I’m fascinated by churn and its implications right now. I want to propose the skeleton of a bare-bones churn prediction model. This will be incomplete and there will be some massive black boxes where an input and process will be assumed to have occurred without details.
Let us start with the simplest model with incredibly restrictive and unrealistic assumptions. We will build towards complexity and veracity.
Let us assume that each individual on Exchange in Time 0 will stay on Exchange in Time 1. Let us also assume that the initial selection in Time is “optimal”Let us also assume that there is only two companies so the decision is switch or stay. Let us also assume that there is a single product offered by each company. Let us assume the price offered for each product to each individual is constant and independent of the choices of other individuals in the market. Let’s assume cost sharing is a function of total medical spending. Let us also assume that the switch is frictionless. Finally, let us assume that each individual is 100% certain about what their future period health costs will be. The optimization problem we are trying to solve then is a cost minimization problem where the cost is premium plus cost sharing.
That gives us the following logic for each individual insured by Company A in Period 0:
IF Total Cost A1 is less than Total Cost B1 then stay else switch.
This would be a completely unsticky market where everyone is buying on price alone as there is no insurance functionality.
That is not what we see. This model is absurdly too simple. Let’s start peeling back some assumptions.
Let’s assume that people have a probability distribution of future costs. There is uncertainty. That uncertainty is a function of not knowing if you will be hit by a bus in the first day of Time 1, there is uncertainty about if and when you will get diagnosed with cancer. This is where the product changes from a discount club card to an insurance product as we begin to deal with future uncertainty.
So the decision process now becomes a bit more complex.
IF Premium A1+expected cost sharing A1 is less than Premium B1+expected cost sharing B1 then stay else switch
Now how do we figure out what future costs could look like and the individual probability distribution is appropriate.
My personal probability distribution is different than the probability distribution of a 23 year All American distance runner. It is certainly different than that of a 28 year old who has been having knock me up sex for the past three months. It is very different than the distribution for my parents.
We’ll make the assumption that people who were expensive in the past will probably be expensive in the future. But then we’ll need to make an assumption that there are differences in cost sharing. Some people have expensive chronic conditions while others just have cats that try to kill them on an ad-hoc basis. Now the equation starts to look like the following:
IF Premium A1 + Cost sharing (which is a function of previous Acute costs + another function of previous chronic condition costs times some multiplier for age)A1 is less than Premium b1 + Cost sharing (which is a function of previous Acute costs + another function of previous chronic condition costs times some multiplier for age)B1 then stay else switch
But switching is not frictionless. Medical records need to be transferred, authorizations and procedures need to be learned. The cost is a variable cost. An individual who has no claims in their entire membership span with Company A has an equal cost of learning Company A’s way of doing things and learning Company B’s way of doing things. An individual who sees a doctor every week with frequent prescriptions and at least annual in-patient admissions will have spent a lot of time and energy learning how to navigate Company A. Going forward the learning costs are far lower if that individual stays with Company A rather than switches to Company B. So far this is overwhelmingly a function of medical risk; individuals with higher medical risk will tend to have developped a stickiness/friction against sticking while minimal utilizers will not have any adhesion to Insurer A.
Networks also need to be compared as part of the frictional costs of transferring. Healthy people will have minimal relationships with their providers. They might have an annual primary care provider appointment, women might have an annual Ob/Gyn appointment and perhaps a few urgent care or physical rehab appointments every few years. There is a minimal relationship at the rendering provider level and the other common services (UC and PT) there is no interpersonal relationship established. However an individual with significant health concerns will have routines and relationships that are valuable to maintain. They’ll hopefully have a PCP that listens to them, they’ll have a cardiologist whose staff knows what a “personal” normal looks like, they’ll have the hematological clinic in-network and nearby. Those are very valuable items to someone managing complex conditions.
If the networks between A and B are identical, there is no network costs. However once some providers are in A but not in B, switching costs rise for people who currently see the in-A not B providers. These costs are very low for the very healthy and could be quite high for people with chronic conditions. Now we get an equation that looks like this:
IF Premium A1 + Cost sharing (which is a function of previous Acute costs + another function of previous chronic condition costs times some multiplier for age)A1 +Costs(Administrative switching as a function of age and health) +costs(network switching as a function of health, geography and probability of providers being in A not B) is less than Costs (B total) then stay in A else go to B.
Finally, still working with the assumption that the selection of Plan A in the first time period was optimal, there is an option value of the network that Plan A had assembled that is unique compared to Plan B. For instance a 29 year old woman who intended to get pregnant in Time Period 0, would see a great amount of value in having a leading Ob/Gyn hospital in network just in case her potential pregnancy went bad. Now if she had the baby and had her tubes tied at the same time in Time Period 0, the value of the Ob/Gyn hospital as a unique selling feature for Time Period 1 goes down dramatically. The same logic applies to a professional pitcher with a nasty curve ball. He wants the best Tommy John’s orthopedic surgeons in network during his playing career. The day after he retires, the option to see those specialists is far less valuable to him.
The same applies to cancer centers and any other high end acute specialty hospitals and specialists.
IF Premium A1 + Cost sharing (which is a function of previous Acute costs + another function of previous chronic condition costs times some multiplier for age)A1 +Costs(Administrative switching as a function of age and health) +costs(network switching as a function of health, geography and probability of providers being in A not B) is less than Costs (B total)+Net Option Value of Network of A then stay in A
From here aggregate cost profiles and estimate net losses. If there is perfect information about members covered by Insurer B, then a mirror image inflow model could be run as well.
I think this is a workable framework that is still absurdly simplistic as it assumes no leakage or inflows from other types of insurance. It assumes only two competitors, it assumes very good information at very low costs, it assumes clear plan designs so people can accurately project their future net costs. This is still absurdly simple.
But I think it is a start of something.