Month: March 2020

I introduced Instantaneous Rates of Change a few days ago thanks to a good suggestion by Brad Morantz, a fellow AI researcher. I had been trying to represent the severity of the curve of deaths over time through a linear fit, something I knew was sub-optimal, but figured was good enough for the purpose. Here’s a good link describing this concept. Now, the IROC gives me the slope of the curve at any given day. This is very interesting now that we are hoping to see these accelerating death curves turn over and decelerate. In the table above, you can see the IROC for 3/30 as well as the Delta IROC which I’m defining (right now) as today’s IROC minus the IROC from 2 days ago. This metric gives us an indicator when the slope of the curve is decreasing.

By the way, looking at the table above, it’s giving us the indication for the first time that deaths from COVID-19 are starting to hit the heartland of America, a region that had been barely affected up until yesterday. The number of deaths is still small in places like North Dakota, Montana, Alaska, etc., but the fact that these states have moved to the top of the IROC chart indicate that they are now experiencing deaths. Previously states like Massachusetts, NY, NJ, WA, and Louisiana dominated the top of this table.

Example:

I found in the data today the example of the state of Delaware. See table below where I’m sorting from lowest Delta IROC to highest. I have been waiting for a suitable example of a negative Delta IROC.

Now see the time series chart below for Delaware and you can see what a Negative slope looks like. Even though this is just an artifact of the fact that Delaware has few deaths right now, this is the signal that we’re looking for in New York or Italy, or some other hard-hit region to give us the notion that the acceleration of deaths in the region has slowed and should continue to do so.

Conclusion: IROC is a good measure for us to see the slope of the death time series curve numerically. I found the example of Delaware, not by searching through time series graphs, but by looking at the sorted IROC numbers. We’ll continue to evaluate this as an important metric in trying to understand this outbreak.

Update: 3/29 saw large bursts of new cases in Cook County, IL (Chicago), Miami/Dade County, FL, Harris County, TX (Houston), and numerous NY, NJ, CT, and RI counties. Below we see the top states by delta instantaneous rate of change of deaths per 1000 persons. This is essentially the tangent of the curve. As we all suspect, these curves are still in their accelerating phases, so the IROC is a much better way to measure the severity of the situation than a linear fit (my old method). The delta IROC that the table is sorted by shows the change in the IROC over the last two days. As the situation gets further along, I will likely expand that to 4 days. Then we should have a number that will tell us when we leave the accelerating phase and move into the decelerating phase.

At this point, most of the data aggregators (including Johns Hopkins) have failed to keep track of the myriad of reporting organizations and have settled for less comprehensive data collections. So I have had to go off and decide which metrics are the most meaningful and aggregate them myself.

Because confirmed cases are so dependent on whether a country/state is testing and also because cases range from no symptoms all the way to stays in the ICU and even death, I have decided that confirmed cases are just a curiosity. In the chart above, you can see that NY has just over 2 confirmed cases per 1000 people. However, the number of deaths per 1000 people in NY is 0.02, 100x lower. Since hospitals must be required to report deaths (and since death is a fairly straightforward metric, whereas a confirmed case requires a positive test), I think this is a much better way to evaluate the severity of the outbreaks around the world.

The above chart makes the case (that I have been trying to document) that the ratio of deaths to cases is quite different in different parts of the world. However, there’s one more important measure that can also reflect on the severity, and that is the velocity and acceleration of this normalized death rate. The velocity over a one day period is easy to calculate. It’s just today’s normalized deaths minus yesterdays. The acceleration is the more useful number to understand, however, as it relates to how rapidly the problem is going to get out of control (or under control). This is because all of these outbreaks across the world appear to be increasing non-linearly. To understand what a non-linear process might look like, think about the old saying, “The Rich get Richer.” Because they’re Rich, they get Richer, and because now they’re Richer, they get even more Richer!

So here is a table showing the slope of the non-linear curve for today and the change in this slope over the last two days. Any of these countries or states with a positively changing slope is accelerating. Any with a negatively changing slope is decelerating (what we want!)

The countries that are accelerating the fastest (inst_roc_delta) are poor little Andorra, San Marino, Iceland, Spain, and then the trio of states NY, Vermont, and Louisiana. As you can see, even a small number of deaths in a country or state with a low population, can contribute to a big change in the instantaneous slope.

