Following methods commonly used in analyses of contributors to
mortality rates, we converted all variables to their natural logarithms
and then conducted tests of association to examine relationships of
each with US state amenable mortality rates.7,8 The transformation to
logarithmic form has two significant advantages. First, in regression
analyses using the double-log form (that is, dependent and independent
variables) coefficients are expressed as elasticities, which are easily
interpreted and compared across measures. Elasticities are interpreted
as the per cent change in the dependent variable that is associated with
a 1 per cent change in an independent variable. A regression of the state
mortality amenable rate on the per cent residents receiving clinically
recommended care, for example, resulting in an elasticity coefficient of
_2.0 would indicate that a 1 per cent increase in the recommended care
rate is associated with a 2 per cent decline in the mortality rate. Second,
we fit regression models of population-based ratios on both sides of the
equation. Regressions with untransformed ratios would yield very large
spurious associations unrelated to the relationships of interest. The use
of double-log transformations eliminates this serious statistical problem.9
Recognizing that income and race are related to insurance, where
people receive care, and care experiences, we examined the correlations
of the natural logarithms of socio-demographic variables with the
health system variables. To determine the extent to which health system
variables are significantly associated with variations in mortality amenable
to health care, we performed a series of multivariate regression analyses
for amenable mortality at the state level and each of the health carerelated
indicators, controlling for race and poverty.
Black rates of amenable mortality are higher than for whites in all
states, and the black population is distributed unequally across states.
To understand mortality variations not attributable to the racial
composition of states, we also performed regressions using state whiteonly
amenable mortality rates along with white-only poverty and
uninsured rates. We employed the STATA version 9.2 statistical
package for all analyses.