On the Explosiveness and Destructiveness of the 1918 Epidemic.

Toward the close of an elaborate statistical treatment of the influenza epidemic of 1918, Pearl' discusses the relation between the explosiveness I and the destructiveness D of the epidemic, between which he finds a high correlation rID = 0.709 and a regression equation D = 2.74 + 0.10651. The explosiveness is defined2 as the ratio I = (P M)/T where P is the death rate (on an annual basis) from all causes during the week in which the epidemic reached its (first) peak, M is the mean death rate prior to the epidemic, and T is the time of rise to the peak; the destructiveness D is defined as the (integral) excess mortality rate during a 25-week period above what would have been expected had there been no influenza epidemic. Whenever one has to deal with a variable such as I which is a function of other variables it is interesting to study those other variables in relation to it and to any further variables with which it is put into relation. Thus the variable p = P M which is the numerator of I correlates3 to D with 7pD = 0.805 and hence the regression equation of D on p = P M would give a closer representation of D than that of D on I. When it is a quotient or a product with which one has to deal it is often better to use the logarithms4 of the variables in place of the variables themselves. The correlation between the logarithms of p and D is PPD = 0.850 and hence log D may be expressed with still greater fidelity by a regression equation on log p; indeed