16 th Nordic Demographic Symposium Helsinki, Finland, 5-7 June 2008 Measures of Health Inequalities that are Unaffected by the Prevalence of an Outcome James P. Scanlan Attorney at Law Washington, DC, USA

Subjects 1. The problem with standard binary measures of differences between rates (relative differences, absolute differences, odds ratios): that all exhibit patterns of correlation with overall prevalence (i.e., among other things, they tend to change as overall prevalence changes) 2. A plausible alternative approach that avoids the problem with standard measures

References Health Disparities Measurement tab on jpscanlan.com – especially E2, E6 Can We Actually Measure Health Disparities? (Chance 2006) (A12) Race and Mortality (Society 2000) (A10) The Misinterpretation of Health Inequalities in the United Kingdom (BSPS 2006) (B6) The Misinterpretation of Health Inequalities in Nordic Countries, 5 th Nordic Health Promotion Research Conference (B7) Journal Review Comment (1988) on Boström and Rosén (SJPH 2003) (D43)

Patterns by which Binary Measures Tend to Change as the Overall Prevalence of an Outcome Changes As an outcome increases from being very rare to being almost universal (viewed, for ease of reference, in terms of a favorable outcome): 1. Relative differences in experiencing it tend to decrease 2. Relative differences in failing to experience it tend to decline 3. Odds ratios tend to decrease until the approximate intersection of Ratios 1 and 2 and thereafter increase 4. Absolute differences tend to move in the opposite direction of odds ratios

Fig 1. Ratio of (1) Advantaged Group (AG) Success Rate to Disadvantaged Group (DG) Success Rate (Ratio 1) at Various Cutoffs Defined by AG Success Rate

Fig 2. Ratios of (1) AG Success Rate to DG Success Rate (Ratio 1) and (2) DG Fail Rate to AG Fail Rate (Ratio 2)

Fig 3. Ratios of (1) AG Success Rate to DG Success Rate (Ratio 1), (2) DG Fail Rate to AG Fail Rate (Ratio 2), and (3) DG Fail Odds to AG Fails Odds

Fig 4. Ratios of (1) AG Success Rate to DG Success Rate, (2) DG Fail Rate to AG Fail Rate, and (3) DG Fail Odds to AG Fails Odds; and Absolute Diff Between Rates

Table 1 Illustration of the Problem and Intimation of the Solution (in terms of a favorable outcome increasing in overall prevalence) Period Yr 0 dir Yr 5 dir Yr 10 dir Yr 15 AG Rate40% I 58% I 76% I 94% DG Rate23% I 39% I 58% I 85% Ratio D 1.45 D 1.31 D 1.11 Ratio I 1.49 I 1.75 I 2.50 Odds Ratio2.23 D 2.16 I 2.29 I 2.76 Absol Diff.17 I.19 D.18 D.09 EES (z).50nc.50 nc.50 nc.50

Table 2 Simplified Illustration of the Solution (in terms of a favorable outcome increasing in overall prevalence) Period Yr 0 dir Yr 5 Alternate AG Rate40% I 58% DG Rate23% I 40% Ratio D 1.43 Ratio I 1.45 Odds Ratio2.23 D 2.07 Absol Diff.17 I.18 EES (z).50 dec.47

Table 3 Illustration Based on Morita et. al. (Pediatrics 2008) Data on Black and White Hepatitis Vaccination Rates Pre and Post School-Entry Vaccination Requirement (see D52) PeriodGradeYearWhRtBlRt Fav Ratio Adv RatioAbsDfEES PreRq519968%3% Post %33% Post %39% PreRq %32% Post %84% Post %89%

Table 4 Illustrations Based on Escarce and McGuire (AJPH 2004) Data on White and Black Coronary Procedure Rates, 1986 and 1997 (see D48) ProcYearWh RtBl Rt Fav Ratio Adv RatioAbsDfEES Angrm %4.31% Angrm %16.10% Angpls %0.32% Angpls %1.60% ArtByp %0.81% ArtByp %2.60%

Table 5: Illustration Based on Hetemaa et al. (JECH 2003) Data on Finnish Revascularization Rates, 1988 and 1996, by Income Group (see D21, D58) GenderYear AG RevRt LowInc RevRt Fav Ratio Adv RatioAbsDfEES M %8.3% M %25.4% F %3.7% F %17.1%

Table 6: Illustration Based on Laaksonen et al. (JECH 2008) Data on Mortality Rates of Finnish Men by Owner or Renter Status (see follow-up on D43) AgeOwnMortRentMortAdvRatioFavRatioEES 40–441.46%4.26% –492.46%6.04% –543.68%9.68% –595.62%13.09% –648.88%19.89% – %29.38% – %41.85% – %57.75%

Table 7 Illustration from Valkonen et al. (EJPH 2000) Based on All Cause Mortality in Finland for Three Time Periods GenderPeriodAGMortDGMortAdvRatioFavRatioEES M %0.96% M %0.93% M %0.85% F %0.35% F %0.36% F %0.35% f

Table 8 Illustration Based on Boström and Rosén (SJPH 2003) Data on Mortality by Occupation in Seven European Countries (see D43 caveats) CountryEES EES Denmark England and Wales Finland Ireland Norway Spain Sweden

Problems with the Solution Always practical issues (we do not really know the shape of the underlying distributions Sometimes fundamental issues (e.g., where we know distributions are not normal because they are truncated portions of larger distributions) Absolute minimum issue (D43,B6) See D43 (including follow-up)

Conclusion If we are mindful of the problems, approach provides, at a minimum, framework for appraising plausibility of conclusions reached through other methods Regardless of problems, approach is superior to reliance on standard measures without regard to the way those measures are correlated with overall prevalence