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# Hospitalizations-to-Cases Ratio Clarifies Climb in Deaths

With hospitalizations climbing, the COVID-19 crisis is clearly escalating. This blog earlier presented an analysis which estimated the time lag between a positive test result and resulting hospitalizations at about 12 days. This post will use that, plus an analysis which computes the ratio between cases 12 days ago and current hospitalizations, to estimate the likely relationship between those two numbers. This will allow us to estimate the numbers of those hospitalized yet to come, within the next 12 or so days. The data used here is from covidtracking.com, collected on Dec. 4 2020.

The red line uses the daily cases data and daily hospitalization numbers, and thus shows the typical up-and-down weekly cycle.

The blue line divides the 7-day average of hospitalizations by the 7-day average of daily new cases. This smooths the line, but also tends to underestimate the actual level present in the last <= 6 days. For the most part, there is a steady relationship between these two numbers, oscillating around the 80% mark until late October: the current observed hospitalization numbers tended to be about 80% of the number of cases observed 12 days ago. A marked decline is apparent in the final two weeks of data on the right side. One possible reason for this is that, warned by doctors to do so, many Americans may have taken COVID-19 tests who would not otherwise have done so. If these turned up additional numbers of asymptomatic or nearly asymptomatic COVID-19 positive test results, the increase in the denominator would have the effect of reducing the resulting ratio. Some of these positive test results may have also identified COVID-19 cases earlier than they would otherwise have been recognized, resulting in a longer lag between the results numbers and the resulting subsequent hospitalizations. In order to estimate a ratio to be used in predicting the near future, two periods were used. A months' worth of data from October 20 through November 20 yielded an average ratio of 74.96%. This is slightly below the average ratio over the entire period since August 18, which was 76.56%. In order to err on the conservative side, we will use the 1-month period before the Thanksgiving week, 74.96%, for the first estimate. If this number is a realistic stable estimate of the hospitalizations we should expect on a 12-day lag, then multiplying this number times the most recent 7-day average of daily cases, 173,404, yields a prediction that in about 12 days we should expect to see about 130,000 hospitalizations. For an even more conservative estimate, we use the most recent 1 month's worth of data, from Nov. 3 to Dec. 3, which gives an average ratio of 66.05%. Multiplying that number times the same most recent 7-day average of daily cases, 173,404, yields a prediction that in about 12 days we should expect to see 114,539 hospitalizations -- a number also far above the most recently observed 7-day average of hospitalizations, which now stands at 95,867. With medical personnel already reporting that their resources are stretched to the limit, these are disturbingly large increases, and they are arriving very soon. We can use a similar technique to cross-check against expected deaths as a result of current hospitalizations. Previous analyses in this blog estimated an 18-day lag between cases and deaths, and a 12-day lag between cases and hospitalizations, so to be consistent we will use a lag of 6 days between hospitalizations and deaths. This is somewhat shorter than the estimates of medical experts, who have cited 10 days instead. We will stick with 6 days for the sake of consistency. Notice that during a period of increasing numbers, as we are in now, this has the effect of producing a lower ratio and therefore more conservative estimate. Over the period from Oct. 20 to Nov. 20, the average ratio of deaths divided by hospitalizations on a 6-day lag is 2.06%. Multiplying this ratio times the most recently observed 7-day average of hospitalizations, 95,867, we can expect to see a 7-day average of deaths of 1,971 daily deaths six days from now. The current 7-day average of deaths is 1,781.

Given the currently skyrocketing numbers of new daily cases, hospitalizations, and deaths, we should not be surprised to see this unfortunate prediction fulfilled.

All opinions expressed in this blog are solely those of the authors, and do not reflect those of University of Texas Rio Grande Valley, or any organizations of which either is a member.

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