ELY/rona

The population of a country shifts over time. Here’s how the population distribution of the United States changed from 2000 to 2010:

There’s a noticeable population bulge from Boomers (born ’46-64, age 36-54 in 2000). For more up-to-date numbers, the Census Bureau helpfully provides a projection estimating the distribution for 2020.

The CDC also provides statistics about yearly influenza burden, with impact bracketed by age group.

Confluenza

We can combine the two data sets to determine not only how many lives are lost due to influenza, but how many expected years of life (ELY). As before, a government agency has relevant data. Finally, we might ask the value of a year of life (often called a Quality-Adjusted Life Year, or QALY); this figure varies by country but a reasonable ballpark figure is $100,000.

We can combine these data sources to estimate the “cost” of a disease. For the yearly influenza season, the numbers come out like so:

Flu::
across pop at age  3, est.    81 deaths (IFR = 0.00399%)
across pop at age  7, est.   106 deaths (IFR = 0.00529%)
across pop at age 12, est.   157 deaths (IFR = 0.00759%)
across pop at age 17, est.   219 deaths (IFR = 0.0104%)
across pop at age 22, est.   289 deaths (IFR = 0.0132%)
across pop at age 27, est.   377 deaths (IFR = 0.016%)
across pop at age 32, est.   433 deaths (IFR = 0.0189%)
across pop at age 37, est.   541 deaths (IFR = 0.0247%)
across pop at age 42, est.   638 deaths (IFR = 0.0313%)
across pop at age 47, est.   760 deaths (IFR = 0.0378%)
across pop at age 52, est.   911 deaths (IFR = 0.0444%)
across pop at age 57, est.  1110 deaths (IFR = 0.051%)
across pop at age 62, est.  2076 deaths (IFR = 0.0988%)
across pop at age 67, est.  3218 deaths (IFR = 0.178%)
across pop at age 72, est.  4516 deaths (IFR = 0.306%)
across pop at age 77, est.  5383 deaths (IFR = 0.535%)
across pop at age 82, est.  5974 deaths (IFR = 0.918%)
across pop at age 87, est. 11404 deaths (IFR = 2.89%)
across pop at age 92, est. 14633 deaths (IFR = 7.25%)
total est loss of 52826 lives, 0.575e6 ELYs lost ($57.48 B)
est whole-population IFR: 0.16%

This is mostly a sanity check, and it looks reasonable, within a factor of two or so from a regular flu season (just barely worse than 2014-2015; about twice as bad as 2015-2016). For what it’s worth, two aspects of the model go beyond direct cross-correlation of data. First, the model estimates a flat 10% infection rate; in reality, rates usually vary between 10% and 20% in different age brackets. Second, the relatively coarse granularity of the CDC’s data would lead to sharp discontinuities in mortality rates between brackets. Another CDC data set provides finer granularity of information for people aged 65+, showing that each decade of age brings a threefold risk from flu. The model uses piecewise linear interpolation to estimate mortality at specific ages.

COVIDity

By changing the fatality rate model to use numbers from South Korea (as of 2020/03/18), we can make an estimation of the likely impact of one full year’s worth of coronavirus circulation. The model does not account for hospital capacity limits (which would raise the effective IFR and thereby the number of deaths) or the lack of population/vaccine-derived immunity (which would raise the population infection rate) or the effect of social distancing (which we assume reduces the population infection rate and thereby the number of deaths).

