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As Covid-19 spreads throughout the world, we need a method to learn from the daily death counts from each geography (countries, states, counties, and cities) and be able to know when we have reached the apex or peak of the “curve”. We are focusing on deaths because currently the number of confirmed cases is a product of the testing strategy in each area). As with all measures, we don’t want to overreact to common cause changes in the number of deaths each day.

Epidemiologists would use a logistic function to model this growth phase of an epidemic, so we should try to approximate that model. Analyzing logarithms of the death count data does this. Our approach is to develop Shewhart charts base on regression of logs of death counts, transformed back to count scale
Here are the steps we have used in the TEMPLATE
1. Use daily count data from your geography
Countries: Our World in Data for countries.
US States: New York Times database on GitHub.
Or use local data you have available.

2. Select start data as day when the first death occurs and end with most recent data available. Need at least 8 days with deaths to get a reasonable chart.

3. Transform the counts using log10 function (log of 0 is not defined, so has to be positive numbers)

4. Calculate the intercept and slope (regression analysis) for the log10 data series. Use to calculate a center line for the chart base on the regression line.

5. Develop a Shewhart I chart using the regression center line and the residuals from the CL

6. Transform the Centerline, upper limit, and lower limit back to the count scale (extending to future dates)

7. Plot control chart with original counts and the transformed CL and limits.

8. The chart will approximate the logistic function for the growth period of the death curve.

9. A special cause below the lower limit is an indication that the growth period has ended and this country has reached the peak in the number of deaths.

Here is are two example charts (US through 4/2 and New York through 4/1.

These charts were recently featured in two US News and World Report articles focusing on countries and U.S. states.

Try this out and share the chart with others in your community.

 National Public Radio’s  “All Things Considered” program on May 7, 2018, discussed the conditions in Puerto Rico since Hurricane Maria, focusing on the emotional detriment of survivors:

“Indeed, the overall suicide rate in Puerto Rico increased 29 percent in 2017 over the previous year, with a significant jump after Hurricane Maria, according to the Puerto Rico Department of Public Health. And that anguish is continuing”.[i]

FiveThirtyEight’s “Significant Digits” newsletter picked up the NPR report on May 9:

“29 percent.  Puerto Rico still has areas contending with terrible living conditions following Hurricane Maria and the lackluster response to the storm from the mainland United States. Even the deadly effects of the storm are far from over: With many still living without power or their lives otherwise disrupted, particularly elderly populations, the overall suicide rate in Puerto Rico increased 27 [sic] percent in 2017 compared to 2016 levels.”[ii]

In the wake of the hurricane, stories about a “significant jump” in suicides tend to resonate with those of us who are sympathetic to the plight of all Puerto Ricans impacted by the disaster and its interminable aftermath. But the seemingly compelling statistic presented – a 29% increase in the overall suicide rate from 2016 to 2017 – misses the point when presented alone. The stories fail to take into consideration historical variation in suicide rates. What insights might we gain from applying Shewhart’s theories and methods to understand variation over time? The 29% increase reported by NPR and FiveThirtyEight is based on historical Puerto Rico Department of Health data on population and the number of suicides reported during 2000—2017.[iii]  I used these same data to create a U-chart, displaying the rate of suicides per 100,000 population:

This chart shows an average rate of 8.2 suicides for every 100,000 residents in twenty-first century Puerto Rico. Seen also are a number of signals of special cause variation in the suicide rate: 

 -       6.8: below the lower control limit in 2002,

-       9.5: two out of three observations near the upper control limit in 2009 and 2010,

-       and 5.8: below the lower control limit in 2016. 

Studying factors impacting the suicide rate during these three time periods could reveal key insights. Conclusions about the 2017 result could be judged relative to their coherence with this history. Note that the 7.6 rate for 2017 is common to the historic system in Puerto Rico. The “29% increase” reported is mostly due to the effect of the unusually low rate in 2016. 

Analyses of single data points are easily abused. Headlines based on single data points are easy to write. Statisticians and other data analysts have a responsibility to produce interpretations that go beyond the single data point. A contribution that NPR could make would be to report on the reduction in the suicide rate that occurred in 2016 and how to maintain that low rate, which likely would be a combination of factors, perhaps one of them being better response to hurricanes.

Provide examples and discussion for applying Shewhart's and Deming's ideas for understanding variation as described in the article:

 http://www.apiweb.org/images/PDFs/understanding-variation26-years-later.pdf