The Fish Doctor’s Fallacy on Improving Population Health Management

Pretend for a moment that you are in ichthyologist, a fish doctor. And your job is to manage the health of tens of thousands of fish in a very large pond, the same job that your colleague had last year.  To accomplish your task, each week you come to the pond Monday through Friday—ichthyologists are in a union and they do not work weekends. And each day you capture and evaluate the health of one hundred fish at random, examining the same fish each day that week.  You find a variety of fish ailments among the fish you examine, and you treat each fish according to its needs.  Over the course of a year you may examine and treat some of the same fish more than once.

Over fifty weeks—you get a two week vacation—you have examined and treated five thousand fish.

Let us examine the question of whether or not your approach to managing the health of the fish in the pond worked.  How can one determine how well have you done your job? If there was a scale to manage the effectiveness of your approach, at one extreme would be that examine the health of all of the fish at the end of the year and record that on average the fish were healthier than they were a year ago. At the other extreme, you would come back at the end of the year and find that all of the fish were doing the backstroke.

Your approach relies on that belief that examining and treating a given fish over a single weeks’ time will give you the information you need to ensure that that fish will be healthy throughout the year.

Your approach also relies on the belief that examining and treating only five thousand of the tens of thousands of fish over the course of a year will give you the information you need to ensure that the average level of health of the fish in the pond will be better than it was last year.

If it sounds simple, that is because it is—too simple.  Too simple to be effective.

I used to be a mathematician; I know that is difficult to believe.  I have forgotten most of what I learned, but I retained just enough to be a boorish hit at parties.  There is something called the Law of Large Numbers. It is used in probability theory. In principle, it describes the result of performing the same experiment a large number of times. In theory, the average of the results should be close to the expected value.  The more trials you perform, the closer you should expect to be to the expected value. Using a large number of trials should result in stable long-term results for the average of these random events.

The Law of Large Numbers has value in the population involved in your experience is too large to run the experiment on the entire population.

As an example of an experiment, think about predicting whether the flip of a coin will result in a head or a tail.  The probability of tossing either a head or a tail is ½.  The probability of tossing five heads in a row is 1/32. There is something called the Gambler’s Fallacy which works as follows.  Most people, who saw the coin come up heads five times in a row would bet that the next toss of the coin would be tails.  Most people would be wrong since there is still a fifty-fifty chance that the next toss will be either a head or a tail.

The Law of Large Numbers also relies on the fact that the trials, the sample data, will asymptotically—I can’t believe I spelled that correctly—approach the expected result.

The converse to the Law of Large Numbers is the Law of Small Numbers, also known as a Hasty Generalization, and the Pigeonhole Principle. Hasty generalization’s fatal flaw is that it relies much more heavily on the belief of the expected outcome than it does on the sample size of the experiment of the population being investigated.  The false belief that was created before the process began that the trials will yield the expected outcome adds a bias that invalidates the approach.

Someone asked me why I think Patient Access/Customer Experience (PACE) plays a vital role in the success or failure of Population Health Management (PHM).

I have spoken with several hospital executives about their efforts to effectively implement a program of PHM.  Some of their names would be familiar to you.  This is what I learned from them about what they are doing.

They believe that the success of their efforts is tied to the amount and quality of the data they can collect on the people who visit the hospital, patients.  Some hospitals even collect data a few days before the person comes to the hospital and for a few days after the person leaves the hospital.

They believe the data do two things for them; manage the health of a given patient over time, and use that person’s data, in conjunction with similar data from other people with similar health problems to foretell the needs and manage the health of that group of people over time.  Lastly, the information from various patient groups could then used to glean the needs and improve the health of the population as a whole.

Ichthyology and Hasty generalization.

  1. Can my health be managed based only on data collected when I am in the hospital?
  2. Is there any data to manage my health if I do not come to the hospital?
  3. Can this approach be effective for managing the health of an entire population?

There is a solution to the problem of the Law of Small Numbers, and fortunately the solution does not require having the entire population at the hospital every day of the year.

What is the alternative to having the success of PHM rely solely on having the hospital capture data on everyone every day of the year?  Why not have the hospital manage data, and draw inference from data that the members of its population input? Why not create an interactive (2-way) vehicle that allows:

  • People to input data about their health:

o   Diet

o   Exercise

o   Adherence to medications

o   Weight

o   Pulse and blood pressure

o   Requests to speak with a nurse or doctor

o   Requests refills

  • Hospitals to monitor the health of an individual:

o   Correlate that data with similar individuals

o   Contact an individual when a person’s data is outside of expected boundaries

o   Send a physician or nurse to the person’s home

Under this type of a Patient Access/Customer Experience (PACE) tool hospitals are no longer limited to only collecting data for people only when they are in the hospital. Using this type of tool hospitals have more data about an individual, and have more data on more individuals.

This same tool can be used to decrease readmissions.  People want to be well, and allowing them to play an active part in communicating their health is a win for both parties.

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