Category Archives: health

The Magic Percentage for Useful COVID Herd Immunity

What percentage of the population needs to be vaccinated to usefully reduce the risk of dying from COVID-19?

We're going to do a back-of-the-envelope calculation to estimate the answer to that question using Arizona's high quality COVID data in general, and the state's data for COVID-related hospital admissions and deaths in particular.

We're also going to build off our previous analysis that synchronized Arizona's figures for the number of positive COVID infection test results, hospitalizations, and deaths according to the approximate date of initial SARS-CoV-2 coronavirus exposure for the Arizonans who became infected and experienced these pandemic-related events. The following chart shows these three streams of data using a logarithmic scale, covering the period from 15 March 2020 through 30 April 2021.

Arizona's Coronavirus Pandemic Experience, Rolling 7-Day Moving Averages of Cases, Hospital Admissions, and Deaths Indexed to Approximate Date of Initial SARS-CoV-2 Coronavirus Exposure, 15 March 2020 through 30 April 2021

We've annotated the chart to indicate two periods of "noise" in the data for deaths, which came into play when the daily number of COVID-related deaths of Arizonans dropped into the single digits. Because of the small numbers involved, having a relatively small change in the daily number can have an outsize effect on the appearance of the overall trend, which accounts for the "noisy" short-term trough that was recorded in mid-September 2020 and the short-term spike in late March 2021. We've added the dotted lines to these areas of the chart to indicate what the overall pattern would look like without the short term noise in the data.

Now to the bigger question. We're going to focus on the ratio of deaths to hospital admissions because these events represent the most serious classes of COVID infections. In Arizona, 75% of COVID-related deaths have occurred among the state's senior population, Age 65 or older. This same demographic has accounted for 46% of COVID-related hospital admissions in the state.

These figures confirm seniors are disproportionately vulnerable to both these outcomes if they become infected by the SARS-CoV-2 coronavirus. This fact is why this portion of the state's population was targeted for early COVID vaccinations once the vaccines became available.

Because the incidence of COVID-related deaths in concentrated in Arizona's senior population, we should see a sustained decline in the ratio of COVID deaths to hospital admissions corresponding to roughly when the population Age 65 or older achieved effective herd immunity. We can then identify what percentage of the state's elderly population had been received at least one vaccine dose at that point in time, which in turn, will give us a reasonable indication of what percentage of the population needs to be vaccinated for COVID to reduce its risk of death.

The next chart graphically shows the results when we combine these points of data together.

Arizona Ratio of Rolling 7-Day Moving Averages Deaths to Hospitalizations Indexed to Approximate Date of Initial SARS-CoV-2 Coronavirus Exposure, 15 March 2020 through 30 April 2021

We find at least 55% of the population would need to have received at least one dose of the COVID-19 vaccines to provide the benefit of reduced risk of death from becoming infected by the coronavirus. That's the percentage of the Age 65 and older population of Arizonans who had been vaccinated as of 28 February 2021, which marks the point in time at which COVID-related deaths in the state began to plunge as a result of the Operation Warp Speed vaccination programs.

That's the low end for our estimate, because it does not consider the portion of the senior population who would have obtained natural immunity from having become infected with the SARS-CoV-2 coronavirus and who recovered from it. As of 28 February 2021, Arizona's senior population accounted for 109,897 known COVID infections, about 13.4% of the state's total at that time. Added to the 696,559 Age 65 or older Arizonans who had received at least one COVID vaccination dose at that date would put the high end of the estimate at 64%.

That upper level figure would explain why public health officials have set a target of 70% of the population for COVID vaccinations, but it seems strange they are not giving more weight to the potential contribution of natural immunity in achieving that goal. If they did, they could focus their limited resources for providing COVID vaccination more effectively.

Looking at Arizona's data, we would say the magic percentage for vaccinations to achieve useful COVID herd immunity is somewhere between 55% and 64% of the population. That's because there is almost certainly a good amount of overlap between those who have recovered from COVID and those who have been vaccinated. It would be more beneficial and less wasteful for public health officials to target the COVID vaccines to those who have not developed any antibodies to SARS-CoV-2 coronavirus infections.

