Suppose we wanted to estimate how many car owners there are in the UK and how many of those own a Ford Fiesta, but we only have data on those people who visited Ford car showrooms in the last year. If 10% of the showroom visitors owned a Fiesta, then, because of the bias in the sample, this would certainly overestimate the proportion of Ford Fiesta owners in the country.
Estimating death rates for people with COVID-19 is currently undertaken largely along the same lines. In the UK, for example, almost all testing of COVID-19 is performed on people already hospitalized with COVID-19 symptoms. At the time of writing, there are 29,474 confirmed COVID-19 cases (analogous to car owners visiting a showroom) of whom 2,352 have died (Ford Fiesta owners who visited a showroom). But it misses out all the people with mild or no symptoms.
Concluding that the death rate from COVID-19 is on average 8% (2,352 out of 29,474) ignores the many people with COVID-19 who are not hospitalized and have not died (analogous to car owners who did not visit a Ford showroom and who do not own a Ford Fiesta). It is therefore equivalent to making the mistake of concluding that 10% of all car owners own a Fiesta.
There are many prominent examples of this sort of conclusion. The Oxford COVID-19 Evidence Service have undertaken a thorough statistical analysis. They acknowledge potential selection bias, and add confidence intervals showing how big the error may be for the (potentially highly misleading) proportion of deaths among confirmed COVID-19 patients.
They note various factors that can result in wide national differences—for example the UK’s 8% (mean) “death rate” is very high compared