phe_sii returns the slope index of inequality (SII) statistic for each subgroup
of the inputted dataframe, with lower and upper confidence limits based on the specified
confidence. The Relative Index of Inequality (RII) can also be returned via an optional
argument.
phe_sii(data, quantile, population, x = NULL, value = NULL,
value_type = 0, lower_cl = NULL, upper_cl = NULL, se = NULL,
multiplier = 1, repetitions = 1e+05, confidence = 0.95,
rii = FALSE, reliability_stat = FALSE, type = "full")The SII with lower and upper confidence limits for each subgroup of the inputted data.frame.
The SII is calculated using linear regression [1]. To allow
for differences in population size between quantiles (e.g. deprivation deciles),
each is given a rank score (or relative rank) based on the midpoint of its range
in the cumulative distribution of the total area population. The quantiles are
first ordered (e.g from 1 most deprived to 10 least deprived for deprivation deciles).
If quantile 1 then contains 12% of the total population, its relative rank is
0.12/2=0.6. If quantile 2 includes 10% of the population, its relative rank
is 0.12+(0.10/2)=0.17. A square root transformation is applied to the regression
to account for heteroskedasticity (the tendancy for the variances of the quantile values
to be related to the size of the values, ie larger values will tend to have larger
variances). A regression model is fitted to the transformed data: \(Y * \sqrt a =
\sqrt a + b * \sqrt a\), where Y is the value of the indicator for the quantile, a is
the proportion of the total population in the quantile and b is the relative rank.
The SII is the gradient of the resulting fitted line, and could be positive or negative
according to the indicator polarity. Since the relative ranks, by definition, range from
0 to 1, the SII is the difference between the fitted value at x=1 and x=0.
The RII is the ratio of the fitted value at x=1,Y1 and the fitted value at
x=0,Y0. which can be calculated as: RII = (Y0 + SII)/Y0
The indicator type can be specified via the value_type parameter. Transformations
can be applied to the indicator value and its confidence limits before calculating the
standard error in cases where the confidence interval around the indicator value is
likely to be non-symmetric. This is a log transformation for rates, and logit for
proportions.
If the standard error is supplied directly to the function from the input dataset, this is used instead of calculating one from the indicator confidence limits.
The SII calculation assumes a linear relationship between indicator value and quantile, and small populations within quantiles can make it unstable.
This function does not include checks for linearity or stability; it is the user's responsibility to ensure the input data is suitable for the SII calculation.
this function is using nest and unnest functions from tidyr version 1.0.0.
The SII and RII are two measures of health inequality. They show the relation between the level of health or frequency of a health problem in different population groups and the ranking of these groups on the social scale.
The input dataframe should be grouped before passing to the function if an SII/RII for each subgroup is required, and quantiles ordered from least to most advantaged.
[1] Low A & Low A. Measuring the gap: quantifying and comparing local health inequalities. Journal of Public Health; 2004;26:388-395.
Other PHEindicatormethods package functions: phe_dsr,
phe_isr, phe_life_expectancy,
phe_mean, phe_proportion,
phe_quantile, phe_rate,
phe_smr