So… takeaway. Deaths in New York, Vermont, and Louisiana are increasing quickly, but are still well below the rates per 1000 people that we’re seeing in Spain, Italy, France, Iran, and even Switzerland (who is also well below the rates of those other hard-hit countries). The point may well be that things will eventually equalize across the world and these numbers will align. Or it may well be that some regions will remain lucky and will be up to 10x less hit with deaths than neighboring countries. It’s hard to tell right now, so we’ll keep watching.

Still wondering if the Latitude effect on COVID-19 is real or just coincidental. I have shown the below chart a few times. In it, you can see that over 90% of the world’s cases have occurred in the band between 30 and 60 N. Latitude.

I have noticed, however, another effect that is interesting. The cases in the more Northern region of this band (between 50 and 60 N. Latitude) seem to have similar numbers of cases, but with far fewer deaths. I looked through the data and built tables and charts to see if this observation was true. Below, you can see a simple bar chart with these results. All the numbers are normalized by 1000 population, which takes into account the fact that the population in the range from 30 to 40 degrees N. Latitude is just over 3x larger than the population in the range from 40 to 50 degrees. Therefore, this chart shows us that per 1000 people, the number of cases in both of these ranges is nearly equal (about .23 cases per 1000 people). HOWEVER, the normalized death rate in 30 to 40 is 3x larger than it is in 40 to 50 (or any other 10 degree range of latitudes for that matter). See the bar chart below and the table in the next block down if you prefer looking at numbers. I think these numbers tell us that — for now at least — this trend is real.

Why might this effect exist? It could be just coincidence… large numbers of countries with aged populations between 30 and 40 N. Latitude? Other factors that amplify the outbreak? Societal factors in the Northern latitudes that enable better social distancing? I have no idea, but am very interested to see if this trend holds.

Today’s numbers are out and we see a new spiking (small) country, San Marino. San Marino (SMR) is a small micro-country fully surrounded by Italy. It shares much of it’s culture with Italy, and is also near the Northern part of Italy where the COVID-19 outbreak started.

It is a very small country, with a population just north of 33,000. To date, they have 187 cases and 21 deaths. This results in nearly 5 active cases per 1000 people and 0.6 deaths per thousand. Their death to confirmed case ratio is 12%, which is extremely high.

The above chart also brings to mind the case of Iceland (ISL), who has one of the larger numbers for COVID-19 cases per 1000. Part of this is because Iceland has created a strategic sampling approach for COVID-19 so they can find out where it is hitting hardest and triage quickly. This article gives us more of the story too…

Fifty-six individuals have recovered from COVID-19, 9,013 individuals are currently in quarantine (681 are in isolation), 2,096 individuals have completed quarantine, and 15 individuals are currently in the hospital diagnosed with COVID-19, two in intensive care, and one in a ventilator. A total of 11,727 tests have been administered. Of those diagnosed with COVID-19 in Iceland, two have died.

This is interesting in light of the chart below, which shows that Iceland’s Confirmed Cases are equal to 70% of the number of hospital beds in the country. But from the data above, only 15 of the ~700 diagnosed people are in the hospital. Because Iceland was randomly testing, they seem to have been able to keep people in quarantine and out of the hospital. This is basically the opposite of the Italy and San Marino experiences. According to the San Marino ministry of health (big kudos to Googles Italian to English translator!), 41% of their confirmed cases are hospitalized (0.2% of their entire population). For comparison, Iceland’s rate of hospitalization is just 2.3% of their confirmed cases and 0.004% of their total population.

Conclusion: This might confirm the strategy of America’s CDC (at least their recent strategy) of “flattening the curve” to spread the infection out and keep the numbers low in the hospitals. But it also makes the STRONG CASE for randomized testing to identify and mitigate more quickly.

See article on LinkedIn with significant analysis and chart material.

Much of the results I’ve been showing in the last few days has been total counts of cases, deaths, etc., usually by country or state. Yesterday i decided that there’s probably enough data at this point to evaluate whether all the counts should be normalized by the country’s population.

Reasons for doing this are probably obvious… we saw a large spike in cases quickly in Hubei Province in China and then later saw a huge spike in cases in Italy. At some point last week Italy passed China in number of counts of cases, but was that really the most interesting measure? Since Italy has a much smaller population than China, the outbreak in Italy per 1000 people living there was much, much higher.

