Unexpectedly Intriguing!
28 October 2020

We've followed the state of Arizona's experience with the coronavirus pandemic since we first recognized the state had become a national hotspot for COVID-19 earlier this summer.

Early on, we employed an analytical method called 'back calculation' to trace changes in trends for the state's COVID data back to significant changes in the incidence of exposure to the SARS-CoV-2 coronavirus. The idea behind back calculation is pretty straightforward. If you know what the median time is from the initial onset of symptom to when someone who has become infected with a serious case is hospitalized, you use any significant changes you see in the trends for new hospital admissions to identify when something changed to affect the rate at which people are being exposed to the virus. Ideally, you can identify a very narrow window of time in which that happens.

Median Post-Exposure COVID-19 Coronavirus Milestones

This kind of analysis also works for data on positive COVID test results and deaths, but the data for hospital admissions works best because it is independent of the factors that affect when test kits are processed or when deaths are reported. It also provides the narrowest potential window of time to consider, the the median time between initial virus exposure and hospitalization falling somewhere between 11 and 13 days, according to the CDC's COVID-19 Pandemic Planning Scenarios.

Working with Arizona's COVID hospital admissions data has been challenging. Mainly that's because the data the state's Department of Health Services makes available is subject to human failings.

As an example, in the latter part of July 2020, Arizona began requiring non-hospital medical facilities to begin reporting their COVID data to the state, which was then incorporated in the statewide data. It shouldn't have been a big deal, but the new reporting suggested Arizona's COVID hospital admissions were far greater than previously released data had indicated. It also suggested that factors affecting changes in trends for hospitalizations were very different from what we were seeing for newly confirmed cases and deaths in the state.

Several weeks ago, Arizona's public health officials found and fixed the problem. It turned out that the number of positive test results collected at urgent care centers in the state were being counted as new hospital admissions, even though in nearly all these cases, the positive-testing patients were never hospitalized in any way. In between, back calculation using Arizona's hospitalization data was highly suspect because of the data corruption. Fortunately, we recognized the issue and worked around it to the greatest extent we could. But it was like not having access to the sharpest scalpel in a doctor's medical bag when you're trying to perform fine surgery.

We wondered if there was any hospital-related data that we could substitute for it, which would have been unaffected by the positive-test contamination issue. And then it struck us! Arizona's COVID data for ICU beds in use falls in an entirely separate category, so it had never been corrupted by the urgent care positive test result data. Here's that data in graphical form (please click here for a full-size version):

So we took Arizona's COVID-19 ICU Bed Usage data for a test drive, adapting our original method for new hospital admissions, and found that it worked nearly as well. The results of that test drive are shown in the following chart showing Arizona's daily COVID ICU admissions chart.

The ICU back calculation chart comes very close to delivering the accuracy we're really after. We think there's a slightly longer lag between initial exposure and ICU admission than there is to just hospital admission, so the predicted timing of changes in trend shown as the purple and green shaded vertical shaded bands in the chart following a significant event are slightly too early. We haven't yet found peer-reviewed data to quantify what that additional lag is, but the changes in trend

In this chart, we're showing two new events we haven't previously discussed that seem to correspond to changes in the overall trajectory for Arizona's COVID ICU admissions. The first, marked with the letter G, corresponds to the Labor Day holiday weekend, which followed the initial reopening of high-risk businesses (like bars and indoor gyms) in most Arizona counties a week earlier.

In this case, we think the impact of social mixing during the holiday weekend itself is responsible for causing the change from a falling to a flat trend. If it had just been the bars reopening, we would have seen the change in trend start a week earlier (we've ruled out other large scale events like the timing of school reopenings or political rallies in the state for similar reasons). We think that while the reopened bars may be tangentally involved as places where social mixing took place during the holiday weekend, they are not the primary contributor to the change in trend that occurred in ICU bed usage in mid-September.

The second change, marked with the letter H, may be partially related to reopened high exposure risk businesses in counties that have seen higher rates of infection within their populations in the weeks since. In this case, we think the delayed reopening of high exposure-risk businesses in Yuma and Greenlee counties on 17 September 2020 may have provided enough additional exposure events to change the trend in ICU hospitalizations from flat to a slowly rising, but steady trend.

Since it is not rising at an exponential rate, we consider the current overall trend to be managable. We think relatively minor steps short of shuttering the just reopened high exposure-risk businesses could be taken to modify the trend in a desirable direction. Those minor steps may include things like contact tracing and continued local ordinance-directed mask usage at public venues and events.

The worst case scenario however would be a repeat of the BLM/anti-police protests from late May and early June 2020, a true superspreader event that made contact tracing useless within the state. The protests took a very managable situation and instead made Arizona a national epicenter for coronavirus infections, amplifying the state's number of positive cases, hospital admissions, ICU bed usage, and deaths until the state implemented its decentralized approach to correct the adverse COVID-19 trend.

Welcome to the world of back calculation. It's easier when you have good data!

Previously on Political Calculations

Here's our previous Arizona coronavirus coverage, with a sampling of some of our other COVID analysis!


Arizona Department of Health Services. COVID-19 Data Dashboard. [Online Application/Database].

Maricopa County Coronavirus Disease (COVID-19). COVID-19 Data Archive. Maricopa County Daily Data Reports. [PDF Document Directory, Daily Dashboard].

Stephen A. Lauer, Kyra H. Grantz, Qifang Bi, Forrest K. Jones, Qulu Zheng, Hannah R. Meredith, Andrew S. Azman, Nicholas G. Reich, Justin Lessler. The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application. Annals of Internal Medicine, 5 May 2020. https://doi.org/10.7326/M20-0504.

U.S. Centers for Disease Control and Prevention. COVID-19 Pandemic Planning Scenarios. [PDF Document]. Updated 10 September 2020.

COVID Tracking Project. Most Recent Data. [Online Database]. Accessed 16 October 2020.

More or Less: Behind the Stats. Ethnic minority deaths, climate change and lockdown. Interview with Kit Yates discussing back calculation. BBC Radio 4. [Podcast: 8:18 to 14:07]. 29 April 2020.

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