James P. Scanlan, Attorney at Law

Illogical Premises II:  The Rate Ratio as a Measure of Association

(Feb. 19, 2010)

Prefatory note:  This page is related to the Illogical Premises, Inevitability of Interaction, and Subgroup Effects sub-pages of the Scanlan’s Rule page of jpscanlan.com. 

The Illogical Premises sub-page of the Scanlan’s Rule page of jpscanlan.com discusses that it is illogical to consider it somehow normal that a factor that affects the likelihood of experiencing an outcome will cause equal proportionate changes in different baseline rates of experiencing the outcome.  Specifically, it is not  possible for a factor to cause equal proportionate changes in different baseline rates of experiencing an outcome and cause equal proportionate changes in rates of experiencing the opposite outcome.  Since there is no more reason to expect that two group with different baseline rates of experiencing an outcome will experience equal proportionate changes in those rates than there is to expect them to experience equal proportionate changes in the opposite outcome rate, there is no reason to regard it as somehow normal that the two groups will experiences equal proportionate changes in either outcome.   The Inevitability of Interaction sub-page discusses that in a clinical study when two subgroups have different baseline rates of experiencing an outcome, interaction always will be observed either as to the outcome or the opposite outcome because if the two groups will experience the same proportionate change in one outcome they necessarily will experience different proportionate changes as to the opposite outcome.

This item illustrates the same essential point with regard to the rate ratio as a measure of association.  Table 1 is based on Table 3 of the 2008 British Society for Population Studies presentation.  That table was intended to illustrate that at different prevalence levels various rate ratios (1.2, 1.5, 2.0, 2.5, 3.0) mean different things with regard to the comparative status of two groups.  While the illustration in cast in terms of the differences between a disadvantaged and advantaged group with respect to an outcome, the illustration could as well be read as showing the strength of the association between membership in the disadvantaged group and the likelihood of experiencing the outcome.  The actual difference between the groups (actual strength of association) is reflected in the EES column, which presents values derived by the method described on the Solutions sub-page of Measuring Health Disparities page of jpscanlan.com. 

A FavRatio column has been added to show the ratio of the advantaged group’s rate of experiencing the favorable outcome (test passage in the hypothetical) to the disadvantaged group’s rate of experiencing the favorable outcome.  Thus, the table illustrates that it would be illogical to regard a particular rate ratio to reflect the same degree of association in the case of different baseline rates since if the rate ratios are the same as to different baseline rates the rate ratios will necessarily be different as to the opposite outcome rate.  .

Table 1  Illustration of Meaning of Various Ratios at Different Prevalence Levels.

Possibly some would maintain, with respect to the first two rows for example, that the strength of the association between group membership and the adverse outcome is the same in the two rows while the strength of association between group membership and the opposite outcome is different in the two rows.  The decision of the National Center for Health Statistics to avoid the implications with respect to the measurement of  health disparities of the pattern whereby relative differences in favorable and adverse outcomes tend to change in opposite directions as the prevalence of an outcome changes (discussed, inter alia, in Section e.6 of the Scanlan’s Rule page and Section E.7 of MHD) may reflect an element of such thinking.  But such thinking is not defensible. 

One may note that in the table with respect to each adverse outcome rate ratio the larger the absolute difference between rates the larger is the EES.  That occurs because for any given rate ratio, the larger the absolute difference the larger will be the EES.  But it should not be deemed to suggest that the absolute difference is a sound measure of association.  See, e.g., the introductory material on the Scanlan’s Rule page and the Relative Versus Absolute sub-page of MHD.  As discussed on the Illogical Premises sub-page, it would not necessarily be illogical to regard the absolute difference as a sound measure of association.  But neither would it be correct to do so.