Here are the rankings (minimum population of 5 million) after being normalized for population.

Now comparisons can be made that are more relevant. Note that Italy and Switzerland have nearly the same number of Active Cases per 1000 population but Italy has about 10x the number of deaths. Why is this? I look across the blended statistics for each country that I’m using to do COVID severity correlations and I see only two things that are really different. 1) Switzerland has over 1 more hospital bed per 1000 people than Italy and 2) Switzerland has a significantly lower number of people over 65 than Italy. Both of these together might make sense.

Here’s my updated Correlation Chart – Now the Slope of the Confirmed Cases is done on Confirmed Cases normalized by population.

Factor	Correlation with Slope (normalized by pop.)
femaleSmokingRate	26.93%
Over 65 Population – %	22.38%
Mean_BMI_male	17.00%
Population Density	8.70%
totalSmokingRate	6.40%
STD_BMI_female	3.88%
IncomeGroup	-1.06%
hospital_beds	-1.56%
STD_BMI_male	-1.96%
Mean_BMI_female	-3.09%
2019 Diabetes – % of pop.	-5.89%
HIV – % of pop.	-7.64%
Diabetes growth in last 10 years	-8.02%
Population Growth Rate	-8.76%
2019 Population	-9.42%
Tuberculosis – % of pop.	-12.21%
maleSmokingRate	-12.50%
Area of Country – sq-ft	-13.11%
2020 Population	-13.59%

How do I capture this slope? I fit a linear regression line to the data after a country hits 50 cases (arbitrary – I’ve seen others use 100). I then take the slope of the fitted line and project that as the rate of increase of confirmed cases for that country. Of course, most of these outbreaks are non-linear, but it’s simpler to fit a line than a curve, so I believe it makes sense to approach the problem this way. Regardless, this slope is a measure of how severe the outbreak is. Now that I’m using normalized data, I think it’s more relevant and better reflects the amount of pressure COVID-19 is putting on a specific country and its population.

Lots of discussion could be had on the correlated factors and why they’re positively or negatively correlated with this COVID-19 pressure. Feel free to weigh in.

I saw a chart a while back that predicted the cases/deaths by latitude. They plotted it over the world map and had colorbands describing COVID-19 potential risk. Something like that… But based on the amount of data we have, that’s a pretty wild, probably overfit, prediction.

Here’s what we DO know about cases by latitude. This chart shows total confirmed cases and deaths stacked on one bar (light blue+red) and current (yesterday) reported cases and deaths stacked on a second bar (green+dark orange).

Takeaway: Most of the cases have occurred between 30 and 60 degrees latitude. Around 40-45% of the world’s population does live in this belt, of course. But we have 92.5% of the cases in this range!

Any ideas why??

I’m entering this late on 3/20 because most of the world’s data is already in. Some interesting things to discuss. First off, we saw a huge spike in Active cases in NY on 3/20. I can only hope that this spike is an anomaly and that we won’t see more like it in the US. You can see this in the bar chart showing change in the last 24 hours, but also in the time series chart immediately following. While we may have hopes that Washington and New Jerseys outbreaks MIGHT be slowing, it is clear that NY continues to accelerate.

As for the rest of the world, you can see in the chart below that Italy continues to accelerate as well. They announced around 6K new cases yesterday and over 600 new deaths. France and Spain also announced ~200 new deaths. One bright spot as an American, though, is that New York’s death rate is extremely small compared to the number of cases. When normalized by the total number of cases, it is far below that of the large European countries and even smaller ones like Switzerland.

Finally, here’s something interesting to watch. I’m looking for any country at all that might be recovering from their initial outbreak. I’ll be watching Japan for the next week or so to see if their recovery cycle-time matches the ~20 days that we saw in the Hubei province data. That might become really interesting data. Note that around the 200 case mark, we see the horizontal distance between the Confirmed line and the Recovery line is now measurable (looks like roughly 22 days. If the recoveries accelerate, then we may see a consistent 20-25 day cycle-time eventually.

There’s not a lot new in today’s data, other than continued increases in confirmed cases and deaths (primarily in Europe). I’ll update the maps and one or two of the charts here. I’m also continuing to work on the correlation effort I posted about in a previous entry. That will improve as the data improves (i.e., more testing).