References

Arizona Department of Health Services. COVID-19 Data Dashboard: Vaccine Administration. [Online Database]. Accessed 10 June 2021.

COVID-19 and the 2021 Border Migration Crisis in Arizona

Three of the four high quality COVID-19 datasets we track for Arizona indicate a new adverse change in trends for the coronavirus pandemic in the state. Arizona's data for positive test results by date of sample collection, new hospital admissions, and ICU bed usage are confirming an increase in the incidence of COVID in the state. The fourth dataset for COVID-19 deaths by recorded date of death certificate does not as yet, but would not be expected to as yet because this data has the greatest lag from a change in the rate of incidence to the confirmation of a change in trend.

We've generated the following animated chart to cycle through each of the charts for these four datasets.

Animated Chart: Arizona COVID-19 Positive Test Results, New Hospital Admissions, ICU Bed Usage, and Deaths, 1 January 2020 - 24 April 2021

Considering the respective lags that apply for each dataset, the likely timing of a significant change in the rate of incidence for SARS-CoV-2 coronavirus infections in the state between 26 March 2021 and 30 March 2021. This period coincides with contemporary news accounts of the Biden administration moving migrants from overloaded Border Patrol migrant facilities in Arizona counties bordering Mexico to facilities and small towns in Maricopa and Pinal Counties.

We think this activity is showing up in Arizona's COVID-19 statistics because these migrants have been exposed to Mexico's higher incidence of COVID-19 infections. While those cases peaked in late January 2021, several weeks after they peaked and began falling in Arizona, the relative difference in infection rates between Arizona's population and the entering migrants is enough to affect the trends for Arizona's COVID-19 data.

On 26 March 2021, Senator Mark Kelly (D-AZ) stated the Biden administration did not have an effective plan for the border. It took another month for President Biden to acknowledge the migration crisis at the U.S. border with Mexico as a crisis.

On 21 April 2021, Arizona Governor Doug Ducey declared a state of emergency and sent Arizona National Guard troops to Arizona's border counties.

Coincidentally, that was the last date we updated our series on the COVID-19 pandemic in Arizona, where our analysis of the trends just before that point of time appeared very early in the morning....

Previously on Political Calculations

Here is our previous coverage of Arizona's experience with the coronavirus pandemic, presented in reverse chronological order.

References

We've continued following Arizona's experience during the coronavirus pandemic because the state's Department of Health Services makes detailed, high quality time series data available, which makes it easy to apply the back calculation method to identify the timing and events that caused changes in the state's COVID-19 trends. This section links that that resource and many of the others we've found useful throughout the coronavirus pandemic.

Arizona Department of Health Services. COVID-19 Data Dashboard: Vaccine Administration. [Online Database]. Accessed 25 April 2021.

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.

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.

Improving COVID Trends Bottom and Flatline in Arizona

Not much has changed over the last two weeks with respect to COVID trends in Arizona. Which is very good news.

That's because of what didn't happen after Arizona's economy fully reopened, which we mark from the lifting of capacity limits on businesses such as bars, restaurants, gyms, and others that would be considered prime territory for spreading coronavirus infections. What didn't happen is significant, because instead of developing a rising trend for COVID-19 cases, hospitalizations, ICU bed usage, and deaths as it did after its first reopening attempt following its first wave of COVID-19, Arizona has instead experienced steady, relatively flat levels for all these measures. What had looked like the potential stalling of a previous trend of improvement is really demonstrating the benefits of the widespread deployment of Operation Warp Speed's vaccines in Arizona. The protections offered by the vaccines are enabling the gains of improvement to be sustained. Even as the kind of activities that would have previously resulted in the reversal of a positive trend for coronavirus infections have expanded.

