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I’m following a new trend that seems to have emerged with increased temperatures. Case growth has slowed in the hardest-hit regions but is increasing in new areas such as Nebraska, Iowa, Minnesota, Kansas, etc. The chart and table above are sorted by the case growth (IROC_confirmed) and you can see that the death rates for most of these new regions are very small. Keep in mind that case growth isn’t the thing we should be scared of (I predict people will continue to get infected by this coronavirus for years). The media is reporting case growth to support state lockdown extensions. I recommend instead that we watch the case growth closely (remember, some of it is surely due to the increased testing that’s happening across the US) and watch the death rates even more closely.

In the cases of the states that have had longer experiences with the virus (Rhode Island, the DC area, Massachusetts, Illinois, Indiana), note that though the current death rates (IROC_deaths) in those states are larger than in the new states, these rates are decreasing every day (dIROC_deaths). This also seems like good news.

Summary

It seems like 1) New infection outbreaks are being managed better due to what we have learned from the older outbreaks and this is resulting in more cases without deaths, 2) COVID-19 has not overwhelmed hospital systems in these new regions, most likely because hospitals have learned better ways of treating COVID-19 patients and are limiting ventilator usage (and using blood thinners), and 3) hopefully nursing homes have learned how to better keep COVID-19 out of their facilities. Perhaps this high case – low death trend continues through the summer.

Where are the cases/deaths and the hotspots in the US?

The above chart shows that the United States follows the trends of the rest of the world regarding zones where the highest numbers of cases and deaths are occurring. The table with the data for this graph is below.

What do we see here? The band from 40 to 45 degrees North latitude has over 3x the number of COVID-19 Cases and pretty close to 5x the number of COVID-19 deaths than the next highest 5 degree latitude band. Regions in this band include NYC, Philly, Detroit, and Chicago, all harder-hit localities. With this region, the US has around 4.0 Cases per 1000 people. Remove this region and it drops to about 1.5 Cases per 1000 people. The former number places us 10th in the world by cases per 1000 and the latter number places us around 40th. So you can see this one 5 degree band makes a very big difference in our case numbers. It has an even more pronounced affect on the death numbers.

I also note that the slope (today’s rate) of the 40-45 band leads the pack but that 35-40 is catching up. No other region is close on this case (and death) growth measure. See below for a graph… This is a picture of “hot-spots”, i.e., regions with more rapid increases.

Fortunately in the harder hit regions, we’re seeing many of the growth rates slowing down (decelerating). Below are regions that have case numbers that are accelerating the fastest. Note that some of these are outside that hard-hit Northeast corridor. Also note that most of these ‘accelerating’ regions still have low case numbers (their case growth is just starting). And the measure we really care about (deaths) is still very low in these regions. As testing increases, this is a trend I’m seeing more… high numbers of cases and low numbers of deaths. Just something to watch.

Above is the flu vaccination rates for 2018 across states. The darker color is higher percentages of the population getting the vaccine. The highest states are RI and Mass with about 60% of the population vaccinated. The lowest are Nevada, Wyoming, and Florida, with about 40%. You’ll notice on the map of COVID-19 cases and deaths per 1000 persons that in general, though, states with lower flu vaccine are also states that haven’t been hit as hard by COVID-19 (and vice versa). Aha! Some may say, the anti-vaccination folks are right! Hold on, slow down…

Is this Causality or Just Correlation?

Many events share dependence with a third, less directly-related event. This can result in something called a spurious correlation. Many times, these spurious correlations can be uncovered quite easily once the “excitement” at the correlation has passed. A textbook example is the correlation between ice cream sales and drownings. This is true. Drownings are always highest in months that have the greatest number of ice cream sales. Of course, thinking about this, you will realize that these are really two independent events that both share a correlation with this thing we call “summer”! There are whole websites dedicated to the comedy value of uncovering spurious correlations. Here’s one of those sites.

Back to the Flu Vaccine – is this a spurious correlation?

Lets mull this over a bit. Our null hypothesis would be that there is no causal relationship between getting the flu vaccine and getting COVID-19. We would have to disprove this null hypothesis in a statistically-relevant way to prove that there IS a causal relationship (i.e., the flu vaccine causes someone to be more susceptible to COVID-19 or some such).

