Modeling: With the four metrics, we can simplify the healthcare system as in Figure 11.
M1
System
Resource
M2 M4
Input1 M3
Input2
Output1
Output2
Figure 11. Simplified U.S. healthcare system.
Suppose the initial evaluation vector is EV0 =
µres
0
per0, I0
∂ .
The quantity res0 is determined by M1 andM2, while M3 andM4 reflect the levels of per0 andI0, respectively.
SinceM1andM2are inputs of the system whileM3andM4are outputs, we can describe the system with two functions:
M3 = f (M1, M2), M4 = g(M1, M2).
Simplifying the Model
Important considerations are:
• Life expectancy (M3) is more sensitive to change in total expenditure on health (M1) than inequities (M4) is.
• Altering ratio of public expenditures to private (M2) produces a more sudden response in inequities (M4) than in life expectancy (M3).
Thus, the model can be simplified to two single-variable functions:
M3 = f (M1), M4 = g(M2).
Constructing the Functions M3, Life Expectancy.
The U.S. spends 15.4% of GDP on health, which is the highest percentage in the world. The input and output of its health system have reached saturation. Despite putting more resources into the system, we get little more output, which doesn’t match the high input.
For a health system, the growth rate is low when the input (expenditure) is too small or too large but high when the input is appropriate. So we choose the logistic model to describe the function forM3:
M3 = ab
b + (a − b) exp(−cM1).
The value of the function isbwhen the independent variable is 0, which stands for the HALE when a country spends none of its GDP on health. We use the HALE of year 1900 for the U.S., so we takeb = 47.3. The value of the function isawhen the independent variable goes to infinity, which stands for the saturation of HALE. The highest expectancy life now is about 78, thus we takea = 80. We use data from 2004 and getc = 0.201. Therefore,
M3 = 80 × 47.3
47.3 + (80 − 47.3) exp(−0.201M1). M4, Inequities.
In our opinion,M4 will decrease asM2(ratio of public to private expendi-ture) increases. For the sake of convenience, we select an inversely propor-tional function:
M4 = k M2
.
We use data from 2004 and getk = 0.548. Therefore, M4 = 0.548
M2
.
Putting Forward Measures
We consider several measures that alter one of the two inputs or both.
Accordingly, the two outputs vary.
1. Altering the ratio of government expenditure on health to private expen-diture. In the U.S. system, the main use of government expenditure on
health is to improve the health level of low-income people. Altering this can change the level of inequity.
2. Limiting the rise of total expenditure on health as percentage of GDP to make it constant at an acceptable level. Though there is a sharp increase of total expenditure on health as percentage of GDP, the health level doesn’t improve much. That is to say, it has reached a saturation point.
3. Limiting the items and the extension of public insurance. In the existing system, public insurance covers a lot of items, some of which may be unnecessary.
4. Increasing the coverage of public insurance.
5. Limiting strictly the use of new medicine, medical equipment, facilities, and medical technology. Research on these has cost too much, and some outcomes are not so important in improving the overall health level.
6. Regulating the cost of medicine.
7. Reducing excessive medical treatment.
8. Promoting positive competition between different hospitals to reduce the patient’s cost on medicine and medical treatment.
All these measures can be divided into three groups by their different effect on the inputs:
• Group A (affect onlyM1): Measures 2, 3, 5, 6, 7, 8
• Group B (affect onlyM2): Measure 1
• Group C (affect bothM1 andM2): Measure 4 Testing Various Changes
Maybe some measures can improve the healthcare system while others have the opposite effect. Therefore, we have to quantify how each kind of measure affects the system.
In Task 4, we got the evaluation vector for the U.S. In this Task, we takeM1andM2as the inputs of the system andM3andM4as the outputs.
Because we are analyzing only one country without comparing it to another, we can’t normalize the original data. If we calculate the vector as same as Task 4, it may lead to abnormal data. So it is necessary for us to modify the calculation method.
EV = (R, I) : R = M1
M3, I = 1 M2. So the initial evaluation vector of the U.S. is:
EV0 = (R0, I0) = (.206, .67).
• Measures in Group A can affect only the total expenditure on health as percentage of GDP (M1). Suppose that its initial value changes by 5%.
CalculatingM3 gives:
– If+5%: EV1 = (.214, .67).
– If−5%: EV1 = (.196, .67).
Hence, decreasing the total expenditure on health as percentage of GDP reasonably can improve the healthcare system of the U.S.
• The measure in Group B affects only the ratio of public expenditure to private (M2). Suppose that its initial value changes by 5%. Calculating M4 gives:
– If+5%: EV1 = (.206, .638).
– If−5%: EV1 = (.206, .705).
Hence, increasing the ratio of public expenditure to private can improve the healthcare system of the U.S.
• The measure in Group C affects bothM1andM2. Suppose that the initial values change by 5%. CalculatingM3andM4 gives:
– Case a: IfM1+ 5%andM2+ 5%: EV1 = (.214, .638).
– Case b: IfM1+ 5%andM2− 5%: EV1 = (.214, .705).
– Case c: IfM1 − 5%andM2+ 5%: EV1 = (.196, .638).
– Case d: IfM1− 5%andM2 − 5%: EV1 = (.196, .705).
Evidently Case c is the best and Case b is the worst.
The measure in Group C is coverage of public medical insurance.
Increasing it on the one hand increases total expenditure of GDP but on the other hand also increases the ratio of public expenditure to private.
So such an increase is similar to Case a.
Strengths and Weaknesses
We have built a model that reveal how the system works based on the four metrics that we created in Task 3. Its parts combine well. Also, it is easy and convenient to test the measures with the model. But there are some weakness when simplifying the model. A single-independent-variable function is not the best to describe a healthcare system.