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I hope someday I won’t feel compelled to write or worry about the coronavirus. However, as the pandemic wears on, it seems to take only a few days for issues to pile up, and I just can’t resist comment. Today I have a couple of beefs with uses of data and concomitant statements I’ve seen posted of late.

People are still quoting case fatality rates (CFRs) as if those cumulative numbers are relevant to the number of deaths we can expect going forward. They are not. Just as hair-brained are applications of cumulative hospitalization and ICU admittance rates to produce “rough and ready” estimates of what to expect going forward. Or, I’ve seen people express hospitalizations as ratios to CFR, as if those ratios will be the same going forward. Again, they are not. Let me try to explain.

The chart below shows the course of the U.S. CFR since the start of the pandemic. It’s taken from the interactive Covid Time Series site. My apologies if you have to click on the chart for decent viewing (or you can visit the site). The CFR at any date is the cumulative number of deaths to-date divided by the cumulative number of confirmed cases. It is a summary of past history, but it is not well-suited to making predictions about death rates in the future. The CFR began to taper a little before Memorial Day, and it is now at about 4% (as of July 13).

Out of curiosity, I also generated CFRs for AZ, CA, FL, GA, and TX, which now average about half of the national CFR. There’s an obvious lesson: if you must use CFRs, understand that they vary from place to place.

Again, CFRs are cumulative. Their changes over time can tell us something about recent trends, but even then they are flawed. For example, case counts have risen dramatically with more widespread testing. Those testing positive more recently are concentrated in younger age cohorts, for whom infections are much less severe. Treatment has improved dramatically as well, so there is little reason to expect the CFR’s of recently diagnosed cases to be as high as the latest CFRs shown above.

There is no easy way to calculate an unflawed “marginal” CFR for a recent period, though an effort to do so might improve the predictive value. Deaths lag behind case counts because the progression from early symptoms to death can take several weeks. Even more vexing for constructing a valid, recent fatality rate is that reporting of deaths is itself delayed, as I explained in my last post. Each day’s report of deaths captures deaths that may have occurred over a period of several weeks in the past, and sometimes many more.

Finally no CFR can capture the true mortality rate of the virus without ongoing, ubiquitous testing. As the state of testing stands, the true mortality rate must reflect undiagnosed cases in the denominator. The CDC’s latest “best” estimate of the true mortality rate is just 0.3%, and 0.05% for those aged 50 years or less. Those figures are based on serological tests for the presence of antibodies to C19 in more random samples of the population. Those findings reflect the extent of undiagnosed and/or asymptomatic cases.

The point is one shouldn’t be too blithe about throwing numbers around like 4% mortality based on the CFR, or even 1% mortality as a “nice, round number”, without heavy qualification. Those numbers are gross exaggerations of what we are likely to see going forward.

The same criticisms can be leveled at claims that hospitalizations will proceed at some fixed ratio relative to diagnosed cases, or some fixed ratio relative to deaths. Again, new cases tend to be less severe, so hospitalizations are likely to be a much lower ratio to cases than what is reflected in cumulative totals. Because of improved treatment, the ratio of deaths to hospitalizations will be much lower in the future as well.

CFRs are not a useful guide to future COVID deaths. The true mortality rate is a much better baseline, particularly for subsets of the population matching the current case load. Finally, and this is the only disclaimer I’ll bother to provide today, we all know that suffering is not confined to terminal cases, and it is not confined to the hospitalized subset. But don’t exaggerate the extent of your preferred interpretation of suffering by applying inappropriate cumulative calculations.