Chapter 7: Technical Notes
yˆ iIS = yi − yˆ iX + y .
(7.11)
IS The distribution of yˆ i (for example, across income) can be interpreted as the distribution of health or utilization that would be expected, irrespective of differences in the distribution of x across income. A standardized distribution of health or utilization across quintiles could be generated, for instance, by IS averaging yˆ i within quintiles.
Direct Standardization The direct method of standardization is more restrictive because it requires grouping health or utilization by categories of living standards. The regressionbased variant of direct standardization proceeds by estimating, for each living standard group (g), an equation such as the following: yi = α g + ∑ βjg x ji + ∑ γ kg z ki + ε i , j
(7.12)
k
which is a group-specific version of equation 7.9. OLS estimates of the ˆ group-specific parameters αˆ g , βjg ,γˆkg , sample means of the confounding variables (x j ), and group-specific means of the nonconfounding variables (zkg ) are then used to generate directly standardized estimates of the health or utilization variable yˆ iDS as follows:
(
)
yˆ iDS = yˆ gDS = αˆ g + ∑ βˆ jg x j + ∑ γˆk zkg . j
(7.13)
k
This method immediately gives the standardized distribution of health or utilization across groups because there is no intragroup variation in the standardized values. For grouped data, both the direct and indirect methods answer the question, what would the distribution of health or utilization across groups be if there were no correlation between health or utilization and demographics? But their means of controlling for this correlation is different. The direct method uses the demographic distribution of the population as a whole (the x–j), but the behavior of the groups (as embodied in βˆ jg and γˆ jg). The indirect method employs the group-specific demographic characteristics (the x–jg), but the population-wide demographic effects (in βˆ j and γˆk). The advantage of the indirect method is that it does not require any grouping and is equally feasible at the individual level. The results of the two methods
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