Coronavirus::
across pop at age  3, est. 0 deaths (IFR = 0.0%)
across pop at age  7, est. 0 deaths (IFR = 0.0%)
across pop at age 12, est. 0 deaths (IFR = 0.0%)
across pop at age 17, est. 0 deaths (IFR = 0.0%)
across pop at age 22, est.   218 deaths (IFR = 0.01%)
across pop at age 27, est.  1175 deaths (IFR = 0.05%)
across pop at age 32, est.  1838 deaths (IFR = 0.08%)
across pop at age 37, est.  1753 deaths (IFR = 0.08%)
across pop at age 42, est.  3677 deaths (IFR = 0.18%)
across pop at age 47, est.  3618 deaths (IFR = 0.18%)
across pop at age 52, est.  7793 deaths (IFR = 0.38%)
across pop at age 57, est.  8273 deaths (IFR = 0.38%)
across pop at age 62, est. 28785 deaths (IFR = 1.37%)
across pop at age 67, est. 24701 deaths (IFR = 1.37%)
across pop at age 72, est. 35716 deaths (IFR = 2.42%)
across pop at age 77, est. 52979 deaths (IFR = 5.27%)
across pop at age 82, est. 44709 deaths (IFR = 6.87%)
across pop at age 87, est. 33357 deaths (IFR = 8.46%)
across pop at age 92, est. 18677 deaths (IFR = 9.26%)
total est loss of 267269 lives, 3.44e6 ELYs lost ($344.2 B)
est whole-population IFR: 0.81%

I find these numbers believable: roughly the logarithmic midpoint between a standard flu season and predictions of millions dead. The difference in impact on “lives” versus “life-years” is moderate but noticeable (5x vs 6.9x). This reflects the disproportionate effect that coronavirus appears to have on those in their 70’s, relative to the flu. As usual, a chart makes the numbers more striking:

The differences are due to the measured fatality rates. Due to the small tallies, the linear scale obscures what’s happening in younger cohorts. Using a logarithmic scale reveals the data:

We can also look at the IFR directly, without scaling by subpopulation sizes. This reveals some artifacts of the estimated IFR. For example, the South Korean data is segmented by decade, so each decade at or below 60 gets the same data, visible as a stair-step pattern. Estimated rates for higher decades were linearly interpolated to produce a more realistic curve. My takeaway from this chart is that the estimated IFR for age 62 should be nudged down.

Contamsion

Stepping back: One sketchy thing going on here is the blurring of “infections” versus “cases”. Should we be concerned that the numbers for coronavirus are biased by preferentially testing those with severe cases?

The CDC estimates that for influenza, only one third of symptomatic illnesses result in medical visits, and only 5% or so of medical visits are severe enough to result in hospitalizations. The ratio of deaths to hospitalizations is about 7.6%; the ratio of deaths to infections is about 0.13%, and the ratio of hospitalizations to infections is about 1.65%.

South Korea has done 274,000 tests finding 8,565 confirmed cases, of which 1.7% are now serious, critical, or dead. This may suggest that their testing has been broad enough to not be massively distorted by oversampling severe cases. (I don’t know offhand how many serious cases eventually recovered).

In contrast, Italy has had 35,713 confirmed cases, of which 14.6% are currently serious, critical, or dead.

Balancing Act

Leaders in the USA and other countries are deciding how to balance public health against economic pain. China’s numbers suggest that economic stasis can slow the infection. At what point does economic harm take precedence? The two are closely linked, especially in places with weak social safety nets; recessions bring lost jobs, homelessness, stress, anxiety, depression, etc. When health insurance is linked to employment, a recession means that society must pay for a pound of cure instead of an ounce of prevention.

The analysis above suggests that the “cost” of the flu (in life-years, not hospital bills or other expenditures) is about $60 billion/year in the United States, and the projected “cost” of the coronavirus would be on the order of $300 billion. These are not trivial numbers, to be sure, but for context, tax revenue for fiscal year 2017 was $3.32 trillion. On this basis, it might make sense to endure economic turmoil equating to a few weeks worth of tax revenue, but not much more/longer than that.

(edit 2020-03-19: Two UC Berkeley economists suggest having the government be payer of last resort to avoid mass unemployment. They estimate a hit to GDP of 7.5% per quarter, i.e. about half a trillion dollars per month, due to the direct economic fallout of social distancing, and estimate that the government’s preventative costs would be half that. Ray Dalio thinks that corporate losses will top $4 trillion.)

(edit 2020-03-20: To clarify, the point of this last section is not to suggest that an amelioration should be rejected because it is strictly more costly than one particular alternative projection. Obviously, there is room for reality to diverge from the above model by at least an order of magnitude. The point is to acknowledge the uncomfortable traffic between dollars and life-years, and use it as one lens through which to see the world.)

Dessert

I admit, it’s a bit bananas to compare apples and oranges like this. But… fruit salad is delicious.

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