This would likely be very hard to do, because one would have to overcome the challenge of multiple third events correlated with both Influenza Vaccination rates as well as COVID-19 infections. One of these events may be that some regions have a perception of historically higher incidences of infectious diseases (like influenza and COVID-19) and have learned to get the flu shot. This seems very likely to me. Conversely, regions that traditionally don’t perceive great challenges with the infectious diseases won’t get flu vaccines as readily as those regions that do. These same regions that don’t traditionally get the flu as badly and therefore don’t get the flu vaccine, are also not getting hit hard by COVID-19 for the same reasons that they don’t get the flu as badly! Population density, cultural expressions, collectivist vs. individualist tendencies, and other factors may be at play, but from a scientific standpoint, if one wished to set up experiments/studies to determine if our null hypothesis was correct or not, they would have to control for these pretty large variables.

Funny Correlations

Here’s a funny example from https://www.tylervigen.com/spurious-correlations

I have added some factors and am exploring the correlation between these factors and overall numbers of cases and deaths (previously, I have been attempting to correlate factors with the severity of rates of cases and deaths. There is enough data now to try to tease out factors that share some dependence with the numbers of cases and deaths.

Things I find Interesting – Case number correlation:

• Average rates of Tuberculosis have the strongest negative correlation with the total number of COVID-19 cases in a country. There may be many reasons for this, but it is an interesting datapoint. Perhaps more so because of the studies into the potential that a TB vaccine might be providing some kind of protection in the regions that still get it (which may well be regions that still have a high TB rate).
• Countries with large numbers of deaths due to Zinc and Iron deficiency have experienced less COVID-19 cases. This might be simply that these deaths removed some potentially susceptible people from the pool of potential cases. Factors that might show this same effect are HIV percentage and even TB percentage (though the latter are more strongly negatively correlated with cases).
• A country with a high Female Smoking Rate is more likely to have larger numbers of COVID-19 cases. This has been pretty consistent. Mean BMI number is also highly correlated with cases. My suspicion is that these individuals present with symptoms more quickly than others and therefore are formally counted as a case whereas others might not be counted. This concept also applies to people over 65. The same theory applies to the number of nurses per 1000. In countries with low numbers of nurses, perhaps many people never get diagnosed, and therefore recorded.
• Population density is less correlated than the above factors, but is still positively correlated with the number of cases.

Deaths Per 1000 person – Correlations

Things I find interesting – Death number correlation:

Here we find the co-morbitities for COVID-19 as well as factors that may have a dependency with the number of deaths per 1000.

• Note that having a high number of citizens over 65 is the highest factor that is positively correlated with deaths due to COVID-19. This is not surprising, but confirms what we are hearing.
• Female Smoking rate is equally correlated with cases and deaths in a country. This would make me suppose that in this case, countries with a high female smoking rate are seeing more females die due to COVID-19 than other countries.
• Countries with a high number of deaths due to eating red meat (how is this measured??) also have a higher number of COVID-19 deaths, but I suspect there’s a lot of similarity between this measure and Mean BMI.
• Countries with a high number of deaths due to lack of calcium also see a high number of COVID-19 deaths. Not sure if this is just correlated (i.e., how drowning deaths are correlated with ice cream sales every year), but it’s one of the few factors related to nutrition that is postitively correlated. Other nutrition-related factors (deficiencies in Iron, Vitamin-A, Zinc) are negatively correlated and the rest of the nutrition factors here have no correlation at all.
• Temperature is very negatively correlated with deaths (as well as with cases). My intuition is that this is causal, but I can’t support that exactly.
• Finally, the Income Group and the Growth Rate are both highly negatively correlated with deaths. I see these as measuring similar things. Countries with a high Growth Rate are also generally growing in weath and moving up Income charts. This weath and what it brings the society (ability to shelter in place? Better health care?) makes them less susceptible to COVID-19 deaths (and cases).

The Instantaneous Rate of Change metric has given us the ability to understand in one number the state of the outbreak in a region regarding case growth and deaths. These are shown above with IROC in the header. This table is sorted by the states where the daily growth rate in cases has decreased the most over the last 3 days. I’d refer to this as “decelerating” rates. Fortunately, New York is finally at the top of a “good” list associated with this outbreak. Hopefully this will signify a long plateau in the rates. Note that in some regions (Singapore is a good example) an early plateau (celebrated widely) was followed by accelerating growth in cases. Perhaps NY will be different due to the extreme penetration of their society by COVID-19. Below is the individual NY time series charts for your perusal.