That's evident in the latest updates to the four charts tracking the trends for each of these measures based on Arizona's high quality data for the numbers of new cases by test sample collection date, hospitalizations by date of admission, deaths by date as recorded on death certificates, and ICU bed usage.

Arizona Positive COVID-19 Test Results by Date of Sample Collection, 1 January 2020 - 19 April 2021
Arizona New COVID-19 Hospitalizations by Date of Admission, 1 January 2020 - 19 April 2021
Arizona New COVID-19 Deaths by Date of Death Certificate, 1 January 2020 - 19 April 2021
Arizona COVID-19 ICU Bed Usage, 10 April 2020 - 19 April 2021

Since our last update, the trend for cases has continued moving sideways, with the trends for both hospitalizations and ICU bed usage now following suit. It will take a little more time to see if the dataset for deaths attributed to COVID-19 will follow the same pattern, but the early indicators are that it will.

The next time we look at Arizona's high quality COVID-19 data, we'll be looking to confirm the answer to a very different question.

Previously on Political Calculations

Here is our previous coverage of Arizona's experience with the coronavirus pandemic, presented in reverse chronological order.

References

We've continued following Arizona's experience during the coronavirus pandemic because the state's Department of Health Services makes detailed, high quality time series data available, which makes it easy to apply the back calculation method to identify the timing and events that caused changes in the state's COVID-19 trends. This section links that that resource and many of the others we've found useful throughout the coronavirus pandemic.

Arizona Department of Health Services. COVID-19 Data Dashboard: Vaccine Administration. [Online Database]. Accessed 20 April 2021.

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.

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.

How Effective Are the Operation Warp Speed Vaccines?

The Wall Street Journal recently reported on the apparent effectiveness of the Operation Warp Speed COVID-19 vaccines:

The U.S. Centers for Disease Control and Prevention has identified a small cohort of approximately 5,800 cases of Covid-19 infection among more than 66 million Americans who have completed a full course of vaccination.

These so-called breakthrough cases, which are defined as positive Covid-19 test results received at least two weeks after patients receive their final vaccine dose, represent 0.008% of the fully vaccinated population.

Officials said such cases are in line with expectations because the approved vaccines in the U.S. are highly effective but not 100% foolproof.

For judging the effectiveness of a vaccine, that's the wrong measure. What we really want to do is compare how well the vaccines protect the portion of the public who have been fully vaccinated with the portion of the population that has either not been vaccinated or has only been partially vaccinated against COVID-19.

So we ran some rough numbers to find out. The following chart reveals a back-of-the-envelope estimate of how well the COVID-19 vaccines are so far working in the U.S.

How Well Do the COVID-19 Vaccines Work? Percentage Share of New Cases in U.S. Population, 15 December 2020 - 8 April 2021

At first glance, the Operation Warp Speed vaccines would appear highly effective.

All our teams make an effort to stay optimistic, but I will say that once our virus division saw the vaccine efficacy data, they started asking for payment up front.

Running Through the Rough Numbers

The first COVID-19 vaccincations of the U.S. public began on 14 December 2020.

On 15 December 2020, the U.S. Census Bureau estimated the size of the U.S. population on 1 April 2020 to be 332,601,000. The Census Bureau based this estimate on demographic analysis, independently of the actual 2020 U.S. Census results, where they estimated the actual population of the U.S. would fall in between a low estimate of 330,730,000 and a high estimate of 335,514,000.

As of 8 April 2021, 66,203,123 Americans (about 19.9% of the population) had been fully vaccinated for COVID-19. Using these figures, that would mean roughly 266,398,000 Americans would be considered either unvaccinated or partially vaccinated on that date [1].

From 15 December 2020 through 8 April 2020, the CDC reported a total of 14,232,649 new COVID-19 cases in the U.S. [2]. If 5,800 is the number of "breakthrough" cases among the 66,203,123 fully vaccinated Americans, subtracting 5,800 from 14,238,649 let's us arrive at the estimated number of cases among the "less-than-fully-vaccinated" population of 14,232,849.

