James P. Scanlan Attorney at Law Washington, DC, USA jps@jpscanlan.com American Public Health Association 136th Annual Meeting & Exposition, San Diego, CA, Oct. 25-29, 2008 Approaches to Measuring Health Disparities that are Unaffected by the Overall Prevalence of an Outcome James P. Scanlan Attorney at Law Washington, DC, USA jps@jpscanlan.com

Presenter Disclosures James P. Scanlan (1) The following personal financial relationships with commercial interests relevant to this presentation existed during the past 12 months: No relationship to disclose

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. An alternative approach that avoids the problem with standard measures: a measure that does not change as overall prevalence changes

References (available on jpscanlan.com) Measuring Health Disparities Page 90 references (articles, presentations, on-line commentary) Solutions Tab Solutions Database Tab (downloadable database) Scanlan’s Rule Page Can We Actually Measure Health Disparities (Chance 2006) Race and Mortality (Society 2000) APHA 2007 Presentation Addendum

Patterns by Which Binary Measures Tend to Change as the Overall Prevalence of an Outcome Changes – Scanlan’s Rules SR1: The rarer an outcome, the greater tends to be the relative difference in rates of experiencing it and the smaller tends to be the relative difference in rates of avoiding it (aka Heuristic Rule X or Interpretative Rule 1; see Bauld, Day, Judge, 2008) SR2: As an outcome changes in overall prevalence, the odds ratio tends to change in the same direction as the larger of the two relative differences and the absolute difference tends to change in the same direction as the smaller of the two relative differences ─ where the numerators are reversed on the two risk ratios (see Semantic Issues tab on Scanlan’s Rule page)

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

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

Fig 3. 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

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 1 Yr 2 Yr 3 Yr 4 AG Rate 40% 58% 76% 94% DG Rate 23% 39% 58% 85% Measures of Difference (Blue=decrease; Red=increase) Ratio 1 1.74 1.45 1.31 1.11 Ratio 2 1.28 1.49 1.75 2.50 Odds Ratio 2.23 2.16 2.29 2.76 Absol Diff .17 .19 .18 .09 EES (z) .50 .50 .50 .50

Estimated Effect Size (EES) Difference between means of hypothesized underlying distributions of risks of experiencing an outcome, in terms of percentage of a standard deviation, assuming normality of the distributions

Table 2 Simplified Illustration of the Solution (in terms of a favorable outcome increasing in overall prevalence) Period Yr 1 Yr 2 AG Rate 40% 58% DG Rate 23% 40% Measures of Difference Change Direction Ratio 1 1.74 1.43 Increase Ratio 2 1.28 1.45 Decrease Odds Ratio 2.23 2.07 Decrease Absol Diff .17 .18 Increase EES (z) .50 .47 Decrease

Table 3 Illustration of Meaning of Various Ratios at Different Prevalence Levels DGFailRate AGFailRate EES 1.2 60.0% 50.0% 0.26 18.4% 15.4% 0.12 1.5 75.0% 0.68 45.0% 30.0% 0.39 2.0 40.0% 20.0% 0.59 10.0% 0.44 1.0% 0.5% 0.24 2.5 24.2% 9.7% 0.60 7.4% 2.9% 3.0 44.0% 14.7% 0.90 14.4% 4.8% 2.7% 0.9%

Table 4 Illustration Based on Morita et. al Table 4 Illustration Based on Morita et. al. (Pediatrics 2008) Data on Black and White Hepatitis B Vaccination Rates Pre and Post School-Entry Vaccination Requirement (see Morita Comment) Period Grade Year WhRt BlRt Fav Ratio Adv AbsDf EES Pre Requ 5 (Y1) 1996 8% 3% 2.67 1.05 0.05 0.47 Post (Y2) 1997 46% 33% 1.39 1.24 0.13 0.34 9 32% 1.44 1.26 0.14 0.37 89% 84% 1.06 1.45 0.24

