I am a psychologist interested in getting a single number to quantify "flattening the curve"---one value for each of 50 geographical areas (states) in the USA. For my purposes, I want to know which states are doing a better job of "flattening the curve". Perhaps epidemiologists or biostatisticians could help. Not interested in qualitative analytics--just need a number for each state (or, better still, a formula that can be applied to each state). Thanks.
Hi Nicholas,
I am not an expert in infectious disease modeling, but let me take a crack at your question. Fist, let's understand what the "curve" is that we are trying to flatten. It is the curve of incident cases versus time. On the Y-axis you plot the number of new cases each day. On the X-axis is the time (in days) since the first case. So, you may see that the curve keeps rising, reaches a peak at a certain time, and then (hopefully!) starts to fall. Suppose there are two strategies to fight the spread of infections: (1) you do nothing and maintain status quo, (2) you implement a total lock down. We can compare the incidence curves under these 2 scenarios. There are different metrics one can use to compare. For example, I can think of two reasonable measures: (1) area under the curve over the same time period, say, over a 6-month period since time zero, and (2) time to attainment of a low number of incident cases. You may pick a strategy that either has a smaller area under the curve; or the strategy that has a faster time to attainment of low number of incident cases.
Flattening the curve can be quantified by estimating the "dispersion" or the standard deviation of the incidence curve. A flatter curve would have a larger dispersion. The two metrics that I described above are not directly related to the notion of flattening the curve. Of course, it is possible to have a flatter curve with a larger area under the curve or with a slower time to attainment of low number of cases.
One important note: the idea of flattening the curve is essentially counterfactual. In reality, you can only observe one incidence curve for each state or country. Hence, flattening or comparing different curves is simply a theoretical modeling exercise, unless you can randomize the population to different containment strategies.
I hope this is helpful.
Best,
Ravi
Fit a polynomial regression to cases vs time with a satisfactory Rsq and take 2nd derivative (rate of change of slope)
Hi Nicolas,
A number you could use on your way to obtain a single number per geographical state is the “time-dependent infection rate” (Rt), described in https://www.medrxiv.org/content/10.1101/2020.02.27.20028928v1.full.pdf. Note that you can calculate such a number for each time point in the epidemic. The plot of this number over time is what I think you are interested in, to compare these plots between states. I’m guessing there are several ways to reduce the obtained “time-dependent infection rates” (Rt) into a single number for each state. The simplest example I can think of is fitting a model (linear/nonlinear) to Rt based on time. Such a model can also be used to make predictions into the future (I did some simple analyses on the South African epidemic some days ago, I will include the plots as attachments. Note that my forecast is a bit on the low side, possibly due to some of the issues described below).
There are several things to consider in when trying to see which states do a better job of “flattening the curve”:
1) Each of the states has a different time at which they had their first imported case and a time at which local transmission started.
2) In the early stages of the epidemic in the different states, there will be a large number of imported cases; this number can also differ between states. I suppose the “flattening the curve” bit is relevant at the point in time when there is mostly local transmission.
3) Covid-19 levels are mainly driven by testing. If testing differs between states or changes over time, that could make your comparison difficult.
4) Efforts to "flatten the curve" have a delayed effect
5) There are probably more things to consider
*Note to the included plots, you can only calculate Rt for the maximum time for which we have notified cases-1 (which is why the Rt plot runs until t=21, whereas we have data in the cumulative cases plot up until t=22).
My first thought is that you could look at the change in spatial concentration of the disease in a given geographic region. Then, construct some metric based on time to compare between geographic regions.
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