This study used two methods to analyze the reimbursement effect of SIMIS. First, descriptive analysis was carried out on the inpatient situation of the patients with serious illnesses, describing the different types of inpatient expenses and reimbursement situation in the year, and then analyzing the reimbursement effect. We divided the hospitalization types into five categories: county hospitalization, referring to the inpatients in Jinzhai County; city hospitalization, referring to the inpatients outside Jinzhai County and in Lu’an City; provincial hospitalization, referring to the inpatients outside Lu'an City and in Anhui Province; outside Anhui Province hospitalization, referring to the inpatients outside Anhui Province; and cross regional hospitalization, referring to the cross regional inpatients.
Second, regression discontinuity (RD) [8,9,10] was used to analyze the relief of medical expenses of rural residents after the implementation of SIMIS. We used RD for the discontinuous characteristics of policy; that is, when the specific index of the research object was greater than the critical value specified by the policy, it would be treated by the policy, and the critical value was the so-called break point (C), or the point at which the line representing X shows a cutoff. As the policy of SIMIS in Jinzhai was to compensate inpatients whose annual serious illness expenses exceeded CNY 20,000 (2,828 USD), we set C = CNY 20,000 (2,828 USD) as the break point in this study. The participants whose annual serious illness expenses exceeded CNY 20,000 (2,828 USD) were included in the experimental group, whereas those whose annual serious illness expenses was less than or equal to CNY 20,000 (2,828 USD) were included in the control group. The basic situation of the expenses near the break point was similar. Thus, whether the participants could benefit from the compensation of SIMIS depended on the random allocation of policies, which could be regarded as a quasi-experiment. Owing to the random grouping, the average treatment effect of SIMIS near the break point could be estimated.
We used STATA 15.0 RD for data statistical analysis. The analysis process was as follows:
- The average and frequency indexes were used to describe the inpatient characteristics and payment status of patients with serious illnesses.
- We determined the optimal bandwidth (H), which refers to the best distance from the break point. Generally, the smaller the H is, the smaller the deviation of objects (i.e., expenses) on both sides of the break point, but such a scenario may lead to fewer observation objects, resulting in excessive variance. Meanwhile, the larger the H, the smaller the variance, but objects far away from the break point tends to be included, resulting in excessive deviation. Therefore, we used the method proposed by Imbens and Kalyanaraman [11] to select the optimal bandwidth by minimizing the mean square error of two regression functions at the break point. Specifically, in proposing the IK method, Imbens and Kalyanaraman derived the asymptotically optimal bandwidth under squared error loss. This optimal bandwidth depends on unknown functionals of the distribution of the data. They proposed simple and consistent estimators for these functionals to obtain a fully data-driven bandwidth algorithm.
- We conducted RD analysis. The dependent variables were the actual medical insurance payment proportion (AMIPP), inside medical insurance payment proportion (IMIPP), inside medical insurance self-payment proportion (IMISPP), and outside medical insurance self-payment proportion (OMISPP). The independent variable (grouping variable) was serious illness expenses. The covariates were age, hospital stay, total medical expenses, sex, and inpatient type. Table 1 shows the definition and basic information regarding the variables. In the two intervals (C-H, C) and (C, C + H), the weighted least square method was used for linear regression, with the weight determined by the trigonometric kernel function. The difference between the estimates of dependent variables of the two functions at point C is called the local average treatment effect, also known as “local Wald estimator” (lwald).
- We conducted the validity test. When conducting RD, we paid attention to the possibility of endogenous grouping. For example, the patients whose serious illness expenses were less than CNY 20,000 (2,828 USD) had known the grouping rules in advance, and as such, they could take the initiative to make their serious illness expenses reach CNY 20,000 (2,828 USD) and benefit from the compensation policy, resulting in endogenous grouping rather than random grouping of patients near the break point.
