This was a cross-sectional and retrospective study. The study setting was Iran. Iran consists of 31 provinces, based on the census 2011, with a population of around 75,149,669 people and located in the Eastern Mediterranean WHO Region (EMRO) with an area of 1,648,195 km2.
In this study, each province was considered as an analysis unit. The data on the number of physicians (general physicians and practitioners) per 10000 populations (PPR), hospital beds per 10000 of populations (HBPR), as well as the number of hospitalized patients were obtained from the Iranian Statistical Center (ISC) and ministry of health (15). In the current study, the number of hospitalized patients was used as health need index (HNI). In addition, data analysis was performed by STATA V.12 (StataCorp LP and USA) and Excel Software.
3.1. Inequality Measures
In the current study, according to other studies (2, 4, 11, 16, 17), to examine inequality in distribution of physicians and hospital beds, the Gini coefficient, Concentration Index and Rabin Hood index were used.
3.1.1. Gini Coefficient and Concentration Index
The Gini coefficient is derived from the Lorenz curve (Figure 1) and is used commonly for measuring inequality in distribution of health care resources. It varies between 1 (perfect inequality) and zero (perfect equality). By Lorenz curve, the Gini coefficient is calculated using the following equation:
(1)
Where:
G = Gini coefficient, A = the area between the Lorenz curve and the 45° line, A + B = the whole area under the 45° line.
Figure 1.
The Lorenz Curve
In the Lorenz curve, the cumulative % of health variable and the cumulative % of population are shown on the Y-axis and X- axis, respectively (4, 7). In addition, we used the following Equation to to calculate the Gini coefficient and its standard error (SE) (18).
(2)
Where:
G: Gini coefficient: the mean value of distribution, y: health variables in the province, N: total number of provinces.
Also, the Jackknife variance estimator for the Gini coefficient is derived from the following equation:
(3)
Where:
V = the value estimators; Gi = the value of Gini coefficient; N = total number of provinces.
In the concentration curve, the Cumulative % of health variable (physician and hospital beds) is plotted on Y-axis and the cumulative % of population ranked by number of hospitalized patients placed on X-axis. The concentration curve can be lied above (negative value) and below (positive value) the 450 line. The concentration index is defined as two times the area the area between the concentration curve and the 450 line (4, 19) and takes values between -1 and +1. In the current study, negative value (concentration curve above the 450 line) indicates that there are fewer physicians or hospital beds in the provinces with more health need index, and vice versa. Moreover, the concentration index is equal zero when there is no inequality in distribution of physician or hospital beds in the provinces of Iran.
We used the following Equation to to calculate the Concentration index (20).
94)
Where:
P is the cumulative % of the population ranked by number of hospitalized patients; L is the cumulative % of the health variable (physician or hospital beds).
3.1.2. The Rabin Hood Index
The Rabin Hood index is based on the Lorenz curve and takes values between zero (perfect equality) and 100 % (perfect inequality). This index is equivalent to the maximum vertical distance between the Lorenz curve and the 450 line. In the current study, this index indicates the percentage of total number of physicians or hospital beds that should be transferred from provinces above the mean for the country to those below that figure to achieve equality in the distribution of physicians or hospital beds in all provinces (21, 22). We used the following equation to calculate the Rabin Hood index:
(5)
Where:
R: Robin Hood index; i: the number of quintile; n: total number of quintile; A: Access in quartile i (%) and N: Need in quartile i (%).
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