Revisiting Pearl's influenza studies by bootstrapping for forward variable selection with a null factor.

In 1919 and 1921 Raymond Pearl published four empirical studies on the Spanish Flu epidemic in which he explored the factors that might explain the explosiveness and destructiveness of the epidemic in America's largest cities. Using partial correlation coefficients he tried to isolate the net effects of the possible explanatory factors, such as general demographic characteristics of the cities and death rates for various diseases, on the variables measuring the severity of the epidemic. Instead of Pearl's correlation analysis, we apply a bootstrap simulation to forward variable selection with a null factor for generalized linear regression with AICc validation. The null factor or pseudo-variable is a random variable that is independent of the response. The number of times it is included in the model selection simulation provides an important metric for deciding which terms should remain in the model. Our results are largely consistent with Pearl's conclusions in that the pre-pandemic death rates from organic heart disease and from all causes are most predictive of pandemic explosiveness or severity. However, our results also contain substantive nuances. Our paper contributes to the literature showing that state-of-the-art methodology for variable selection proves useful for historical epidemiology.