2040 MATTERS

Model 1.0

The rationale for California’s extraordinary stay at home order is to ensure that the number of COVID-19 cases requiring hospitalization does not overwhelm the capacity of the healthcare system. This raises a number of modeling questions:

1. What data do we need to model hospital capacity during the COVID-19 pandemic?
2. When would the State have reached healthcare capacity if the stay at home order had not been issued?
3. Could we have reached healthcare capacity under the public health measures put in place before the statewide stay at home order?
4. What will happen to healthcare capacity under the stay at home order? If we do not reach full capacity, how much unused capacity will we have?

The State has not yet answered these questions. As a result, we have no way of assessing the success of the stay at home order. The government, in effect, is telling us that it “will know success when it sees it.” We should strive for something more objective and timely. As the analysis below makes clear, we should be able to demonstrate by April 6th whether we have sufficient healthcare capacity, and I am increasingly confident the answer will be that we do.

This Post provides one methodology for answering these critical questions (based on my experience as the founder and CEO of a successful applied analytics firm and a baseball analytics nerd). It then summarizes the results of a few healthcare capacity models to help the public understand the pressure our healthcare system may (or may not) be under in the next three-to-four weeks.

It is important to note at the outset that the emphasis in the media on total confirmed cases and total number of beds does not provide much insight into healthcare system capacity. This is because confirmed cases may not require hospitalization and, for those that do, new hospital admissions will be partially offset by patient discharges over the course of the pandemic. In addition, there is a substantial backlog in test reporting and, to make matters more complicated for modeling, it appears that many of the unreported tests were likely negative (i.e., there is selection bias in reporting results). We also do not know the precise lag between testing and reporting. We need to build a “flow” model with many assumptions until the government improves its reporting and we have more reliable data.

It is also important to note that this is a statewide model. I recognize that localities may face very different circumstances regarding confirmed cases and hospitalization rates (e.g., Santa Clara vs. Santa Barbara). For this reason, municipalities and counties should be performing their own modeling using their local data.

So with these key points in mind, how do we make sense of the trajectory of the pandemic and its potential impact on healthcare capacity in our State?

1. What data do we need to model hospital capacity during the COVID-19 pandemic?

Governor Newsom initially stated we needed 20,000 dedicated hospital beds to handle the COVID-19 pandemic. In his most recent comments on this topic, he stated that we needed 50,000 hospital beds. For the purpose of my modeling, I am going to assess whether 20,000 hospital beds – devoted solely to COVID-19 patients – is sufficient to withstand the pandemic.

In order to build a model, I need to make a number of assumptions (which may be revised as actual data are reported):

• We do, in fact, have 20,000 beds across the State that can be devoted to COVID-19 cases. (Another modeling effort estimated 22,800 were available). If we actually have fewer beds, this will obviously reduce our capacity. As I have written previously, I would like the State to confirm its actual bed capacity for COVID-19 cases (while simultaneously meeting the needs of all other candidates for hospitalization) and begin reporting on daily COVID-19 hospital admissions across the State.
• Modeling normal hospital beds is the core capacity issue. I am not modeling normal hospital beds vs. ICU beds. To do so would require even more data from the State.
• The hospitals are fully resourced and staffed. Thus, we can utilize all necessary beds indefinitely (in theory). If we are under-resourced and cannot use all the beds we have, then our capacity will be less than total beds.
• The 20,000 beds reflect all the capacity gained through social distancing, which should substantially curtail the transmission of other communicable diseases and thus free-up bed space that would have otherwise been needed to treat these diseases. If this has not been taken into account, then our actual capacity may be higher. (I could not determine whether other models are accounting for this possibility). I would like the State to report on this as well. This is just one of the many reasons I have previously called on the State to release its model for peer review.
• The average duration of a hospital stay is 11 days. This is an estimate. There is limited data on this issue, despite the fact that it is central to accurate modeling. The longer the average duration, the less capacity we have (and vice-versa). (Another model suggests 12 days). I picked 11. The model will be revised if there is sufficient public evidence to calculate a more accurate average.
• There will not be any therapeutics available between now and April 17th to reduce the hospitalization rate and/or shorten the average hospital stay. If successful therapeutics are introduced during this window, this will substantially increase hospital capacity and the model will need to be updated.
• This a model for calculating bed capacity – how many daily hospital admissions can we handle in California. It is not a model for the actual spread of the virus.
• The key challenge for running the model is estimating the number of hospital beds being used by COVID-19 patients on Day 1 in the absence of any reporting on this by the State.
• Testing data may be of limited value in developing the model, even using a number of assumptions:
  • Testing continues to be administered primarily to people who are symptomatic and does not extend to random sampling or widespread community testing before April 17th. If the testing rate increases dramatically outside the symptomatic population during this time, then hospitalization rates for confirmed cases will decrease dramatically and the model will need to be revised to address changes in the relationship between these two data elements.
  • The testing backlog (which currently stands at roughly 48,600) will be cleared over the next 15 days and then testing and reporting will be timely. This is critical for aligning model results with State reporting.
    o There is selection bias in the testing backlog – test providers have reportedly delayed reporting negative test results. I am estimating the positive test results in the current backlog to be 1800 (4%), well below the positive rate on reported tests, which is trending upward toward 16%.
    o These 1800 positives will be included in my model between 3/26 – 3/30 on the assumption that if the symptoms of those already tested become serious, they will seek hospitalization during this window. (Note: The lag in testing later caused the State to create a reporting category for these admissions – suspected COVID-19 hospitalizations). If confirmed positives increase by more than this amount, I will update my model.
  • There are virtually no false positives (which would erroneously reduce the hospitalization rate) and virtually no false negatives (which would erroneously increase the hospitalization rate).
• The hospitalization rate for confirmed positives is at least 12% according to a CDC preliminary CDC report from March 18th. I performed a survey of 9 counties in California. It shows that the average hospitalization rate is 20% (skewed by Santa Clara County) and the median is 14%. I assumed 14% in my model for purposes of estimating new daily hospitalizations at the outset. If there is sufficient public evidence that a different number should be used, then the model will be revised (to reflect a different starting point).
• Based on the above and limited reporting on hospitalizations, I am estimating 61 new daily hospitalizations across the State on March 24th. This is the starting point for my model. If the State starts reporting the actual number of new daily hospitalizations, I will update the model accordingly.

