Health Insurance Pool Example

Let's complicate the previous example a bit by making the model more accurate and use it to calculate how much it will cost to provide medical coverage for a pool of 100 people.

Just as before, 20% of the healthy people become sick in any given year. However, you have observed that young people tend to be more likely to recover than do old people. So, rather than assume 25% of all sick people die, you will use the following equation to represent the probability of dying:

P=1.0035^Age-1

To simplify the application of this equation, assume that all 100 people are newborns. That way, everyone is always the same age and their age is the same as the stage number.

The results for this model will be similar to those for the last model. However, one of the probabilities is variable.

Now, let's assume that health coverage costs $500 per year for each healthy person and $4,000 for each sick person. You can reflect this in the model by creating a new root node with the definition

Annual Cost:=(Root,500*Healthy+4000*Sick)

Annual Cost performs two steps: First, it evaluates Root, causing the Markov model to progress to the next stage, and then it uses the results of the stage simulation to calculate the medical costs for that year.

What you really want is to know is the NPV of costs over all stages. To do this you need to add two additional nodes as follows:

Present Value:=npv(10%,Cash Flow)

Cash Flow:=(clear,makelist((reset,Annual Cost),n,0,100))

Cash Flow resets the model (clear) then evaluates Annual Cost 101 times. This results in a list of 101 cash flow values. Finally, Present Value performs a simple NPV calculation.