A Reply to Duffy

Abstract

Duffy ( 1 ) argues that a mathematical distribution model, like the lognormal, can only be a first approximation to empirical distributions of self-reported alcohol consumption, since such distribution not perfectly satisfy this mathematical relation. This is, of course, correct, but the point is trivial. To my knowledge, no modern students of distribution phenomena have believed that mathematical models of social phenomena can be anything but approximations. Duffy obviously interprets my sratemenc (5, p. 771) that 'The study of the distribution of alcohol consumption is a prerequisite for a meaningful study of aggregate relations between per capita consumption and mortality rates, ., as equivalent to saying that the distribution is constant and exactly conforming to a mathematical distribution function everywhere. This is, indeed, a strange interpretation. Duffy continues by saying that Skog later detracts from this somewhat conceding that the distribution may vary from population to population. . Maybe this latter observation ought to have warned him that the first interpretation was misguided. Let me spell out detail the point I was trying to make: Unless the risk a person runs for experiencing a certain consequence is a linear function of his consumption level, the aggregate relation between per capita consumption and the total volume of this consequence the population will depend on the shape of the distribution. (If the riskfunction is linear, the shape of the distribution is immaterial.) Since several diseases have curvilinear risk-functions, it becomes important to study the shape of empirical disuibutions-in fact it becomes a necessary prerequisite. Duffy finds the so-called social interaction theory (2, 3, 4 ) unnecessarily complicated. He argues that in populations with a high prevalence of excessive use, average consumption has to be high, while other populations with a low prevalence of excessive use mean consumption will be low, and this obvious interpretation seems to be as much as the evidence will bear. Duffy does effect suggest that the relation between per capita consumption and prevalence of heavy use has a strong tautological element and that this is all that can be said. I strongly disagree with both statements, but space does not permit a thoroughgoing discussion. Suffice it here to say that the tautological element is indeed racher weak. In principle, a population with higher per capita consumption than all western drinking cultures (say 25 litres per year) could have zero prevalence of heavy users (normally defined as persons drinking more than 10 or 15 centilitres per day, i.e., 36.5 or 54.75 litres per year). This would happen if the variance of the distribution was very low. On the other hand, populations with very low per capita consumption levels, say 5 litres, could contain a very significant proportion of heavy users. If the distribution was strongly bimodal, the prevalence rate could fact lie between 5 and 10% such a cultureI In effect, the regularity observed empirical distributions of alcohol consumption, particular the convex relation between per capita consumption and prevalence of heavy use, is not a strict logical necessity. It must be the result of real physiological, psychological, and social forces and mechanisms and the so-called social interaction theory tries to capture some of these forces.