That's how you get the numbers we used to calculate the percentages in the chart. 5,800 breakthrough cases among 66,203,000 fully vaccinated Americans works out to be a percentage of 0.0088%.

Meanwhile, the 14,232,849 newly reported cases among the 266,398,000 unvaccinated or less-than-fully vaccinated portion of the U.S. population during the period of time vaccinations have been available for the U.S. public represents 5.3% of that portion of the population.

Based on this rough reckoning, it would appear the vaccines are working very well in limiting the spread of new infections from the strains of SARS-CoV-2 coronavirus active within the United States [3].

Notes

[1] None of this back-of-the-envelope analysis considers the number of Americans who already had and recovered from COVID-19, who have gained at least partial if not full immunity to the infection for at least some period of time as a result. As of 8 April 2021, that potential additional total is 30,181,371 (30,737,477 cases minus 556,106 deaths). We're also not considering the 46,843,488 Americans the CDC reports have received at least one dose of the COVID-19 vaccines as of 8 April 2021 either, who it would consider partially vaccinated.

We opted to not consider these additional categories because the CDC has not indicated how many of the fully or partially vaccinated portions of the population in the U.S. has previously tested positive for SARS-CoV-2 coronavirus infections. By grouping them in the unvaccinated or partially-vaccinated category however, our rough estimates understate the relative benefits of vaccination. Even so, the apparent relative benefit is massive.

[2] This figure almost certainly includes the results of positive COVID-19 test results whose samples were collected days and weeks before the Operation Warp Speed vaccines began to be introduced to the U.S. public. The CDC does not report test results by sample collection date, which would provide higher quality information.

[3] We're also not considering political factors that have affected how the U.S. vaccination program has been rolled out by various state governments.

Reliving a Day of Panic in the Coronavirus Pandemic

Today marks the anniversary of the most pivotal moment in New York Governor Cuomo's COVID nursing home deaths scandals. Because one year ago today, Governor Cuomo and senior members of his administration reached the point of panic as they struggled to address the greatest challenge of his tenure in office.

We originally presented that story on 12 May 2020. Today, we're re-running that original article, in which we recreated critical information that influenced the most consequential decision Governor Cuomo made on that day. The deadly repercussions of what resulted from that day of panic are still rippling through New York and making national news a year later. Let's get started....


COVID-19 - Martin Sanchez via Unsplash: https://unsplash.com/photos/Tzoe6VCvQYg

We're fascinated with how politicians use data and models in setting the policies they pursue, where knowing both what they knew and when they knew it can explain a lot about why they made the choices they did at the time they made them.

To that end, we've been paying attention to how Governor Andrew Cuomo has been managing the difficult task of coping with the coronavirus epidemic in New York, and in New York City in particular, which has been the focal point for both the number of cases and the spread of the SARS-CoV-2 coronavirus across the United States. We've assembled a timeline of Governor Cuomo discussing the predictive models for how fast the coronavirus infection would spread within New York, which provides insight into how that information affected his decisions for how to allocate the limited health care resources over which he had influence during the worst part of the epidemic in his state.

We're going to pick up the action shortly after 7 March 2020, the date Governor Cuomo declared a state of emergency because of the coronavirus epidemic in New York, when the number of coronavirus cases within the state had 'soared' to 89. The following article is the earliest in which we find a reference to coronavirus modeling projections for New York City, which had been put together by New York City Mayor Bill de Blasio's staff:

9 March 2020: Coronavirus Cases in New York State Rise to 105:

Mayor Bill de Blasio said Sunday that the city had 13 confirmed cases, including a new case of a man in the Bronx. Based on modeling, his team estimated there could be 100 cases in the next two or three weeks, but for most people, the illness would result in very mild symptoms.

Three days later, New York City had nearly reached that total and was set to blast through it, prompting Governor Cuomo to ban all public events with more than 500 people in attendance and to require gatherings with fewer than 500 people to cut capacity by 50%. The faster than previously projected growth in the number of COVID-19 infections drove a change in public policy.

