James P. Scanlan, Attorney at Law

Relative Excess Due to Interaction (RERI)

(August 15, 2012)

Prefatory note: This subpage was prompted by an article by Vonneilich et al (Vonneilich N, Jockel K, Erberl R, et al. Does socioeconomic status affect the association of social relationships and health.  International Journal for Equity in Health 2011,10:43(doi:10/1186/1475-9276-10-43) that uses the relative excess due to interaction (RERI) to identify and measure differences in the effects of adverse social relationships on adverse health outcomes of different socioeconomic  groups.  The subpage is related to the Reporting Heterogeneity, Concentration Index, and Gini Coefficient subpages of the Measuring Health Disparities and the Subgroup Effects and Inevitability of Interaction subpages of the Scanlan’s Rule page.

The Reporting Heterogeneity subpage of the Measuring Health Disparities page (MHD) and the

Subgroup Effects subpage of the Scanlan’s Rule page (SR) explain the error in the view that it is somehow normal that a factor that similarly effects two groups with different baseline rates of experiencing an outcome will cause equal proportionate changes in rates of experiencing an outcome and that departures from that pattern reflect meaningful subgroup effects/interaction.  As explained in those subpages, for reasons related to the shape of normal distributions, there is reason to expect that a factor that diminishes health will cause a larger proportionate increase in the adverse health outcomes for the group with the lower baseline rate of experiencing that outcome (generally the higher socioeconomic  group), while causing a larger proportionate decrease in the opposite outcome for the other group.  As discussed in the Comment on Delpierre BMC Public Health 2012, identifying expected patterns (i.e., patterns to be observed when there exists no meaningful differential effect) is more difficult when effects are measured with odds ratios. 

In exploring whether and how adverse social relationships similarly affected the health of socioeconomic groups with different baseline rates for certain adverse health outcomes, Vonneilich et al. used the relative excess due to interaction (RERI).  I leave to the Vonneilich article explanation of its methodology and its findings.  This item is limited to demonstrating that the RERI is systematically affected by the prevalence of an outcome in the same way that more standard measures used to identify interaction are affected and hence is a flawed measure for determining whether a factor differently affects groups with different baseline rates of experiencing an outcome in a meaningful way. 

In order for measure to usefully appraise the size of differences between rates for purposes, for example, of determining whether a health disparity has changed over time the measure must remain the same when there occurs a change in overall prevalence akin to that effected by the lowering or raising of a cutoff on a test.  Table 1 of BSPS 2006 illustrates that the four most standard measures of difference between rates – relative differences in one outcome, relative differences in the opposite outcome, absolute differences between rates, and odds ratios.  The same values in that table are used for illustrating the problematic nature of the  Concentration Index, and Gini Coefficient (as illustrated in the MHD subpages bearing those names) as well as the Phi Coefficient and  Cohen’s Kappa (as discussed in Sections A.13 and A.13a of the Scanlan’s Rule page).

When the issue is whether a measure can effectively identify subgroup effects or interaction, the approach is slightly different.  The question regarding that issue is whether the measure will show the same changes to different baseline rates when there occurs a change in overall prevalence akin to the lowering of a cutoff (i.e., a change that involves no meaningful interaction).  But the values in BSPS Table 1 still can provide the basis for an illustration of whether a particular measures meets the criterion, as is done, for example, in Table 1 of the Subgroup Effects subpage of SR.  That table, which treats the disadvantaged group as the controls and the advantage group as the treated, shows the standard measures of change in a baseline result when an intervention has the effect of shifting the mean of the underlying distribution by.5 standard deviations.  It thus show the way various measures of difference of the change in the control group baseline rates yield different values for different baseline rates, hence illustrating the problematic nature of each measure.  That is, an effective measure would show the same value for each baseline rate.

In RERI Table 1 below, the same data are used in a somewhat different manner to test the utility of the RERI for exploring interaction is used below.  The table shows the RERI value for each baseline rate as there occurs a change in overall prevalence akin to the lowering of a cutoff.  Thus, for example, the first row  reflects the situation where a cutoff is lowered from Point 01 to Point N3, which results in an increase in the fail rate of the advantaged group (AG) from 1% (OAGF) to 3% (NDGF) and increase in the fail rate of the disadvantaged group (DG) from 3.44% (ODGF) to 8.38% (NDGF).  The situation reflected in these changes involves no meaningful.  Rather, there has there has merely occurred a change in overall prevalence effected by the lowering of a cutoff.[i]   EES figures (see Solutions sub-page of MHD)  and for the change experienced by the AG and DG would be approximately .44 (with any difference between the two figures being a result of inexactness of my methods.)  Similarly, were the RERI in fact an effective measure of interaction its value would be zero in each row.

But the RERI is not zero in each row and changes from row to row.  That the RERI changes and the manner in which it changes may warrant some exploration.  But the fact that it is not zero is what demonstrates that it is an ineffective tool for identifying interaction.

 RERI Table 1.  Illustration of RERI Values in Circumstances of Lowering of Cutoff Points in Circumstances Where Two Group Have Normal Distributions of Test Scores With Same Standard Deviation and Means that Differ by Half a Standard Deviation.