I’m still interested in the Rates of Reproduction and the tracking of this number. I picked 7 countries that were interesting to me for various regions and began tracking their numbers (including Ro) over time. Above you can see some of the results. Notable observations: Germany’s Ro on 4/15 was the highest of the group of 7 at 1.3. This means, in theory, that one new infected person would infect 1.3 more people. On 4/15, we also see a number of countries that are struggling now with Ro numbers less than 0.5 (Mexico, Brazil, Russia, Singapore. Singapore, especially, is interesting because 4/15 was in between their first (small) wave of infections and their current (larger) wave. Now you can see Singapore’s number is up to 1.46 and Brazil and Mexico are much higher. The US peaked somewhere around 4/30 and is trending slowly downward. Germany, however, has moved down quite a bit, signifying that their outbreak is under control. Sweden, with the most unique strategy for COVID-19 immunity, has held pat at just under 1.0 for the entire duration. I wonder if this is an artifact of their systematic approach?

Now, see below for the top 11 countries by Ro (with more than 1K cases) over those same time periods. Just like above, you can see some countries dramatically decrease their Ro (Portugal, Turkey) while new countries replaced them at the top of the list. Note also that right now, a high Rate of Reproduction isn’t equaling a high deaths per 1000 number. This may be due to new countries experiencing outbreaks, or may be due to some other factor (temperature? Immunity? Better approaches to medical care?)

Recently Germany began to share that they were reopening their economy with an eye on their Rate of Reproduction calculation. They had been seeing Ro in the 0.7 range and decided to back off of some of their lockdown restrictions. Now they were seeing Ro creeping up to 1.0 (edit: I’m calculating their Ro too and I don’t see this movement. Maybe they have data that I don’t) and they were getting concerned. This seems like a data-driven approach to reopening the economy, but is it a good one?

Some Background on Ro

I have published on methods to calculate Ro in previous articles. There may be other ways to do this, but one very simple way is to use the Susceptible, Infected, Recovered (SIR) equations that come from epidemiology. This is why having these three numbers published by a nation or locality is so important (note this, US Governors!). Below is a list of locations where Ro is highest, per my calculations.

The Ro is purported to describe how many people an infected person will transmit the virus to. Therefore, if Ro is over 1, the virus will expand in society. If Ro is 2, one person will transmit to two others, thus creating a non-linear growth pattern. Traditionally, Ro is calculated by multiplying the Transmissibility factor (above on the chart), which is what we actually back out of the SIR equations, by the number of days a person with the disease is infectious.

Problems with this…

1. I cannot find any references to what the actual number of infectious days is for COVID-19. In my calculations, I guess at the 14 day number that is all around us and I get the same numbers that I see published for European countries. So I suspect they’re using 14 days too. But I kind of doubt that’s the right number because for other infections the number of infectious days ranges from 2-10. If my assumption is correct, then I suspect that this could be inflating the Ro numbers associated with COVID-19. Not a huge deal (the transmissibility numbers still give an indicator of whether a country is in a highly-infectious period) but might be giving false comparisons to other diseases.
2. I also can’t find any data on reinfection percentages for COVID-19. This isn’t surprising, of course, as this is a novel coronavirus, but I also have to assume a value for reinfection in the SIR equations. If it turns out that reinfection is higher than we thought, this will lower our transmissibility values (seems counterintuitive, but it’s complicated).
3. Superspreaders are a real problem for Ro. A superspreader is an event or person associated with large numbers of infections. Typhoid Mary, who was a non-symptomatic Typhoid Fever carrier, is a good example. She infected 76 people singlehandedly with Typhoid Fever. Imagine then if the Ro for a disease is 2 and one person infects 100 people? This acts like accelerant on a wildfire! The same applies for an event that acts as a superspreader, such as the Spanish Flu Liberty Loan parade in Philadelphia. Within 72 hours of this superspreading event every hospital bed in Philadelphia was full. Within a week there were 4K deaths. The CDC paper linked above states about this: “SSEs (Super Spreading Events) highlight a major limitation of the concept of R₀. The basic reproductive number R₀, when presented as a mean or median value, does not capture the heterogeneity of transmission among infected persons; 2 pathogens with identical R₀ estimates may have markedly different patterns of transmission. Furthermore, the goal of a public health response is to drive the reproductive number to a value <1, something that might not be possible in some situations without better prevention, recognition, and response to SSEs.” (Frieden and Lee, 2020)
4. The Ro measure is being co-opted by researchers who seek to “improve” it. This paper on MedRxiv is non-peer reviewed, but seems to be influencing the German government’s calculation of Ro. A summary of the approach is that the researchers are making assumptions about how to modify the Ro equation to take account of mobility restrictions and quarantines. I’m not a big fan of this paper, as it seems to be more reliant on buzz words and popular assumptions than facts. Also, I see no calibrations for super spreading events. This approach does seem immature, but it does appear that European nations are using this approach in their calculations. If these researchers are wrong in their assumptions on the value of mobility restrictions, of course, or the uniformity of transmission then the whole equation could be off.

