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I'm looking at plotting county coronavirus case density growth rates (moving 7 day window) and am finding that when cases first appear the new case growth rate is very large due to the fact that there are only a few cases and a few more cases can double or triple the totals causing spiking growth rates until more cases appear. When a county gets it's first handful of cases, the growth rate jumps. This causes every county to show a large peak early and once a significant number of cases appear the growth rate settles down. Is there a name for this? I'm hoping I'm getting my point across.

Let me further explain my methods based on Alexis comment. I have a set of case totals by date for every county in the US. I'm taking those case totals and creating a case density using county population information. Once I have that, I have case density numbers for every county for every day since the counties first infection. In order to identify case density change I've created a moving 7 day window that looks at the weekly change in case density and calculate a growth rate on these numbers. My ultimate goal is to plot the case density growth rates by county for every day but that creates an very noisy series that is affected by the timeing of test results. So I applied a 7 day moving average to this series.

Is there a statistical method that I can apply that would mute the effect and not show large growth rates early when there are only a handful of cases to work with? I'd consider dropping some of the early dates in the series for each county but hoped not to lose any data. It may be my only hope but how do I apply it to all of the counties in the use when each one has different case totals.

Any help would be greatly appreciated. I'm trying to visualize this on a map and keep it simple but my current visualization is quite noisy.

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    $\begingroup$ Compare incidence rates (specifically incidence proportions), not counts of incident cases in absolute terms. $\endgroup$
    – Alexis
    Commented Jul 15, 2020 at 6:20
  • $\begingroup$ Actually I mis-wrote. I'm not comparing case totals I'm comparing case density (per 1000 of population) change in the 7 day window. I think waiting to display the growth rates until the case totals reach 20% of the current cases might be the best I can think of so far. $\endgroup$
    – jport
    Commented Jul 15, 2020 at 14:11
  • $\begingroup$ You should edit your answer to incorporate an explicit mathematical definition of your measure. (I am suspicious that what you are calling case density is not, but need to see the details). $\endgroup$
    – Alexis
    Commented Jul 15, 2020 at 16:27
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    $\begingroup$ The problem is probably that you're looking at change in terms of a ratio when a difference would be more cogent. $\endgroup$
    – AdamO
    Commented Jul 15, 2020 at 19:26
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    $\begingroup$ You are not creating a case density, put an incidence proportion, since each individual in the population at risk is contributing the same amount of time to your number. $\endgroup$
    – Alexis
    Commented Jul 16, 2020 at 1:49

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