Four days after that, Governor Cuomo had clearly been presented with projections that showed the exponential growth in the number of cases that had gotten underway in New York.

16 March 2020 - Audio & Rush Transcript: Governor Cuomo is a Guest on CNN's Cuomo Prime Time:

"I see a wave and the wave is going to break on the health care system ... You take any numerical projections on any of the models and our health care system has no capacity to deal with it."...

"Yeah. I think you look at that trajectory, just go dot, dot, dot, dot, connect the dots with a pencil. You look at that arc, we're up to about 900 cases in New York. It's doubling on a weekly basis. You draw that arc, you understand we only have 53,000 hospital beds total, 3,000 ICU beds, we go over the top very soon."

At this point, Governor Cuomo was beginning to appreciate that the thousands of hospital beds across the state of New York were really a scarce resource. He expanded on that realization the next day after an overnight surge in the number of reported cases:

17 March 2020 - Video, Audio, Photos & Rush Transcript: Governor Cuomo Announces Three-Way Agreement with Legislature on Paid Sick Leave Bill to Provide Immediate Assistance for New Yorkers Impacted By COVID-19:

"There is a curve, everyone's talked about the curve, everyone's talked about the height and the speed of the curve and flattening the curve. I've said that curve is going to turn into a wave and the wave is going to crash on the hospital system.

I've said that from day one because that's what the numbers would dictate and this is about numbers and this is about facts. This is not about prophecies or science fiction movies. We have months and moths of data as to how this virus operates. You can go back to China. That's now five, six months of experience. So just project from what you know. You don't have to guess.

We have 53,000 hospital beds in the State of New York. We have 3,000 ICU beds. Right now the hospitalization rate is running between 15 and 19 percent from our sample of the tests we take. We have 19.5 million people in the State of New York. We have spent much time with many experts projecting what the virus could actually do, going back, getting the China numbers, the South Korea numbers, the Italy numbers, looking at our rate of spread because we're trying to determine what is the apex of that curve, what is the consequence so we can match it to the capacity of the health care system. Match it to the capacity of the health care system. That is the entire exercise.

The, quote on quote, experts, and by the way there are no phenomenal experts in this area. They're all using the same data that the virus has shown over the past few months in other countries, but there are extrapolating from that data.

The expected peak is around 45 days. That can be plus or minus depending on what we do. They are expecting as many as 55,000 to 110,000 hospital beds will be needed at that point. That my friends is the problem that we have been talking about since we began this exercise. You take the 55,000 to 110,000 hospital beds and compare it to a capacity of 53,000 beds and you understand the challenge."

Faced with the potential shortage of needing 110,000 beds and only having 53,000 to provide care to coronavirus patients in New York, Governor Cuomo lobbied President Trump for support, which resulted in President Trump ordering the U.S. Navy's hospital ship USNS Comfort to sail to New York City the next day, and also lobbied for the U.S. Army's Corps of Engineers to begin identifying public facilities in New York City to be converted for use as temporary hospitals to handle the projected overflow of coronavirus patients from regular hospitals.

USNS Comfort would arrive in New York City on 30 March 2020, and the Army Corps of Engineers would have 1,000 beds ready at New York City's Javits Center ready on 27 March 2020, and were working to expand it to a 2,500 bed temporary hospital facility by 1 April 2020. But during the time in between, the updated projections of the coronavirus models led Governor Cuomo to panic.

24 March 2020: Andrew Cuomo: Apex of coronavirus outbreak in NY two or three weeks away:

Cuomo, speaking at his daily COVD-19 briefing in Manhattan, said the state's projection models now suggest the apex of the coronavirus crisis could hit New York within 14 to 21 days, rather than the 45 days the state projected late last week.

He likened it to a "bullet train" headed for New York, urging the federal government to deploy as many ventilators and as much protective medical gear it can to the state as quickly as possible.

"Where are they?" Cuomo said. "Where are the ventilators? Where are the masks? Where are the gowns? Where are they?”

