COVID-19 Topic: Hospitalization Flow

cumulative flow diagram for Pima County hospitalization charts. Data source: Pima County

Here’s a topic I have written about in the distant past (March?) that is of high interest to me. I agree with the “flatten the curve” strategy if an area is in imminent danger of overrunning their capacity to hospitalize people. One challenge with the strategy, though, is that to do this effectively one needs to understand the “flow” of patients through a hospital system. The chart above (that I hand built using reports from Pima County located here) is a rough start at this. What is it?

Cumulative Flow Diagrams

I use cumulative flow diagrams often at work to understand how “value” flows across a process consisting of a number of steps into the “hands of the customer”. The best way to visualize this is to think of a factory with a number of assembly and test operations that a product flows across on its way to the customer. At each one of these operations, some set of unique actions takes place. These actions all take some amount of time and then the product moves to the next operation (the movement takes time too!). This is how we assemble something called a value stream map. This map is a supremely valuable thing because it allows us to understand what’s happening in the factory. Are the operations taking the correct amount of time? How many products (Work in Progress) are flowing in the factory? Are products stalling at one of the operation and creating a problem by backing up the factory? The cumulative flow diagram can give us a nice visualization of all this.

What can we see regarding Pima County Hospitalization from this Diagram

First, the only data we can measure about the “hospitalization flow process” comes in the reports of hospital admissions, deaths, and recoveries. In a sense, these are the “operations” in the value stream map. I agree with you that these are pretty crude measures to use to try to understand something as complex as the hospital network in a county. But apparently its all the county asks for. What would I want to measure in order to do a better job of understanding the flow through the hospitals?

How about these potential measures:

  1. Time/Day a person arrives at the hospital and checks in.
  2. Time/Day the person’s symptoms are reviewed and a disposition is made (send them home, refer them to a doctor, assign them a bed).
  3. Whether a person tests positive for COVID (we might filter this data on this field)
  4. Time/Day a person is assigned to a more specialized form of hospitalization (ICU? Other?)
  5. Time/Day a person is put on a ventilator/intubated?
  6. Time/Day the person is discharged from the hospital (Recovery)
  7. Time/Day of death if appropriate.

With the above, we could build Cumulative Flow Diagrams that could tell us an awful lot about why the COVID recovery rate is over two weeks. We would learn where most of the time is spent (the bottleneck). If one knows this information, then they can take measures to relieve the bottleneck (add new nurses, add beds, improve the check-in process, etc.). I have to believe that the hospital already has very detailed measures like the above for their internal purposes, but from the standpoint of a County or a State evaluating the state of their hospital networks, this approach could be a game changer.

What do We See in Pima County?

Even from these crude measures which I assembled by hand into this CFD chart, we can see a few things.

  1. The “Work in Progress”, i.e., number of COVID-19 hospitalized patients in the system right now appears to have grown during our current summer outbreak from about 700 in mid-June to about 930 right now. It isn’t clear where these people are in this system, because we have no information on ICU discharges.
  2. The “Cycle Time” of the COVID-19 treatment process in the hospital system appears to be about 21 days. I’ll show a CFD or two from some European countries next and we’ll see if that’s good or not. This is the measure of the horizontal line between admissions and recoveries+deaths. You can think of it this way, go to any point on the y-axis (I’m showing this from 1500 counts) and calculate how many days it took the 1500th individual to get admitted to leave the hospital system. Obviously this presents an average since we don’t know the disposition of individual cases, but essentially the time between the 1500th admission and the 1500th “departure” is around 21 days. Note that this is an improvement from around the 500th count where we can see the cycle time was 28 days. I presume this positive trend has a lot to do with the improvements in the efficiency of care at the hospitals, along with new, better treatments, etc.
  3. The slope of the Recovery line is roughly the same as the Admission line. This is not optimal because we want the cycle time to close. Once we see the slope of the Recovery line increase and become larger than Admissions, we have a good idea that either the cases are slowing or the hospitals are improving, or both.
  4. Remember that much of what we believe that we can learn from this chart could be bogus if the data collection is haphazard or if the data is wrong. All the more reason for taking this seriously.

Cumulative Flow Diagram for Germany

Here is what a very good CFD looks like for Germany, where data collection was prioritized. This is not exactly the same CFD as what I show for Pima County, because we don’t have good access through the John’s Hopkins data to hospitalization numbers. So instead of hospital admissions, this CFD shows confirmed cases. If we had the hospitalization data, it would be a line somewhere in between the orange and the green lines.

If you draw the horizontal line connecting the orange and green curves pretty much anywhere, you can see that the cycle time for “Case to Recovery” ranges from about 14 days (each vertical line is 2 days) to maybe 18 days. Compare this to the hospitalization cycle time for Pima County of about 21 days! Note how the number of active cases (the WIP) in Germany was well over 50K cases back in April but closed to maybe 1000 cases or so in recent months. One thing, though, that I’ll also point out is that the WIP has opened a bit in the last week. Note how the orange line is curving upwards and the green line isn’t? That’s a reminder that even when this pandemic seems under control, one needs to keep measuring and watching the trends to be able to take quick action.

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