Conclusion

This outbreak, because it is a novel virus and a situation we haven’t really been in since 1918, has been a learning experiment. New methods have been tested (nation-wide lockdowns, mandatory face masks), different strategies have been derived (Iceland, Sweden, China, and the US all have very different approaches), and data instrumentation and analysis has been exposed. Using Ro as a single metric to return to economic function seems on the surface to be a good idea, but challenges with the Ro metric itself need to be understood as limitations.

I saw a paper from UCSF and UC Berkeley while I was looking for the specificity values of COVID-19 antibody tests and it made me think of a topic to talk about that might be interesting and useful to folks. It certainly will have lots of applications outside COVID-19 tests or antibody tests. Specificity is the parameter that tells us whether the test can separate true positive results from false positives. A high specificity value tells us that a test has low false positives.

Why do we care about False Positives?

This is a fun subject to me and is always part of my statistics classes. In radar processing we refer to it as a false alarm rate. As most signal processing engineers know, a radar can appear to be a world-beater, but if it has a high false alarm rate, there’s a good chance that most of it’s detections are not airplanes flying overhead or any other desired target. In medical tests, false positives present a similar challenge. Many “detections” from the test turn out to not be the thing we hope to detect. The below example might be helpful. In this case, we’re using a nominal-but-high estimate of the total number of COVID-19 cases per 100 people (2). This is about 10x higher than what the data is showing for the US as a whole, so there’s a significant fudge factor here. My false positive rate comes from the UCSF/UCB paper, which stated that even though many of the COVID-19 Antibody tests they were evaluating had a 5% false positive rate, “Several of our tests had specificities over 98 percent, which is critical for reopening society.” So I picked 98% for my example to demonstrate why even this nice-sounding number is still unacceptable.

Looking above, this is a simple way of evaluating a test. In this case, since we’re applying this to the country as a whole, we’re using our inflated number of 2% of Americans that are likely to have contracted COVID-19 (this comes from our data plus a 10x safety factor to prevent underestimation). You can see that means MOST of the 175M adult Americans (the 98%) when tested, fall into the “True Negative” category. That means they don’t have the disease and test negative for antibodies. This is good and what we hope for. However, due to our 2% False Positive Rate, we find out that there are a very large number of Americans who never had COVID-19 who test positive for antibodies. In this case, close to 3.5 million of them. When we go to the top of the decision tree and look at the 2% who data tells us have had the disease, we find that our test accurately catches 99.9% of them (We’re also assuming a really small problem with false negatives… this might be unrealistic, but lets assume it’s a really good test for this). This translates into… 3.5 Million Americans who have had COVID-19 and who test positive for antibodies! The false negatives are unimportant because they come out to 3.5K people due to our test.

The critical takeaway here is that in the scenario above with realistic assumptions we have 7M Americans testing positive for antibodies, but we know that only 1/2 of the really do! This is not even meaningful because if you test positive with this specific test, you still cannot predict if you actually have the disease (or antibodies). This points out that there is really no good reason to run this test in the current state on the population at large because the results are not that informative.

Where Should We Test Then?

