﻿ 上海市卫生总费用预测及影响因素分析——基于灰色模型

# 上海市卫生总费用预测及影响因素分析——基于灰色模型Prediction and Analysis of Influencing Factors of Total Health Expenditure in Shanghai—Based on Grey Model

Abstract: Objective: To scientifically predict the expenditure trend and financing structure of the total health expenses in Shanghai, analyze the factors affecting the total health expenses in Shanghai from the perspectives of population, economy, policy and health, and put forward reasonable suggestions for the medical and health departments in Shanghai to formulate the medical and health policies and develop the medical and health undertakings to control the medical and health expenses. Methods: The data were obtained from the statistical yearbook of Shanghai from 2010 to 2017. The GM(1,1) grey prediction model and grey correlation model were used to predict the total health expenditure in Shanghai and analyze the correlation degree of influencing factors. Results: In the decade from 2018~2027, the total health expenditure, government health expenditure, social health expenditure and personal health expenditure of Shanghai all showed a rising trend; per capital disposable income of rural residents, the proportion of rural residents’ medical and health expenditure in per capita consumption expenditure, and the grey correlation degree of per capita disposable income of urban residents rank the first three, while the number of permanent residents and the proportion of government health expenditure in the total expenditure rank the last two. Conclusion: The Shanghai health financing structure is more reasonable, improve people’s health level, economic factors and health consumption are the main factors influencing the total health expenses in Shanghai, policy factors, the number of the population of permanent residents in demographic factors influence on the total health expens-es in Shanghai the weakest.

1. 引言

2. 上海市卫生总费用现状分析

Table 1. Total health expenditure and its composition in Shanghai from 2001 to 2017

3. 基于灰色GM(1,1)模型上海市卫生总费用预测分析

3.1. 级比检验，建模可行性分析

3.1.1. 建立上海市卫生总费用时间序列

$\begin{array}{c}{X}^{\left(0\right)}=\left({x}^{\left(0\right)}\left(\text{1}\right),{x}^{\left(0\right)}\left(2\right),\cdots ,{x}^{\left(0\right)}\left(\text{8}\right)\right)\\ =\left(751.99,931.00,1092.35,1248.68,1347.79,1536.60,1838.00,2087.09\right)\end{array}$

3.1.2. 求级比

$\sigma \left(k\right)=\frac{{x}^{\left(0\right)}\left(k-1\right)}{{x}^{\left(0\right)}\left( k \right)}$

$\sigma =\left(\sigma \left(\text{2}\right),\sigma \left(\text{3}\right),\cdots ,\sigma \left(\text{8}\right)\right)=\left(\text{0}\text{.81},\text{0}\text{.85},\text{0}\text{.87},\text{0}\text{.93},\text{0}\text{.88},\text{0}\text{.84},\text{0}\text{.88}\right)$

3.1.3. 级比判断

3.2. 用GM(1,1)建模

3.2.1. 对原始数据X(0)作一次累加

${X}^{\left(\text{1}\right)}\left(k\right)=\underset{m=1}{\overset{k}{\sum }}{X}^{\left(0\right)}\left(m\right)\text{}\left(k=1,2,3,\cdots ,\text{8}\right)$ 得：

$\begin{array}{c}X\left(1\right)=\left({x}^{\left(1\right)}\left(1\right),{x}^{\left(2\right)}\left(2\right),{x}^{\left(1\right)}\left(3\right),\cdots ,{x}^{\left(1\right)}\left(\text{8}\right)\right)\\ =\left(751.99,1682.99,2775.34,4024.02,5371.81,6908.41,8746.41,10833.50\right)\end{array}$

