COVID-19 Risk and Incidence

Recent case incidence is useful for estimating risk.

In these days and months of COVID-19, we wonder about risk. When I go out in public, what is my risk? The answer in part depends on prevalence: How many people in my area are infectious?

In the United States, we don’t have an adequate testing program, and we don’t know how high the prevalence is. What we do know is case incidence–the number of cases found today and in recent days. These counts are often listed in news sources or displayed like this:


The graph is a bit cluttered, and it’s not obvious what to do with the information. The daily counts fluctuate with day of the week reporting and other factors that carry little information. Most of these graphs include a curve that is a moving average of the daily counts to smooth out these fluctuations.

The case counts go up and down, but what does that tell us about current risk? The experts at Harvard Global Health Institute have developed a framework that adds context. It categorizes COVID-19 risk level as Green, Yellow, Orange, or Red based on daily case count per 100, 000 people.

For our use, it is valuable to combine the smoothed daily case count with this risk scale. COVID Action Network provides graphs that look like this:

CAN exampleThe stylish color change in the curve would delight data visualizers. Unfortunately it is likely to take too much cognitive effort for other viewers. Something simple and bold is probably better.


Prediction bias

“Predictions are hard, especially about the future.” Often attributed to Yoga Berra, it appears that the original author is unknown. ( Nonetheless, this statement is clearly true.

This graph of world GDP growth contains 42 predictions, almost all too high. This consistent prediction bias does not happen without incentives. The outcome is so consistent that its presenters must believe that optimism is more important than accuracy.

The graph is drawn to show that the 5 year predictions are all 4.5+, when the reality is usually about 3.5. In some cases even the one year predictions are significantly high.

Another way to look at the data is to observe the predictions that are made in any one year. That is to read the graph vertically rather than following the lines. This is another way to see that the predictions for farther in the future are more optimistic.

Including predictions and actuals for years before 2011 would be interesting, even if the graph still begins with 2006. Similarly it would be interesting to see if predictions for years beyond 2017 are still so optimistic.

Source: The predictions were developed by the International Monetary Fund (IMF) and published in their semi-annual World Economic Outlook.

Showing changes

Europe is decreasing CO2 emissions. The United States not so much. And the Europeans will find it difficult to meet their Paris treaty commitment. [The Economist July 8, 2017]

The accompanying chart is relevant but murky.

The chart baseline is 1997, but the treaty reference is 1990. There appears to be little difference between the EU and the US on this scale. China appears to have a huge output but is not mentioned in the article.

Charts that show percent changes from a year are common in finance but can be questionable. Why was that year chosen? Is it representative? Are the series close enough in scale that the comparison makes sense?

The data look like

This graph makes it clearer that the EU is decreasing emissions faster than the US. Also China is clearly not going to achieve a 40% reduction from 1990, but its output is only about twice the US—rather less dramatic than suggested in the original chart.

Data from

Statistics Explained ( – 16/06/2017 and

Source: Boden, T.A., Marland, G., and Andres, R.J. (2017). National CO2 Emissions from Fossil-Fuel Burning, Cement Manufacture, and Gas Flaring: 1751-2014, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, doi 10.3334/CDIAC/00001_V2017

A sketch can work

A graph can be good without being dry and sober.

This one has the character of a rough sketch. Yet it communicates better than plain words and has more emotional resonance than a polished graph would. Even without refinements, we have an expectation of how to read a time series plot that works for this example.

The grapher is Charles Hutton, and he’s a hoot.

Interestingly Charles Hutton is also the name of the man credited with inventing contour plots in 1778.