James P. Scanlan, Attorney at Law

Measures of Association

(May 20, 2010; rev. March 17, 2013)

Prefatory note:  This page has not been materially modified since October 10, 2010.  Since that time a good deal of material has been created concerning the fact that the rate ratio is an illogical measure of association.  See the Illogical Premises and Illogical Premises II subpages of the Scanlan’s Rule  page and the February 25, 2013 comment on Hingorani in BMJ (“Goodbye to the Rate Ratio”).

A great deal of the material on this site, especially the discussion or references made available on the Measuring Health Disparities page (MHD) and its sub-pages, the Scanlan’s Rule page and its sub-pages, and the Mortality and Survival page, involves the fact that standard measures of differences between outcome rates are problematic for appraising the size of such differences between outcome rates because each is affected by the overall prevalence of an outcome.  Most notably, the rarer an outcome, the greater tends to be the relative differences in experiencing it and the smaller tends to be the relative difference in avoiding it.    

Most of this material, and especially the several score on-line comments found in Section D of MHD pertain to the appraisal of race/ethnic and socioeconomic differences in outcome rates.  But, while it is not invariably discussed in such terms, this material all relates to strength of association.  In Table 1 of the Mortality and Survival page, for example, the examination of racial differences by age group is simply a matter of appraising the effects of black race for each age group.  One could as well be examining the effects of smoking for each age group. 

Further, it should be borne in mind that all the examples discussed in the referenced materials could be looked at from a different perspective.  With regard to Table 1 just mentioned, one could just as well be appraising the effects of age on mortality in each racial group.  The issue of whether racial differences as to some outcome are larger among higher or lower socioeconomic groups could as well be examined in terms of whether the effects of higher or lower socioeconomic status on the outcome are different for different racial groups.  Similarly, as discussed in the Comment on Guthrie,[i] issues concerning whether overall outcome rates are changing more in one setting than another raise the same issues as whether outcome rates are changing more for one group than another.

Thus, in the same way that the aforementioned references call into question the soundness of health disparities research they call into question the soundness all efforts to measure strengths of association.  And the same reasons that support measuring health disparities in the manner not affected by the overall prevalence of an outcome described on the Solutions sub-page of MHD support such approach for measuring the strength of any association.  See Subgroup Effects sub-page of the Scanlan’s Rule page and the Comment on Sun.[ii]