We keep hearing that Covid-19 cases may be rising but the death rate is dropping. This is usually supported by appealing to the trends of cases and deaths. Here is an example for the state of Illinois:
Both cases and deaths are expressed as index values relative to April 1st so they can be directly compared. If you pick a date and compute the death rate as deaths divided by cases, the graph above seemingly shows a declining death rate.
While we all wish this to be true, it is too good to be true. The simple analysis described above ignores the timing of deaths. Typically, someone who dies from Covid-19 does not die on the same day s/he gets diagnosed. Death may come up to a month or longer after the positive test. Take the deaths from December 1st. These patients likely tested positive mid October to mid November. So to compute the death rate, we should divide by cases from about a month ago, not the cases from December 1st.
Notice that cases surged in November, and most of those infected won't show up in mortality counts until December. If we divide deaths on Dec 1st by cases on Dec 1st, the surge of cases is what drives the death rate down. The declining "death rate" is less due to lower deaths but fast-growing cases.
A clearer analysis requires dividing deaths of each day by the cases from about 20 days ago. I described how this is done back in April in this post about Lombardia in Italy. Today, I apply this methodology to current data for the states of Illinois and Iowa.
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In Illinois, the lag between cases and deaths is around 25 days.
The thin gray line is the same line as in the first graph. Here, I lag it by 25 days, shifting the curve to the right. Doing so matches the deaths from one week with the cases from 25 days ago. You can see the matched dates on the bottom axis.
Both lines start at 100 on July 1st. You can see that deaths pretty much follow the shape of the trend of cases. This indicates that the chance of dying from Covid-19 given that one has tested positive has been relatively stable during these many months.
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In Iowa, the lag between cases and deaths is around 17 days.
A similar picture emerges.
It's difficult to compare state-level statistics because each state has its own set of rules for reporting. Also bear in mind that all dates are reporting dates, and don't necessarily reflect the day of infection or the day of death. So the error bar around the exact time of lag is pretty wide.
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