3.2.2. 构造数据矩阵B及数据向量Y

$Z=\left(\begin{array}{c}{Z}^{\left(1\right)}\left(2\right)=\frac{1}{2}\left[{x}^{\left(1\right)}\left(1\right)+{x}^{\left(1\right)}\left(2\right)\right]=\text{1217}\text{.49}\\ {Z}^{{}^{\left(1\right)}}\left(3\right)=\frac{1}{2}\left[{x}^{\left(1\right)}\left(2\right)+{x}^{\left(1\right)}\left(3\right)\right]=\text{2229}\text{.17}\\ {Z}^{\left(1\right)}\left(4\right)=\frac{1}{2}\left[{x}^{\left(1\right)}\left(3\right)+{x}^{\left(1\right)}\left(4\right)\right]=\text{3399}\text{.68}\\ {Z}^{\left(1\right)}\left(5\right)=\frac{1}{2}\left[{x}^{\left(1\right)}\left(4\right)+{x}^{\left(1\right)}\left(5\right)\right]=\text{4697}\text{.92}\\ {Z}^{\left(1\right)}\left(6\right)=\frac{1}{2}\left[{x}^{\left(1\right)}\left(5\right)+{x}^{\left(1\right)}\left(6\right)\right]=\text{6140}\text{.11}\\ {Z}^{\left(1\right)}\left(7\right)=\frac{1}{2}\left[{x}^{\left(1\right)}\left(6\right)+{x}^{\left(1\right)}\left(7\right)\right]=\text{7828}\text{.41}\\ {Z}^{\left(1\right)}\left(8\right)=\frac{1}{2}\left[{x}^{\left(1\right)}\left(7\right)+{x}^{\left(1\right)}\left(8\right)\right]=\text{9789}\text{.96}\end{array}\right)$

$B=\left(\begin{array}{cc}-{Z}^{\left(1\right)}\left(2\right)& 1\\ -{Z}^{\left(1\right)}\left(3\right)& 1\\ -{Z}^{\left(1\right)}\left(4\right)& 1\\ -{Z}^{\left(1\right)}\left(5\right)& 1\\ -{Z}^{\left(1\right)}\left(6\right)& 1\\ -{Z}^{\left(1\right)}\left(7\right)& 1\\ -{Z}^{\left(1\right)}\left(8\right)& 1\end{array}\right)=\left(\begin{array}{cc}-1217.49& 1\\ -2229.17& 1\\ -3399.68& 1\\ -4697.92& 1\\ -6140.11& 1\\ -7827.41& 1\\ -9789.96& 1\end{array}\right),\text{}Y=\left(\begin{array}{c}{x}^{\left(0\right)}\left(2\right)\\ {x}^{\left(0\right)}\left(3\right)\\ {x}^{\left(0\right)}\left(4\right)\\ {x}^{\left(0\right)}\left(5\right)\\ {x}^{\left(0\right)}\left(6\right)\\ {x}^{\left(0\right)}\left(7\right)\\ {x}^{\left(0\right)}\left(8\right)\end{array}\right)=\left(\begin{array}{c}931.00\\ 1092.35\\ 1248.68\\ 1347.79\\ 1536.60\\ 1838.00\\ 2087.09\end{array}\right)$

3.2.3. 最小二乘法估计求参数列P = (a, b)T

3.2.4. 建立模型

${X}^{\left(\text{0}\right)}\left(k\right)-0.1\text{32909927}{Z}^{\left(1\right)}\left(k\right)=\text{769}\text{.9371871}$ 解得时间响应序列为：

${\stackrel{^}{X}}^{\left(1\right)}\left(k+1\right)=\left({x}^{\left(0\right)}\left(1\right)-\frac{\stackrel{^}{b}}{\stackrel{^}{a}}\right){\text{e}}^{-\stackrel{^}{a}k}+\frac{\stackrel{^}{b}}{\stackrel{^}{a}}=\text{6544}{\text{.914614e}}^{0.132909927k}-\text{5792}\text{.924614}$

3.2.5. 求生成数列值及模型还原值

$k=\text{1},\text{2},\cdots ,\text{7}$ 代入时间响应函数可算得 ${\stackrel{^}{x}}^{\left(1\right)}\left(1\right)={\stackrel{^}{x}}^{\left(0\right)}\left(1\right)={x}^{\left(1\right)}\left(1\right)=751.99$ 其中取由累减生成 ${\stackrel{^}{x}}^{\left(0\right)}\left(k\right)={\stackrel{^}{x}}^{\left(0\right)}\left(k\right)-{x}^{\left(0\right)}\left(k-1\right)$，得还原值：

