In his excellent book on the importance of understanding uncertainty titled The Flaw of Averages, Sam Savage introduces the key notion that “plans based on average assumptions are wrong on average.” A current example of this in practice is Intensive Care Unit capacity in Florida. The governor of Florida recently stated that there was excess ICU capacity in the state since only 80% of the ICU beds are now occupied. However, this is an average. Some hospitals in larger and more populous counties have more capacity than smaller, less populated ones. An excess in a large hospital does not offset a smaller hospital in a far away hospital that is maxed out.
I recently spoke to Sam Savage and he encouraged me to look at his SIP Math standard. Sam is the head of Probability Management, a nonprofit organization that promotes the use of simulations in project management. You can download a free add-in and do your own simulations in Excel from https://www.probabilitymanagement.org/tools.
I implemented a simple simulation using SIP Math that shows how even though there may be excess average capacity among multiple hospitals, it is still possible to max out capacity in one hospital. As a simplex example, suppose there are two hospitals. One has 10 ICU beds and the other has 40, for a total of 50. Further assume that if ICU capacity used is a random variable, and is proportionally distributed between the two. The smaller hospital is likely to have fewer people in their ICU than the larger one. However, as this is not a single number, this can vary. For example, if 80% of ICU capacity is used, there are 40 people total who need to be placed in an ICU. On average, 40*.2 = 8 people will need ICU beds in the smaller hospital, and 40*.8 = 32 will need ICU beds in the larger hospital. But there is variation around these averages. If the split is instead that 16 people need ICU beds in the smaller hospital and 24 need beds in the larger hospital, there will be six people who will not be able to be placed in the ICU in the smaller hospital because the capacity of the smaller hospital is exceeded. Exceeding ICU capacity is one of the worst possible outcomes, as it is likely to increase the mortality rate from the virus if the health care system is overwhelmed.
I modeled this scenario using SIP Math, and found that for this simple example, ICU capacity becomes an issue when the ICU capacity used is greater than 60%. See the graph below for a comparison of the chance that ICU capacity will be exceeded in at least one hospital as a function of ICU capacity.
From the graph, you can see that when the ICU capacity is 80%, the chance that ICU capacity will be exceeded is 16%. This is a simple example, but it makes the point that just because their is some unused average capacity individual hospitals may still have exceeded their capacity and are not able to care for critically ill patients. According to this interactive map, there are 23 counties now in Florida with no ICU beds available.
For those interested, I have attached the Excel spreadsheet I used to do the simulations. You do not need SIP Math to open the file or see the results, as SIP Math makes ingenious use of Excel’s Data Tables to output simulations in native Excel. Click the link below to download the spreadsheet:
https://christianbsmart.com/wp-content/uploads/2020/07/ICU-Capacity-Example-with-SIP-Math-3.xlsx