The CDC did do one thing wisely with COVID-19 testing early on when they saved the tests for the most affected. I doubt this was accidental, but rather, had to do with this effect I’m showing here. Because, if you can determine that a community has a higher probability of having a disease, this reduces the false positive problem. When we know that specific symptoms (losing smell, temperature, difficulty breathing, etc.) raise the likelihood that a person has COVID-19, say from our nominal 2% probability up to 25% probability, a test with a 2% false alarm rate gives us different results. Then, instead of our true positives being equal to our false positives, our true positives are now around 17X larger than our false positives. This means that if you already exhibit symptoms, the test is statistically more valuable to you because it is more effective at predicting if you really have the disease or not.

Summary

Maybe this is boring, but it applies to cancer tests, tests on an assembly line, and anywhere else where a test is less than 100% accurate (that would actually be all tests for the most part). I’ll recap by scaling the numbers above to a “universe” of 1000 people to make a better comparison.

1) In this universe of 1000 people where statistically 2% have been exposed to a disease (we’ll call this the healthy universe), a test with a 2% false positive rate will give the following results:

• 20 people: Have disease/antibodies and test positive for disease/antibodies.
• 0 people: Have disease but test negative
• 20 people: Don’t have disease/antibodies, BUT test positive for disease/antibodies
• 980 people: Don’t have disease and test negative

2) In the adjacent universe of 1000 people (the obviously symptomatic universe) where statistically 25% with those symptoms are sick, the 2% false positive test will give the following results:

• 250 people: Have disease/test positive
• 0 people: Have disease/test negative
• 15 people: Don’t have disease/test positive
• 735 people: Don’t have disease/test negative

Hope this is a helpful explanation of a couple of things 1) why the antibody tests aren’t really trustable yet and 2) why we give tests to the ones most likely to have the disease (because then the test is effective at predicting the sickness accurately).

I’ve been reading articles that have been getting published in the last few days on how the COVID-19 pandemic and the response to it was anywhere in between a hoax or at least an exaggeration, and all the way down to the end of civilization as we know it. Obviously there’s a lot of pent-up fear and frustration on the parts of different folks, but I can’t help but observe that every political side has been able to fit the available data to their position. I’ll try to provide the data and some history here that will help you make up your mind about these new conversations in the hopes that it will be useful.

First, there ARE a lot of deaths

I continue to hear that this outbreak is no different than the seasonal influenza, but I’m not hearing much in the way of details as to why. Yes, in a bad flu year, we might have 60K deaths in the US. We have only had 2-3 months of COVID-19, though, and have hit the 60K mark yet have no idea how it will respond in the future. Additionally, COVID-19 has proved to have rates of reproduction (Ro) that were much higher than influenza (see here for my analysis of this). Really bad flu years (1968, 2009) have seen Ro values for influenza in the 1.5 to 1.8 range while normal years see around 1.2. Of course these are average numbers, but many countries are seeing Ro rates for COVID-19 STILL in the 1.5 range after the peak. Some regions are still seeing Ro between 2 and 3 even now, which implies that the numbers were higher before things started slowing down. The real peak Ro numbers are hard to pin down because we still aren’t totally sure exactly when the pandemic started. After this is all over the NIH will do a large statistical survey and will arrive at some numbers for incident and case fatalities, transmissability, etc., but right now, outside deaths, we just don’t have hard facts. Based off these high transmissability rates and the high death rates, however, it does appear that this outbreak is unique and all the evidence I have indicates it is worse than a bad round of the flu.

Right now there are 12 counties in the USA that have had more deaths in two to three months of 2020 classified as COVID-19 than they had in 2018 due to all diseases except heart disease and cancer. I’ll restate that. In two to three months of COVID-19 across a large number of counties, COVID-19 deaths have exceeded all 2018 deaths due to respiratory diseases, flu, alzheimers, etc. Plus, there are hundreds of counties who are close to this number. This rate may change, there may be no more deaths in 2020 due to COVID-19, etc. We have no idea. But at this point, this essentially means that due to COVID-19 at a minimum disease deaths in these counties will be doubled for 2020. You can see the numbers, it amounts to a few hundred to a few thousand extra deaths per county per year. This is very unusual due to one disease and if we see significant increases in other kinds of deaths like homicides and suicides, it becomes very newsworthy (Chicago). Will these deaths irrevocably change these counties? I suspect that is an exaggeration. But there will be an impact, not least of all psychologically. And of course the economic impact will also not be fully understood for months either.