A few caveats before getting to the models:

• Normally I would test a model before publishing it, but I do not have the data needed to test nor the time to devise a creative work-around.
• The model could undoubtedly be more precise if I had more time:
  o I believe that total bed capacity will not be the problem in California; rather, it will be bed location (the State will have unused capacity in certain areas and insufficient bed numbers in others).
  o Normally when working on a business process model, I would interview experts in the business process. Interviewing medical professionals at this stage of the pandemic is simply not possible. Armed with more business process data, I could potentially develop a more precise model for hospital admissions and ICU stays and the associated capacity constraints. But then I would still run into the data challenges noted above. This level of precision may also be unnecessary. My modeling shows the State has ample capacity.
  o I am sure there is a lag between a positive test and a hospital admission in many instances. But I do not have any data on this issue, so my model effectively assumes none for this admission category. What this means for the model is that hospital admissions could increase for a few days at the end of the model period even though confirmed positive cases have stabilized. We may see this in the data. If I can calculate the lag, I will adjust my model.
• Models are meant to be iterative. This is version 1.0.

2. When would the State have reached healthcare capacity if the stay at home order had not been issued?

To answer this question, we need to make two more assumptions:

• Assumption 1: The number of hospitalizations would increase by 1.3x per day. This rate roughly corresponds to the estimates of the unchecked rate of virus spread (number of infected roughly doubles every three to four days). Or,
• Assumption 2: The number of hospitalizations would increase by 1.2x per day. This rate roughly corresponds to the rate of increase that would likely occur if California simply froze its State and Local public health measures on March 18th and made no further changes in public health policy.
  o Critically, once the measures reached maximum effectiveness after roughly 14 days, the curve would be flat as long as those measures were maintained. This does not mean the number of new cases each day will be precisely identical, but rather that the numbers would fall within a narrow range. This type of “flattened curve” is starting to appear in the daily new case totals in Italy (I haven’t had time to look for hospitalization totals by day in Italy), which are falling within a fairly narrow range of their average of 5400 new cases per day. Put simply, I am assuming it is possible to flatten the curve hospital admissions curve.

Under Assumption 1:

With the unchecked rate of spread, the California healthcare system would have reached maximum capacity on April 10th. With 35,000 beds, we would reach capacity two days later.

In this scenario, once reaching maximum capacity, the healthcare system would have been unable to provide hospital beds for many COVID-19 cases requiring hospitalization. This capacity crisis would have lasted for the foreseeable future. This is the outcome that the State sought to avoid by issuing the statewide stay at home order on March 19th.

Thus, there is no question the State and Local governments needed to act to prevent the unchecked spread of COVID-19 in order to flatten the curve. Without action, the outbreak would have overwhelmed the healthcare system. This is clear from the data. The question is whether the State needed to adopt a statewide stay at home order to achieve this goal.

Under Assumption 2:

In this scenario, the State did not need to issue the statewide stay at home order. With the March 18th public health measures frozen in place, the California healthcare system would never have reached its maximum capacity for responding to COVID-19. We would have needed roughly 7,300 beds to handle the outbreak indefinitely under this scenario. (Reminder: This is at the State level; localities may be different).