To address the possibility of endogenous grouping, this study used the method proposed by McGrary [12] for testing the discontinuity of the density function of the grouping variable at the break point. The grouping variables were subdivided equidistantly on both sides of break point C. The group distance was B, the center position of each group was noted as variable Xj, and then the standardization frequency of each group was calculated, which was noted as Yj. Using trigonometric kernel and local linear regression on both sides of break point C, the estimated value and standard error of density function could be obtained per the value of the grouped variables. By comparing the estimated values of the density function at the break point, we could determine whether the density function was continuous at the break point.
In addition, even if the conditional density function of covariates at break point C also had a jump, it was not appropriate to attribute all policy effects to the implementation of policies. Indeed, the implicit assumption of RD was that the conditional density of covariates was continuous at the break point. To test this hypothesis, we took each covariate as the dependent variable and the serious illness expenses as the independent variable, and then carried out RD again to check for jumps in its distribution at the break point.
Table 1. Basic information of variables
Variable
|
Variable definition
|
C ≤ 2,828 (n = 5,984)
|
C >2,828 (n = 1,370)
|
Mean
|
SD
|
Mean
|
SD
|
Dependent variable (%)
|
AMIPP
|
Proportion of total medical insurance payment to total medical expenses
|
48.16
|
13.52
|
51.93
|
11.47
|
IMIPP
|
Proportion of total medical insurance payment to total inside medical insurance expenses
|
59.48
|
13.19
|
61.39
|
11.93
|
IMISPP
|
Proportion of inside medical insurance self-payment to total expenses
|
32.69
|
11.96
|
32.81
|
11.14
|
OMISPP
|
Proportion of outside medical insurance self-payment to total expenses
|
19.15
|
10.99
|
15.26
|
10.71
|
Independent variable (grouping variable)
|
Serious illness expenses
|
Total of ceiling self-payment, necessary clinical treatment cost, self-payment under NRCMS
|
1.38
|
0.27
|
2.41
|
0.28
|
Covariates
|
Age
|
Age of inpatients
|
49.82
|
18.39
|
50.45
|
17.15
|
Hospital stay
|
Length of hospital stay in days
|
23.26
|
29.38
|
26.46
|
36.34
|
Total expenses
|
Total annual inpatient medical expenses
|
4.78
|
2.42
|
7.49
|
3.27
|
Sex
|
Female = 1
|
0.58
|
0.49
|
0.57
|
0.49
|
Inpatient type
|
Inpatient grade (1–5)
|
4.06
|
1.06
|
4.24
|
1.16
|
Source: Jinzhai Medical Insurance Management Center
Sample
The research data came from the medical insurance management center of Jinzhai County, Anhui Province, covering the individual annual hospitalization reimbursement data of NRCMS from 2013 to 2016 (n = 73,042 in 2013, n = 73,571 in 2014, n = 75,330 in 2015, and n = 71,928 in 2016). The use of data had been approved by Jinzhai County. Case information included the following: basic information of inpatients, hospitalization, and medical expenses payment. To analyze the SIMIS reimbursement effect, we merged the four-year data (2013–2016, n = 29,3871).
We focused our RD on the objects near both sides of the break point. To ensure the same span on both sides of the break point, we selected the patients from the merged data of 2013–2016 whose serious illness expenses was between CNY 10,000 (1,414 USD) and CNY 30,000 (4,242 USD) as the analysis objects (n = 1,553 in 2013, n = 1,797 in 2014, n = 2,147 in 2015, and n = 1,856 in 2016, total n = 7,353). The descriptive analysis of SIMIS reimbursement objects covered the merged data of 2013–2016 (n = 468 in 2013, n = 535 in 2014, n = 831 in 2015, n = 886 in 2016, total n = 2,720). Table 2 shows the distribution of serious illness expenses from 2013 to 2016.
Table 2. Distribution of serious illness expenses in Jinzhai County from 2013 to 2016
Expenses
|
Frequency
|
Frequency ratio(%)
|
0.0–
|
285,501
|
97.15
|
1.0–
|
5,983
|
2.03
|
2.0–
|
1,370
|
0.47
|
3.0–
|
493
|
0.17
|
4.0–
|
221
|
0.08
|
5.0–
|
303
|
0.10
|
Source: Jinzhai Medical Insurance Management Center