Numeracy Illustration
(November 21, 2013)
The is one of a number of subpages to the Scanlan’s Rule page of jpscanlan.com using publicly available data to illustrate the pattern whereby the rarer an outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it. Similar subpages include Framingham Illustrations, NHANES Illustrations, Life Tables Illustrations, Income Illustrations, Credit Score Illustrations.
In “Race and Mortality” (Society, Jan./Feb. 2000) (reprinted in Current, Feb. 2000), I explained that assuming the Race and Health Initiative led generally to improvements in health and healthcare one would likely observe increasing racial differences in adverse health and healthcare outcomes but decreasing relative differences in the corresponding favorable outcomes. In the Paradox of Success and Failure section of the article, I used test score data to illustrate the pattern whereby the rarer an outcome, the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it. Specifically, I showed that lowering a cutoff, thereby reducing the frequency of test failure while increasing the frequency of test passage, would tend to increase relative differences in failure rates while reducing relative differences in pass rates. A recent narrative illustration of the pattern may be found in my “Misunderstanding of Statistics Leads to Misguided Law Enforcement Policies” (Amstat News, Dec. 2012) and recent graphic illustration may be found in Figure 1 of my Federal Committee on Statistical Methodology 2013 Research Conference presentation, “Measuring Health and Healthcare Disparities.”
In “Race and Mortality,” after presentation the test cutoff illustration I noted that if the literacy program President Clinton announced a month after he announced the minority health initiative proved to be successful, it can be expected to increase racial disparities in illiteracy rates while reducing racial disparities in literacy rates. I did not subsequently look for data to support that point, though it would extraordinary to find it to not to be true.
Recently, however, in preparing a page regarding the problematic nature of guidance the Institute of Medicine (IOM) provides on health and healthcare disparities research (something I touched upon in a February 4 comment in the BMJ regarding an article on an IOM conference) , I discovered a paper commissioned by the IOM’s Roundtable on Health Literacy titled “Numeracy and the Affordable Care Act: Opportunities and challenges,” which, in its Table 1 (at 6), presented some data on health numeracy for persons with insurance and without insurance. The data are reproduced in Table 1 below.
Table 1. Proportions of Uninsured and Insured Populations Falling Into Four Categories of Health Numeracy.
|
|
Level
|
Uninsured
|
Insured
|
|
Below Basic
|
28.80%
|
18.20%
|
|
Basic
|
33.40%
|
31.90%
|
|
Intermediate
|
29.30%
|
35.30%
|
|
Proficient
|
8.60%
|
14.60%
|
Based on the figures in Table 1 above, Table 2 below then for each of the three cut points separating the four categories, the proportions of the uninsured and insured populations falling below and above the cut points, along with the ratio of uninsured rate of falling below the point to the insured rate of falling below the point, and the ratio of the insured rate of falling above he cut point to the insured.
Table 2. Proportions of Uninsured and Insured Populations Falling Below and Above Three Cut Point for Health Numeracy, with Ratio Ratios
|
|
Cut Point
|
PropUninsBelow
|
PropInsBelow
|
PropUninAbove
|
PropInsurAbove
|
Unins/Insur Below
|
Ins/Unins Above
|
|
Basic
|
28.80%
|
18.20%
|
71.20%
|
81.80%
|
1.58
|
1.15
|
|
Intermediate
|
62.20%
|
50.10%
|
37.80%
|
49.90%
|
1.24
|
1.32
|
|
Proficient
|
91.50%
|
85.40%
|
8.50%
|
14.60%
|
1.07
|
1.72
|
Table 2 thus shows that way the higher the level, the greater tends to be the relative difference in meeting it and the smaller tends to be the relative difference in failing to meet it. It also shows that
Thus, the general improvements in health numeracy (such as, for example, that would move everyone with a basic numeracy into the intermediate category, will tend to increase the relative difference in failing to achieve the level while reducing the relative difference in achieving the level (or better). That is, the rate ratio for failing to meet the level would rise from 1.24 to 1.58, while the rate ratio for meeting the level would decline from 1.32 to 1.15.
I have not examined the commissioned paper to determine whether issues I raise about the IOM’s interpretation of data bear on anything in the paper. In light of the title of the commissioned paper, however, it should be borne in mind that consideration of the way measures tend to be affected by the prevalence of an outcome will importantly affect interpretations of patterns of the affects of the Affordable Care Act on health and healthcare disparities just as those considerations importantly affect interpretations of the effects of the Race and Health Initiative on health and healthcare disparities.