillance will be defeated. This reminder is key, and not just to those of us collecting the data. It should serve as a spur to policy makers, who must permit and promote the collection of meaningful information, even if this means opposing standard Russian policies. The paper by Grassly et al. reaches for a different goal*/to predict the limits of the course of the epidemic by explicit modeling. The problem with such models is that as the parameters become more explicit, they become more corrupted by inaccurate data. Furthermore, if the predictions of such models differ from what a reader would like to conclude, a reader begins to search for errors. Once an error (or errors) is identified, a reader can feel satisfied in disregarding the model. I found myself doing this when I read the Grassly paper for the first time. I was struck dumb by Figure 1b, which estimates the HIV prevalence among all adults. The data used in the model have led the authors to suggest that it is likely that a majority of adults will be HIV infected within 10 years of the start of the epidemic. Only in the most affected populations in sub-Saharan Africa have prevalence rates exceeded 25% in adults 15 /49 (UNAIDS, 2002). Grassly et al. are predicting an even worse and more explosive heterosexual epidemic for Russia within the next few years. Unwilling to accept so bleak a prediction, I looked for an obvious error. While the model itself seems sound, some of the parameters are questionable. An easy target was an estimate derived from our work on HIV infectivity through shared syringes (Kaplan & Heimer, 1992). Our estimate combines the acute, clinically latent, and frank AIDS stages of HIV infection in arriving at a seven in a thousand chance of transmission. Grassly et al. double the risks during the early and late stages, potentially exaggerating the extent of transmission, especially early in the epidemic. But more troubling are the values given for the sexual transmission variables. The authors estimate that the * Tel.: /1-203-785-6732; fax: /1-203-785-7552. E-mail address: robert.heimer@yale.edu (R. Heimer). International Journal of Drug Policy 14 (2003) 87 /88