16th Nordic Demographic SymposiumHelsinki, Finland, 5-7 June 2008

Measures of Health Inequalities that are

Unaffected by the Prevalence of an Outcome

James P. ScanlanAttorney at Law

Washington, DC, USAjps@jpscanlan.com

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, 5th 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

0

1

2

3

4

5

1 3 5 10 20 30 40 50 60 70 80 90 95 97 99

Cutoffs Defined by AG Success Rate

Ra

tio

s (1) AG Succ Rate/DG Succ 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)

0

1

2

3

4

5

1 3 5 10 20 30 40 50 60 70 80 90 95 97 99

Cutoffs Defined by AG Success Rate

Ra

tio

s (1) AG Succ Rate/DG Succ Rate

(2) DG Fail Rate/AG Fail Rate

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

0

1

2

3

4

5

1 3 5 10 20 30 40 50 60 70 80 90 95 97 99

Cutoffs Defined by AG Success Rate

Ra

tio

s (1) AG Succ Rate/DG Succ Rate

(2) Ratio DG Fail Rate/AG Fail Rate

(3) DG Fail Odds/AG Fail 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

0

1

2

3

4

5

1 3 5 10 20 30 40 50 60 70 80 90 95 97 99

Ra

tio

s

(1) AG Succ Rate/DG SuccRate

(2) Ratio DG Fail Rate/AG FailRate

(3) DG Fail Odds/AG Fail Odds

0

10

20

1 3 5 10 20 30 40 50 60 70 80 90 95 97 99

Cutoffs Defined by AG Success Rate

Pe

rce

nta

ge

Po

ints

Absolute Diff Betw 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 Rate 40% I 58% I 76% I 94%DG Rate 23% I 39% I 58% I 85%

Ratio 1 1.74 D 1.45 D 1.31 D 1.11 Ratio 2 1.28 I 1.49 I 1.75 I 2.50Odds Ratio 2.23 D 2.16 I 2.29 I 2.76Absol Diff .17 I .19 D .18 D .09 EES (z) .50 nc .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 Rate 40% I 58% DG Rate 23% I 40%

Ratio 1 1.74 D 1.43 Ratio 2 1.28 I 1.45 Odds Ratio 2.23 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)

Period Grade Year WhRt BlRtFav

RatioAdv

Ratio AbsDf EES

PreRq 5 1996 8% 3% 2.67 1.05 0.05 0.47

Post 5 1997 46% 33% 1.39 1.24 0.13 0.34

Post 5 1998 50% 39% 1.28 1.22 0.11 0.29

PreRq 9 1996 46% 32% 1.44 1.26 0.14 0.37

Post 9 1997 89% 84% 1.06 1.45 0.05 0.24

Post 9 1998 93% 89% 1.04 1.57 0.04 0.26

Table 4 Illustrations Based on Escarce and McGuire (AJPH 2004) Data on White and Black Coronary Procedure Rates, 1986 and 1997 (see D48)

Proc Year Wh Rt Bl RtFav

RatioAdv

Ratio AbsDf EES

Angrm 1986 8.56% 4.31% 1.99 1.05 0.04 0.25

Angrm 1997 22.83% 16.10% 1.42 1.09 0.07 0.14

Angpls 1986 0.99% 0.32% 3.09 1.01 0.01 0.32

Angpls 1997 2.57% 1.60% 1.61 1.01 0.01 0.15

ArtByp 1986 3.06% 0.81% 3.78 1.02 0.02 0.41

ArtByp 1997 5.86% 2.60% 2.25 1.03 0.03 0.27

Table 5: Illustration Based on Hetemaa et al. (JECH 2003) Data on Finnish Revascularization Rates, 1988 and 1996, by Income Group (see D21, D58)

Gender YearAG

RevRtLowIncRevRt

FavRatio

AdvRatio AbsDf EES

M 1988 17.9% 8.3% 2.16 1.12 .096 0.48

M 1996 41.2% 25.4% 1.63 1.27 .159 0.44

F 1988 10.0% 3.7% 2.70 1.07 .063 0.51

F 1996 30.8% 17.1% 1.80 1.20 .137 0.45

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)

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

Table 7 Illustration from Valkonen et al. (EJPH 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

M 1986-90 0.53% 0.93% 1.75 1.00404 0.21

M 1991-95 0.46% 0.85% 1.86 1.00395 0.22

F 1981-85 0.29% 0.35% 1.21 1.00060 0.07

F 1986-90 0.26% 0.36% 1.36 1.00095 0.11

F 1991-95 0.24% 0.35% 1.48 1.00113 0.14

f

Table 8 Illustration Based on Boström and Rosén (SJPH 2003) Data on Mortality by Occupation in Seven European Countries (see D43 caveats)

Country EES 1980-84 EES 1990-94

Denmark 0.14 0.13

England and Wales 0.11 0.15

Finland 0.16 0.23

Ireland 0.10 0.19

Norway 0.12 0.16

Spain 0.12 0.23

Sweden 0.14 0.17

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