# Why do they use the death number per million?

Why do they calculate the number of death per million in https://www.worldometers.info/coronavirus/. Is it to make the results comparable? given that canada has a smaller population than the USA?

If we want to compare canada and the USA: the death per million for canada is $$236$$ whereas it's $$456$$ for the USA for the covid mortality rate. So on that rate Canada is then better than the USA. But if we divide $$\frac{nbdeath}{totalnbinfected}$$ then the USA then has a lower death rate.

The number of deaths per million essentially gives an estimate of the likelihood of death attributable to coronavirus in the overall population, normalizing the number of deaths to the population of a country (note this only counts death attributable to coronavirus, as it cannot count undiagnosed cases). Countries with larger population will naturally have more deaths, so dividing by the population makes these numbers comparable. The number of deaths divided by the number of infected essentially gives the likelihood of death in the diagnosed population only. Note that how cases are diagnosed can have a big impact on these figures, since these numbers will tend to be high when few tests are done and only severe cases are diagnosed, and will tend to fall as testing becomes widespread and less severe cases enter into the denominator of the "diagnosed population".

Overall, these statistics show that over the course of the pandemic so far, a random Canadian would have been less likely to die from diagnosed coronavirus than a random person in the US, since their deaths per million are lower. On the other hand, a random Canadian diagnosed with coronavirus would have been more likely to die than a random person in the US who was diagnosed, since they have a higher ratio of deaths per case. (I've updated this section to focus on diagnosed individuals rather than infected individuals, since we do not know the true number of infected individuals at any time.)

Do note that there are lots of complexities surrounding how different countries/region count coronavirus cases and deaths. It's certain there are more cases of coronavirus than confirmed by a test, but all these stats can measure are reported, confirmed cases and death. The pandemic is also ongoing, so deaths will naturally lag cases by a few weeks, meaning that these stats do not count people who are currently infected and will die, but have not yet. Overall, the current case fatality rate may not accurately reflect the true mortality rate of an ongoing pandemic, although it will generally become more accurate over time.

• Using "likely" overstates the meaning of these statistics. You would be on firmer ground characterizing them as summarizing what has happened rather than as a risk or likelihood.
– whuber
Jul 28, 2020 at 18:25
• @whuber True, past performance does not indicate future results - since these are total figures over the whole pandemic, it may not accurately represent death rates today and in the future due to changing testing, treatment, and prevention measures. I've couched the language a bit to be strictly backwards-looking. Jul 28, 2020 at 18:28
• By continuing to characterize these statistics as "likelihood of death," either in the overall population or the infected population, you still mischaracterize them. Even if the death rates were constant over time (which they are not), these statistics probably underestimate actual likelihoods or rates because not all the deaths attributable to Covid-19 in any population have yet occurred or been recorded.
– whuber
Jul 28, 2020 at 19:07
• @whuber Likelihood is a legit term for retrospective observational studies.
– user289381
Jul 28, 2020 at 19:34
• @ping maybe, but it's inappropriate here: this is not a study. These are survival statistics and characterizing them as "likelihoods" or even estimates of likelihoods is incorrect. After your comment, Sergio posted an answer explaining some of this.
– whuber
Jul 28, 2020 at 20:33

The number of deaths among the number of diagnosed cases is called case fatality rate. The number of deaths scaled to the size of the population is called mortality rate.

One can't say that "so far, a random Canadian would have been less likely to die from coronavirus than a random person in the US", because there is a lag between infection and death (or recovery).

For example, if the number of infected people is growing much more in country $$A$$ than in country $$B$$, the $$A$$ case fatality rate drops just because the denominator grows and new infected people do not yet die (or recover).

The "true" proportions can be only calculated when the pandemic is finished.

EDIT

Let's try a very simple simulation.

Logistic growth model

A simple logistic growth model may be:

pop <- 30000                        # population size
K <- 10000                          # carrying capacity (max number of infected people)
cfr <- 0.1                          # constant case fatality rate
weeks <- seq(0, 20, length.out=50)  # time index
N0 <- 1                             # number of infected people at weeks = 0
N <- K * N0 / ((K - N0)*exp(-0.7 * weeks) + N0) # logistic growth model


Notice that the case fatality rate, CFR, is constant.

As you can see in the right graph, the observed CFR is increasing and approaches the true CFR.

To guess the decreasing difference between observed and true CFR's, you need a model.

Exponential growth model

We can replace the last line with:

N <- N0 * exp(0.7 * weeks)


and get:

The observed CFR is now constant, but lesser than the true CFR, because the steep growth of the number of infected people inflates the denominator.

To guess the constant difference between observed and true CFR's, you need a model.

You could try building a model by looking at what has happened "so far", but if you just look at current rates, then "so far" means nothing :)

IMHO, of course. I'm not an epidemiologist.

• But the "so far" makes that statement perfectly accurate. Up until the point those numbers were published, a random Canadian would indeed have been less likely to die from coronavirus. The case fatality rate is a snapshot in time, which may change tomorrow as infected people die or recover. The current case fatality rate may indeed under or overestimate the ultimate likelihood of death among the diagnosed, which is why the "so far" is needed. Jul 29, 2020 at 3:36
• IMHO, this is a naive point of view. Jul 29, 2020 at 12:19
• I generally agree these are dodgy estimators. But to Nuclear Wang’s point, what better estimates do we have of the case fatality rate or the mortality rate while we are in the pandemic? Jul 29, 2020 at 14:24
• @ThomasBilach Their time series, I suppose. Jul 29, 2020 at 15:27