ti {healthequal}

Theil Index (TI)

Description

The Theil Index (TI) is a relative measure of inequality that considers all population subgroups. Subgroups are weighted according to their population share.

Usage

ti(pop, est, se = NULL, conf.level = 0.95, ...)

Arguments

pop

The number of people within each subgroup. Population size must be available for all subgroups.

est

The subgroup estimate. Estimates must be available for all subgroups.

se

The standard error of the subgroup estimate. If this is missing, 95% confidence intervals of TI cannot be calculated.

conf.level

confidence level of the interval.

...

Further arguments passed to or from other methods.

Details

TI is calculated as the sum of products of the natural logarithm of the share of the indicator of each subgroup, the share of the indicator of each subgroup and the population share of each subgroup. TI may be easily interpreted when multiplied by 1000. For more information on this inequality measure see Schlotheuber, A., & Hosseinpoor, A. R. (2022) below.

Interpretation: Greater absolute values indicate higher levels of inequality. TI is zero if there is no inequality. TI is more sensitive to differences further from the setting average (by the use of the logarithm).

Type of summary measure: Complex; relative; weighted

Applicability: Non-ordered; more than two subgroups

Warning: The confidence intervals are approximate and might be biased.

Value

The estimated TI value, corresponding estimated standard error, and confidence interval as a data.frame.

References

Schlotheuber, A., & Hosseinpoor, A. R. (2022). Summary measures of health inequality: A review of existing measures and their application. International Journal of Environmental Research and Public Health, 19 (6), 3697.

Ahn J, Harper S, Yu M, Feuer EJ, Liu B, Luta G. Variance Estimation and Confidence Intervals for 11 Commonly Used Health Disparity Measures. JCO Clin Cancer Inform. 2018 Dec;2:1–19.

Examples

# example code
data(NonorderedSample)
head(NonorderedSample)
with(NonorderedSample,
     ti(pop = population,
        est = estimate,
        se = se
        )
     )