This finding is crucial for assessing our policy options going forward. By April 4th – April 6th we should know whether and to what extent the pre-March 19th State and Local measures flattened the curve. If they did, the State should have substantial flexibility to lift the stay at home order and adopt more narrowly tailored public health measures to manage the outbreak.

3. Could we have reached healthcare capacity under the public health measures put in place before the statewide stay at home order?

Yes, but these conditions would require substantially changing the assumptions made above:

• Increase the initial hospitalization rate for confirmed cases to 20% (rather than 14%) for Day 1

Under the pre-March 19th public health measures, if the hospitalization rate were 20% of all confirmed cases on Day 1, the healthcare system would never exceed capacity. We would need roughly 10,400 beds to handle the outbreak indefinitely while the measures were in place.

• In addition to the assumption above, increase the average duration of a hospital stay to 12 days

Under the pre-March 19th public health measures, the healthcare system would never exceed capacity. We would need roughly 11,300 beds to handle the outbreak indefinitely while the measures were in place.

• In addition to both of the assumptions above, increase the rate of hospitalizations from 1.2x/day to 1.24x/day before flattening the curve

Under the pre-March 19th public health measures, with the three assumptions made above, the healthcare system would never exceed capacity. We would need roughly 17,300 beds to handle the outbreak indefinitely while the measures were in place.

• In addition to all of the above assumptions, assume the curve temporarily flattens for 10 days before starting to rise again, gradually

Under these assumptions, the healthcare system would run out of capacity on April 19th. (Of course, with additional beds, this analysis would be different).

4. What will happen to healthcare capacity under the stay at home order? If we do not reach full capacity, how much unused capacity will we have?

Although the data will reveal the effectiveness of the pre-March 19th public health measures, those measures were replaced by the statewide stay at home order. The key question facing us today, therefore, is: What will happen to our healthcare capacity under this order?

To answer this question, we need to make an assumption about how effective the stay at home order will be when compared to the pre-March 19th measures that were in place.

• My model conservatively assumes the stay at home order reduces the rate of spread/hospitalizations by an additional 10%

In this scenario, the healthcare system will never reach system capacity while the stay at home order is in effect. We will need roughly 6,300 beds to handle the outbreak during this period, creating unused capacity of roughly 13,700 beds.

I will refer to this as “Model 1.0” or the “March 26th Model” to distinguish it from any updated models going forward.

If my model is accurate, it does not mean that the State could abandon all public health measures on April 16th. If the State adopted this approach, the virus would begin to spread rapidly again, imperiling system capacity in a short period of time.

But the State would have the ability to start implementing less disruptive public health measures while preserving system capacity. The impacts of less disruptive measures would need to be modeled and then monitored once implemented to ensure ongoing system capacity. We will have clues in the data from March 22nd to April 6th to help guide this effort. I am confident that with the right data surveillance and reporting, this could be managed effectively through regular modeling updates and incremental policy changes.

Conclusions

The key question we face today as a State is whether 20,000 hospital beds constitute the healthcare capacity we need to withstand the COVID-19 outbreak. As of March 26th, the answer is: “We probably have enough hospital beds, but it depends on your assumptions.”

Had we done nothing to manage the outbreak, the answer would be “no.”

But we have taken many steps to curb the outbreak and we now need to see how those steps translate into hospitalizations and average duration of hospital stays. If the State collects and reports data on these variables, we should know by April 3rd through April 6th whether we have sufficient system capacity. I believe we do.

Of course, if the State increases the number of beds that can be dedicated to COVID-19 to an amount above 20,000, and if those beds can be resourced and staffed, then my qualified “probably” would become something more like a “quite likely or almost certainly.”

What do we do now?

Based on my modeling, my advice to the government today is simple: Collect and publish the data we need to build more precise models and assess the success of public health measures. Plan for success. Begin modeling less disruptive approaches to flattening the curve so that we can begin returning to more normal life as early as April 17th.

My advice to the public at this time is simple as well: Do not assume that our healthcare system will be overrun. It will have ample capacity under a wide array of realistic assumptions. Do your part to maximize the chances it will not be – comply with the stay at home order. Starting on April 3rd, pay very close attention to the data. We should know by April 6th how well the stay at home order is working. If it is succeeding, you should call your elected officials and insist that they lift the stay at home order and replace it with more carefully tailored public health measures that will manage the pandemic while we gradually return to normal life.

Until then: Be smart. Stay healthy.

KEY UPDATE: Please note that this model has been superseded by Models 3.0 and 3.1. Please review those models for my latest predictions. With the State now reporting hospitalization data it may be possible to track performance in the next several days.

Updated April 2, 5, and 6.