In the very challenging economic conditions in which businesses operate nowadays, it is vital that executives make the right decisions. The use of analytic tools is crucial for these modern companies. Using past data helps a company forecast:
- how profitable an emerging market is,
- how the currency might change, or
- the risk of a financial breakdown.
Making the best decisions means not only using the available data and the right model, but also understanding its implications and limitations. Then, companies can take the risks that could lead them to them the best possible outcomes. Analytic tools help companies when they are dealing with delicate decisions, for example, when signing a contract with another company, or when they need to decide where to open a new store.
One of the markets that has risk is the health system: Talking about health also means talking about risks and money. For an insurance company, a customer might represent a profitable business when the customer makes no or just a small amount of claims, but if the customer requires special treatment it could result in a huge cost for the company. Although it may be unpopular to say, insurance companies are always placing a bet in favour of their customers’ health.
How does a health insurance company work?
Health insurance companies receive money from their members, who in exchange can be treated for their conditions in any of the hospitals that the company recognises. When a patient is admitted into a hospital and receives treatment, the insurance company pays the hospital for every procedure carried out, according to a set of pre-contracted prices. It is therefore vital for the insurance company to have good price agreements with the hospitals in order not to incur excessive costs.
When an agreement with a hospital comes to a contractual end (it expires), the hospital and the insurance company enter into a negotiation and work together to find a new agreement for the coming years. Sometimes hospitals can leverage their quality or strategic geographical position to get very favourable deals, giving insurance companies a difficult decision: do they accept the hospital’s new conditions (and close a possibly unfruitful deal) or do they derecognise the hospital and stop working with them? In the past, this decision was often made based only on the perception or the feelings of the managers, whereas now a new analytical methodology has been introduced that helps insurance managers have a clearer picture of the consequences of their decision, and hence make the best choice.
Derecognising a hospital
Derecognising a hospital has two main side effects that need analysing:
- What is the impact on members?
- What is the impact on other hospitals?
The first question asks how important a particular hospital is in its geographical area. What would be the impact of derecognising that hospital in terms of their users? In order to learn this, the company measures what percentage of medical procedures would still be available for its members if a hospital were derecognised. If the hospitals in the surrounding area (usually considered within a 30-minute drive) can perform the same medical procedures as the hospital under consideration, then it is deemed as being not vital for their insurance system.
If a hospital stops being available for members, the insurance company provides a list of nearby alternative hospitals. Management then need to forecast how exactly patients will redistribute themselves.
Once the forecast has been produced, the management will whether the alternative sites have enough capacity to deal with the upcoming volume of visits; if this check has a positive outcome then the hospital can be derecognised.
The forecasting methodology
In order to forecast which hospital the members will likely end up visiting, a simple methodology has been developed. It assumes that the members are more likely to visit bigger hospitals than smaller ones, where the size of a hospital is measured by the number of members that visit a particular hospital, that is, the market share. The probability of a member visiting hospital A is estimated simply as the market share of that hospital in the area that lies within 30 minutes of the derecognised hospital. These probabilities can then be used to predict how many members each alternative hospital will end up receiving.
For example, let’s suppose that the management is considering to derecognise a hospital with 100 members. In the 30-minute area around that hospital, the members have to choose between three alternative hospitals: A, B and C, where A holds 40% of the market share, hospital B holds 10% of the market share and hospital C holds 50% of the market share. According to the model, we forecast that the number of members going to hospital A is $100 \times 0.4 = 40$, and similarly we forecast 10 members going to hospital B and 50 to hospital C. If hospital A is able to handle those 40 new members, hospital B is able to handle 10 new members and hospital C is able to handle 50 new members, the insurance managers can safely assume that the surrounding hospitals will be able to handle the redirected volumes.
Thanks to this simple methodology, the management has a quantitative tool that helps the company make decisions based on actual measurements. If they decide to derecognise a particular hospital, they might save money by not going through with a bad deal, plus they might improve their relationship with the alternative hospitals, as these are receiving more patients and hence more money. Alternatively, if they decide to accept the negotiation with that hospital, then they know they are making the right decision for the coming years.
You might also like…
- Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
- Modelling a Saturday afternoon on Oxford Street
- Nira Chamberlain, one of the UK's top 100 scientists, shares his experiences as a black mathematician.
- Our first interview celebrating Black Mathematician Month
- A summer essential or an embarrassment risk on the streets of Ibiza?
- How to win a game when your expected score is 0