At this point, we should show what one of the more influential coronavirus models that Governor Cuomo was using looked like. The following chart is taken from the Institute for Health Metrics and Evaluation (IHME)'s 25 March 2020 projections showing its estimates of the minimum, likely, and maximum number of additional hospital beds that would be needed in the state of New York to care for the model's expected surge of coronavirus patients.

IHME Forecast of All Hospital Beds Required for COVID-19 Care Beyond Available Capacity in New York State, Projection from 25 March 2020

This is just one of several coronavirus models whose projections were being combined and presented to Governor Cuomo by consultants from McKinsey & Co., where the IHME's coronavirus model's projections for New York are consistent with the figures and timing of a peak cited by Governor Cuomo in the days preceding his panic.

Faced with what appeared to be an imminent shortage of hospital beds and other medical resources, the Cuomo administration appears to have adopted an emergency triage strategy, one that would have devastatingly deadly consequences. Here, to free up as many beds as possible in New York's near-capacity hospitals, the Cuomo administration would try to move as many patients infected with the SARS-CoV-2 coronavirus as they could out of these facilities into others, even though they could still be contagious and present the risk of spreading infections within the facilities to which they would be transferred.

25 March 2020: The facilities in which they chose to place them were predominantly privately run nursing homes, where a directive issued by the state's Department of Health on 25 March 2020 mandated they must admit them into their facilities, where refusals could mean the loss of their New York state-issued licenses to operate.

New York Department Of Health Directive to Nursing Homes Mandating Admission of Coronavirus-Infected Patients, 25 March 2020

Flashing forward to the end of March 2020, the coronavirus epidemic forecast models Governor Cuomo was using in making his decisions were pointing to the peak still being ahead:

Cuomo said various predictive models being used by New York indicate the apex of the surge for hospitals will come anywhere from 7 to 21 days from now.

“The virus is more powerful, more dangerous than we expected,” Cuomo said. “We’re still going up the mountain. The main battle is on top of the mountain.”

Four days later, the coronavirus models were predicting the peak was almost upon New York:

While giving an update Saturday on the frantic work to ready New York hospitals for the most intense period of the coronavirus (COVID-19) crisis, Gov. Andrew Cuomo said that the state’s models put the so-called apex about four-to-eight days out.

“By the numbers, we’re not yet at the apex. We’re getting closer,” he said at his daily press briefing. “Depending on whose model you look at, they’ll say four, five, six, seven, days, some people go out 14 days. But our reading of the projections is that we’re somewhere in the seven-day range. Four, five, six, seven, eight-day range.”

“Part of me would like to be at the apex, and just, let’s do it,” Cuomo continued. “But there’s part of me that says it’s good that we’re not at the apex because we’re not yet ready for the apex, either. We’re not yet ready for the high point...the more time we have to improve the capacity, the better.”

But on 6 April 2020, the IHME model revised its estimates for New York and the U.S. downward, indicating the peak Governor Cuomo feared would overwhelm New York's hospitals was not going to come anywhere close to what it had previously projected. On 8 April 2020, it indicated New York had already passed its peak in number of daily new cases.

Ordinarily, that would be a good thing. Except, Governor Cuomo had taken an action by which he intended to avoid the spectacle of having pictures of sick New Yorkers not able to get medical treatment in the media, but instead ensured the state's death toll from its coronavirus epidemic would no longer be small. That part of the story has its own special timeline, which we've moved here from the bottom of the article where we had previously been piecing together this part of the story of COVID-19 in New York....

Image credit: unsplash-logoMartin Sanchez


The explosion of Cuomo scandal news has prompted us to launch a new blog to host the timeline we had been updating regularly in this space! We officially launched the new site a week ago. If you haven't yet seen it, may we introduce A Timeline of New York Governor Andrew Cuomo's Nursing Home Scandals.

The Governor Who Kills Grandmas?

Now serving all your Cuomo nursing home scandal news needs!