Combined social and private health insurance versus catastrophic out of pocket payments for private hospital care in Greece

Equation (1): SS corresponds to the required sample size. “\(Z^{2}\) is the abscissa of the normal curve that cuts off an area \(\alpha \) at the tails (1 - \(\alpha \) equals the desired confidence level, e.g. 95%), e is the desired level of precision, p is the estimated proportion of an attribute that is present in the population, and q is 1-p” (Israel 1992:3).We used as inputs the Z-value of 1.96, a margin of error (e) of 5% and an estimate of the (p) prevalence of insured hospitalization in private hospitals. Similarly, in Eq. (2): SS is the sample size,\(X_{\left( 1 \right) }^2 \)is the chi-square value (3.84), N is the known number of hospitalization cases in private hospitals under EOPYY’s coverage, p and q are the population proportions and \(d^{2}\) is the desired degree of accuracy (0.0025) (Kraska-Miller 2013). The new SHI organization covered 6.171 million people with insurance capability in 2013, while for the same year almost 440.000 cases were reimbursed as inpatient under EOPYY contract mechanisms in a broad spectrum of private hospitals (Minister’s of Health press conference in November 2014, Athens). Therefore, the estimated proportion (prevalence) of EOPYY insured hospitalization in private hospitals was amounted to 7.13% (0.440/6.171). Both the above equations, indicating that the minimum number of hospitalization events we had to gather in order to obtain a representative sample of EOPYY’s hospitalized insured population on private providers is 102 responses. Therefore our sample which includes 362 SHI respondents is representative. As we have already mentioned in the introduction section, the people covered by PHI in Greece reached the 12.5% of total population in 2013. Therefore, the estimated prevalence of PHI holders with mandatory SHI coverage (EOPYY), who had received hospitalization health services in affiliated with EOPYY private hospitals for the same year, it could be p = 0.125*0.0713 = 0.0089. Thus, the minimum number or observations for this subgroup was amounted to 14 observations based on the utilized ‘sample for proportions’ equations. We succeeded in gathering data from 64 SHI and additional PHI policyholders.

The regression coefficient \(\beta \) reflects the values for concentration indices. Continuing, yi is whenever the examined health variable of interest, \(\mu \) its mean, \(\sigma _R^2 \) is the variance of the fractional variable of N insured individuals in socioeconomic distribution ranking by their income.Ri reflects the insured individual cumulative proportion in the annual gross income distribution where observations are classified in ascending order to sum up to 1, based on the formulation of Lerman and Yitzhaki (1989):\(R_i =\frac{1}{n}\sum _{j=1}^{i=1} w_j +\frac{1}{2}w_i \) . Although, the simplicity of the most common computational method of convenient covariance \(C=2cov\left( {\frac{y_i }{R_i }} \right) \mu \) (Wagstaff et al. 2003) of calculating concentration indices, we imply the convenience regression method in order to estimate the standard errors of CE or CO.