Table 5 Illustrations Based on Escarce and McGuire (AJPH 2004) Data on White and Black Coronary Procedure Rates, 1986, 1997 (see Escarce Comment) Proc Year Wh Rt Bl Rt Fav Ratio Adv AbsDf EES Angrm (Y1) 1986 0.86% 0.43% 1.99 1.05 0.04 0.25 (Y2) 1997 2.28% 1.61% 1.42 1.09 0.07 0.14 Angpls 0.10% 0.03% 3.09 1.01 0.01 0.32 0.26% 0.16% 1.61 0.15 ArtByp 0.31% 0.08% 3.78 1.02 0.02 0.41 0.59% 2.25 1.03 0.03 0.27

Table 6: Illustration Based on Seghal (JAMA 2003) Data on Black and White Rates of Adequate Hemodialysis, 1993 and 2000 (see APHA 2007 Addendum) Year W B Fav Ratio Adv AbsDf EES 1993 46% 36% 1.28 1.19 0.10 0.26 2000 87% 84% 1.04 1.23 0.03 0.14

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, see Bostrom Comment; cf. ICPHS 2008, Fig. 6 Absolute minimum issue (Bostrom Comment, BSPS 2006, Race and Mortality)

Conclusion If we are mindful of the problems, the approach provides a framework for cautiously appraising the size of differences between rates. Regardless of problems, the approach is superior to reliance on standard binary measures of differences between rates without regard to the way those measures tend to be correlated with the overall prevalence of an outcome.

Implementation Formula to derive EES? Database downloadable from jpscanlan.com

Example of 8 of 76,960 rows in table downloadable from jpscanlan.com EES AG Fail DG Fail 0.60 0.50399 0.72907 0.5 0.72575 0.72241 0.49601 0.71905 0.30 0.62172 0.61791 0.6141 0.61026

Supp Table 1: Illustration Based on Hetemaa et al Supp Table 1: Illustration Based on Hetemaa et al. (JECH 2003) Data on Finnish Revascularization Rates, 1988 and 1996, by Income Group (see Hetemaa Comment 1, Hetemaa Comment 2) Gender Year AG RevRt LowInc Fav Ratio Adv AbsDf EES M (Y1) 1988 17.9% 8.3% 2.16 1.12 .096 0.48 (Y2) 1996 41.2% 25.4% 1.63 1.27 .159 0.44 F 10.0% 3.7% 2.70 1.07 .063 0.51 30.8% 17.1% 1.80 1.20 .137 0.45

Supp Table 2: Illustration Based on Laaksonen et al Supp Table 2: Illustration Based on Laaksonen et al. (JECH 2008) Data on Mortality Rates of Finnish Men by Owner or Renter Status (see follow-up on Bostrom Comment) Age OwnMort RentMort AdvRatio FavRatio EES 40–44 1.46% 4.26% 2.91 1.03 0.46 45–49 2.46% 6.04% 2.45 1.04 0.42 50–54 3.68% 9.68% 2.63 1.07 0.49 55–59 5.62% 13.09% 2.33 1.09 0.47 60–64 8.88% 19.89% 2.24 1.14 0.5 65–69 14.33% 29.38% 2.05 1.21 0.53 70–74 24.62% 41.85% 1.70 1.30 0.48 75–79 36.55% 57.75% 1.58 1.50 0.56

Supp Table 3 Illustration from Valkonen et al Supp Table 3 Illustration from Valkonen et al. (JEPH 2000) Based on All Cause Mortality in Finland for Three Time Periods Gender Period AGMort DGMort AdvRatio FavRatio EES M 1981-85 0.64% 0.96% 1.50 1.00321 0.15 1986-90 0.53% 0.93% 1.75 1.00404 0.21 1991-95 0.46% 0.85% 1.86 1.00395 0.22 F 0.29% 0.35% 1.21 1.00060 0.07 0.26% 0.36% 1.36 1.00095 0.11 0.24% 1.48 1.00113 0.14 f