As explained in various places discussed or made available on the Measuring Health Disparities (MHD) and Scanlan’s Rule (SR) pages of jpscanlan.com, observed patterns of standard measures of differences between outcome rates (proportions) will be functions of both (a) the overall prevalence of an outcome and (b) the size of the difference between means of the underlying distributions of factors associated with experiencing the outcome.The patterns by which the measures are affected by the prevalence of an outcome – which patterns are described most completely in the introductory section of SR – are functions of the shapes of the underlying distributions of factors associated with experiencing the outcome and I shall here refer to the forces driving those patterns as the distributional forces.
If the difference between the means of two groups’ distributions is the same in two settings, then one will generally – i.e., absent distributional regularities, including those addressed on the Truncation Issues sub-page of SR, or factors such as that described on the Irreducible Minimums sub-page of MHD – observe the patterns described in the introduction to SR.Thus, for example, the setting with the lower prevalence of an outcome will generally show the larger relative difference in experiencing the outcome and the smaller relative difference in avoiding the outcome.Also, when the outcome is uncommon in both settings (less than 50% for both groups) the absolute difference between rates will be higher in the setting with the greater prevalence;when the outcome is common in both settings (more than 50% for both groups) the absolute difference between rates will be higher in the setting with the lower prevalence.And patterns of comparative size of differences measured by odds ratios will be the opposite of those measured by absolute differences.
But where the difference between the group’s means is larger in one setting than another, for any given prevalence level, all measures of difference will be larger in the setting with the larger difference between means.At different levels of prevalence the setting with the larger difference between means may or may not show larger differences for all measures.That is, for example, if prevalence is lower in the setting with the larger difference between means, that setting will certainly exhibit the larger relative difference in experiencing the outcome, but may or may not exhibit the larger relative difference in avoiding the outcome.This matter probably is discussed most fully in Race and Mortality (Society 2000), BSPS 2006, and Comment on Huijts EJPH 2009. The matter is discussed with regard to reasons for differing expectations when the settings are differentiated temporally and differentiated otherwise in Section A.9 of SR.
When discussing the role of the distributional forces, it is important to recognize that it would be a mistake to believe that the distributional forces are not present simply because they are not evident, as, for example, when both the relative difference between the rates at which two groups experience an outcome and the relative difference between the rates at which the two groups avoid the outcome are larger in one setting than the other.Presumably, the distributional forces are operating but the size of the difference between means of the underlying distributions sufficiently large relative to the size of the difference in prevalence that the distributional forces are not evident.
The main purpose of this item is to illustrate, using life table information, circumstances where the distributional forces will tend to predominate simply because the differences in prevalence are very large.But I also illustrate that the issue of whether the difference in prevalence in the two settings is greater than the difference between means in the two setting can be approached scientifically.
As discussed in Section A.8 of SR, what I refer to as overall prevalence is not overall prevalence as the term would ordinarily be used in epidemiology, since strictly speaking overall prevalence is a function of the rates of each group and the proportion each group comprises of the total population.I use the term to refer to a general pattern, as best identified with reference to the rate of the advantaged group at least where the advantaged group is the majority of the population.One could as well use the disadvantaged group’s rate as the benchmark for overall prevalence.
Using a particular groups’ rate as the benchmark for overall prevalence, one can measure differences in prevalence using the same approach that I have in various places maintained is the only useful measure of differences between outcome rates.Such approach, which is described in the Solutions sub-page of MHD and for which a downloadable database is made available on the Solutions Database sub-page of MHD and which has existed in 1934 in the form of the probit, involves deriving from a pair of outcome rates the difference between underlying means measured in terms of the percentage of a standard deviation.We can see from Table 1 of British Society for Population Studies 2006, for example, that where the advantaged and disadvantaged groups’ adverse outcome rates are 10.0% and 21.8%, the difference between means is .50 standard deviations. Other illustrations may be found in the tables of British Society for Populations Studies 2008 and Nordic Demographic Symposium 2008.
Without getting into the details of the variation in differences between means, it is easy to understand that one situations where one will commonly observe the pattern whereby the rarer an outcome the greater the relative difference in experiencing it and the smaller the relative difference in avoiding involves examination of mortality rates by different age groups, at least when the age groups compared have substantially different mortality rates.
The point can be illustrated with the life table data on white and black men set out in Table LT1 below, which is an abbreviated, and simplified, portion of Table A the Life Table Information document.The complete Table A also presents the same information for white men and women, white and black women, and black men and women.As explained in the introduction to the Life Table Information document, the information in Table A is based on proportions of a cohort surviving /failing to survive to various ages.As shown in Table B of the document, patterns based on proportions of persons surviving to one age who then survive/fail to survive to the next age, may differ in small ways.And I note that the latter figures are more reflective of the proportions at issue when observers draw conclusions about patterns of effects of age or socioeconomic status on mortality.But the information from Table A is suitable for instant purposes.
Table LT1 – Patterns of Measures of Differences between White and Black Rates of Failing to Survive to Various Ages [b1312 a 5][i]
Compare the figures for white and black men dying by age 30 with the figures for those dying by age 60.The difference between the prevalence of mortality/survival as to the two periods, based on the rate of the advantaged groups, is quite large.Using the Solutions/Probit approach, one would find the 2.63% and the 13.96% mortality figures for white men to reflect an EES of .856 (i.e., difference between underlying means of .856 standard deviations).Thus, even though the EES is larger for 60 than 30 (.39 versus .27), the mortality ratio is larger for age 30.
On the other hand, the difference in prevalence of mortality/survival is not as large for age 60 compared with 50 as age 60 compared with age 30.The 7.35% and 13.96% figures for white men dying by ages 50 and 60 reflect an EES of .36.Thus, the EES reflecting the difference in mortality between the advantaged and disadvantaged groups is sufficiently larger for age 60 than age 50 (.39 versus .32) to outweigh the tendency for the relative different in morality to be smaller at age 60 (where mortality is more common).