The use of measures of influence in epidemiology

In epidemiological studies the units of observation often consist of political entities such as countries, each of which has its own specific inner structure. When a multiple regression is performed it is therefore of particular interest to analyse not only the overall behaviour of the dataset, but in addition, to investigate how each individual country contributes to, and deviates from, this overall behaviour. By means of the example 'relation between infant mortality and structural data of countries' several ways are discussed of how each individual country can influence the regression model. Firstly the potential influence which each country might exhibit due to the explanatory variables alone is analysed. Then the actual influence of each country is analysed by taking the explanatory variables and the target variable into account simultaneously. This is done by means of statistical measures not generally familiar to epidemiologists, which have been developed in recent years (leverage values, Cook's distances). These measures also point to deviations of countries from the model, and suggest directions in which to search for explanation. Finally the influence of the 'size' of the countries is investigated.