$\begin{array}{c}{\stackrel{^}{x}}^{\left(0\right)}=\left({\stackrel{^}{x}}^{\left(0\right)}\left(1\right),{\stackrel{^}{x}}^{\left(0\right)}\left(2\right),\cdots ,{\stackrel{^}{x}}^{\left(0\right)}\left(8\right)\right)\\ =\left(751.99,930.34,1062.59,1213.63,1386.14,1583.18,1808.22,2065.26\right)\end{array}$

4. 模型检验

Table 2. GM (1,1) model test table

Table 3. Fitting accuracy of GM(1,1) prediction model

Table 4. Predicted value of total health expenditure and financing structure in Shanghai from 2018 to 2027

5. 上海市卫生总费用的影响因素关联度分析

5.1. 指标的确定

Table 5. Index classification of total health expenditure in Shanghai

5.2. 指标相关情况

Table 6. Original data of total health expenditure and influencing factors in Shanghai from 2010 to 2017

5.3. 灰色关联分析

5.3.1. 初值化处理

Table 7. Initial value processing results

5.3.2. 求差数列找最大最小值

Table 8. Difference sequence results

5.3.3. 关联系数计算

${\xi }_{ij}\left(t\right)=\frac{{\Delta }_{\mathrm{min}}+k{\Delta }_{\mathrm{max}}}{{\Delta }_{ij}\left(t\right)+{\Delta }_{\mathrm{max}}},\text{\hspace{0.17em}}t=1,2,3,\cdots ,M$ (1)

(1)式中， ${\xi }_{ij}\left(t\right)$ 为因素 ${X}_{j}$${X}_{i}$ 在t时刻的关联系数， ${\Delta }_{ij}\left(t\right)=|{X}_{i}\left(t\right)-{X}_{j}\left(t\right)|$${\Delta }_{\mathrm{max}}=\mathrm{max}\mathrm{max}{\Delta }_{ij}\left(t\right)$${\Delta }_{\mathrm{min}}=\mathrm{min}\mathrm{min}{\Delta }_{ij}\left(t\right)$，k为介于[0, 1]区间上的灰数。 ${\Delta }_{ij}\left(t\right)$ 的最小值是 ${\Delta }_{\text{min}}$，当它取最小值0时，关联系数 ${\xi }_{ij}\left(t\right)$ 取最大值 $\mathrm{max}{\xi }_{ij}\left(t\right)=1$

$\frac{\text{1}}{\text{2}}\left(\text{1}+\frac{{\Delta }_{\mathrm{min}}}{{\Delta }_{\mathrm{max}}}\right)\le {\xi }_{ij}\left(t\right)\le 1$ (2)

Table 9. Correlation coefficients of comparison series to reference series

Table 10. Ranking of grey correlation degree of comparison sequence to reference sequence

6. 结论

6.1. 卫生总费用与筹资结构的预测结果分析

2018~2027十年内，上海市卫生总费用稳步增长，同时上海市卫生总费用的增长速率多年前就已经高于GDP增速，卫生总费用占GDP的比重也逐年上升，一方面，一个国家或地区卫生总费用占GDP的比重可以反映其对卫生工作的支持力度和对人民健康的重视程度 [12]。因此上海市卫生总费用上升意味着上海市政府高度重视卫生事业的发展和人民健康程度，上海市医疗卫生事业蓬勃发展，另一方面，卫生总费用占GDP比重过快增长，会进一步推高财政赤字和债务水平 [13]。对地区经济产生不利影响，因此上海市在发展医疗卫生事业的过程中，应采取措施控制医疗费用的过快增长，把医疗费用增长速度控制在合理的范围之内。只有增长速度在合理区间内上升，才能保证满足居民的合理卫生需求，使得医疗卫生事业实现持续协调发展 [3]。

6.2. 影响因素的关联度结果分析

6.2.1. 经济发展和居民卫生消费是影响上海市卫生总费用的主要因素

6.2.2. 人口因素对卫生总费用的影响

6.2.3. 卫生资源因素和对卫生总费用的影响

6.2.4. 政策因素对卫生总费用的影响

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