British Society for Population Studies 2007 Annual Conference St. Andrews, Scotland, Sep 2007 Methodological Issue in Comparing the Size of Differences Between Rates of Experiencing or Avoiding an Outcome in Different Settings James P. Scanlan Washington, DC

Four Binary Indicators of Difference 1 Relative differences between rates of experiencing an outcome (Ratio 1) 2 Relative differences between rates of avoiding an outcome (Ratio 2) 3 Odds ratios 4 Absolute differences between rates

Fig 1: Ratio of (1) DG Failure Rate to Ag Failure Rate

Fig. 2: Ratio of (1) DG Fail Rate to AG Fail Rate and (2) AG Pass Rate to DG Pass Rate

Implications re (1) and (2) ● changes over time ● comparing inequalities in different populations or subpopulations - countries or regions - British civil servants vs. rest of UK - high-ed vs. low-ed US blacks and whites - young vs. old ● healthcare disparities ● comparing effects sizes ● what is a striking disparity?

Fig. 3: Ratio of (1) DG Fail Rate to AG Fail Rate, (2) AG Pass Rate to DG Pass Rate, (3) DG Fail Odds to AG Fail Odds ●

Fig. 4: Ratio of (1) DG Fail Rate to AG Fail Rate, (2) AG Pass Rate to DG Pass Rate, (3) DG Fail Odds to AG Fail Odds; plus (4) Absolute Difference Between Rates

Fig. 4a: (4) Absolute Difference Between Rates - Rescaled

Two Contrasting Studies Trivedi et al. Trends in the quality of care and racial disparities in Medicare managed care. N Engl J Med 2005;353: Jha et al. Racial trends in the use of major procedures among the elderly. N Engl J Med 2005;353:

Further analyses of quality and inequality Trivedi et al. Relationship between quality of care and racial disparities in Medicare health plans. JAMA 2006;296: correlations between quality and inequality - process outcomes versus clinical outcomes

Implications re (3) and (4) As a favorable outcome increases in prevalence, absolute differences will tend to increase in Zone A and decline in Zone B and do both when there is crossover between zones Opposite will occur when the outcome declines Odds ratio will behave in the opposite manner So what happens when you need the refinement of a logistic regression?

Fig. 5: Illustration with Near Normal Data – Based on Black and White Rates of Falling Below or Above Various Percentage of the Poverty Line

Fig. 6: Illustration with Normal Data (as in Fig 4) Limited to Universe Below Point Defined by 30 Percent Failure Rate of AG

Fig. 7: Illustration Based on Systolic Blood Pressure of Black and White Men Age 55 to 65 (from NHANES and )

Fig. 8: Illustration Based on Systolic Blood Pressure (SBP) of Black and White Men Age 55 to 65 (from NHANES and ) – Limited to SBP > 139

Which measure is best? None really indicates whether a change between rates is other than solely a consequence of changes in prevalence Further, each can change in one direction even when there in fact is a meaningful change in the opposite direction

How can we measure inequalities over time? Identifying departures from the standard, as, for example, when both relative differences change in the same direction (as discussed in the prior BSPS paper) - only useful when it happens (not often) - possible distributional irregularities make approach highly speculative

Other possibilities Longevity – no (see BSPS paper) SF 36 scores – no Metabolic syndrome measures – no Cardio risk indexes – no Allostatic load – possibly Components of allostatic load – possibly Cortisol level – possibly Self rated health on a continuous scale - possibly