Second, this does NOT seem to be like the Spanish Flu

The Spanish Flu was devastating to the world not just due to its large number of deaths, but in who it killed. I heard in a podcast featuring John Barry, who wrote the most important book about the Spanish Flu that the median age of those who died was 27. In some region, this meant that 3% of factory workers died from Spanish Flu. This obviously has far-reaching impact on a region’s productivity, their economy, the number of health care workers and first responders, etc., when people are cut down in their prime contributing ages. COVID-19 is not killing these people by anyone’s measure. The median age in most nations is somewhere around 80 and typically 85-90% of all deaths are over 65. This is not to say there is any difference in the value of lives at different ages (though I have seen recent articles that come close to saying this). But, there is a much more measurable impact on the society when individuals who are counted on to keep the economy running and people fed and cared for are suddenly removed. This is what the Spanish Flu did and what COVID-19 has not done to date.

One other thought on the Spanish Flu. It came in three waves, with the third one being the most devastating. Exposure to the first or second wave did not seem to provide immunity to the third wave.

Third, this DOES point to the Dangers of Society’s not Understanding Science and Statistics

I am not surprised when I see that a model has over-stated an effect. This is a known challenge of models. Most people who build simulations know that “All models are Wrong, but Some Provide Useful Information” and factor that in to decisions. But in society, this seems to be poorly understood, not just by the general public, but especially by politicians, influencers, and journalists. The public’s poor understanding of statistics was exploited repeatedly by news media on both political spectra. If we can’t improve our teaching of statistics at the high school and college levels, then we are probably not going to get out of this bad cycle. I strongly support reimagining how we structure math education in general (the Algebra-Geometry-Algebra II sandwich would be a good place to start).

However, scientists and modelers also need to better understand how to provide predictions to government and journalist groups in ways that are clearer and less likely of being misconstrued or misappropriated. I heard Dr. Chris Murray, director of the University of Washington’s well-respected Institute of Health Metrics and Evaluation (IHME) say on a Nate Silver podcast that the early COVID-19 models in the west were based on Hubei Province data. I think it’s pretty clear by now that Hubei Province data was created by local politicians and did not accurately measure the truth on the ground. So the most important part of that model was fit on data we now know was at best heavily filtered by a Chinese provincial government. I don’t think this was even known outside IHME until recently. My point is that in general, scientists understand the usefulness of their models but struggle to communicate a model’s limitations to a politician or journalist. This is, in a sense, a failing of science to understand how the rest of the world works. This may have gotten us into trouble during the early days of COVID-19, but perhaps there was some willfulness to understand simulation results in the context of a pre-existing bias by leaders and journalists.

Notice in the above, it’s barely perceptible, but the latitude effect is still holding regarding latitudes 40-50 which have greater numbers of cases per 1000 and deaths per 1000 than any other latitude range. This has been the case for a while, but the other latitude ranges north of 30 have been catching up for a while. Now take a look at the same graph when we look at the hot spots, i.e., areas that have the highest rates of growth of cases per 1000 and deaths per 1000. It looks a bit different.

Now you can see one thing that has been obvious to observers, the growth rates in the range from 40-50 N. Latitude which had been hit so hard up until now are clearly slowing. The hottest spot for death rates per 1000 right now is the range from 60-70 N. Latitude. This is largely due to large numbers of deaths in Sweden’s elder care homes. Also node that Latitudes 10-20 S. Latitude are the hottest spot in the Southern Hemisphere. This is almost exclusively due to Brazil. South Latitudes 20-30 barely even show up, which is interesting. These are countries primarily in Southern Africa and the southern-most part of South America like Paraguay, Zimbabwe, and Namibia. They have reported about 20 deaths due to COVID-19 across this whole band. Perhaps this is because there are reasons that COVID-19 isn’t a threat in that region, perhaps it’s because they get lesser world travel, or maybe they have it but haven’t noticed?

Finally, you’ll note that 40-50 degrees S. Latitude is actually showing up as negative. This implies the rate of growth is negative overall, which doesn’t really make sense. See what this looks like below. The negative slope is inaccurate because it has to do with the third order polynomial fit overshooting a bit. But as you can see, case growth is essentially zero in New Zealand. It’s a story of aggressive testing and data collection, honest communications, and attention to detail. See how New Zealand and Australia have fought the virus despite two very different governing styles.