Statistical problems in studying the relative specificities of association between environmental agents and different...

If an environmental agent is strongly associated with only one disease then that is greater evidence in favour of a casual relationship than if that agent were also strongly associated with other unrelated diseases. Standard regression and correlation analysis are shown to be incapable of answering questions about disease specificity. A simple index, based upon regression, is proposed. The standardised regression coefficients in a regression equation based on the logistic transformation of a death rate are shown to have a particularly simple interpretation in terms of our index. The work is illustrated on an example drawn from the controversy concerning the association between area differences in ischaemic heart disease mortality and water hardness.