Testing only sick or symptomatic patients will not get us to the truth. To see why who we test matters, consider the flu. Its mortality rate is around 0.1%—meaning that of everyone infected with the flu, tested or not, 1 in 1,000 die of it. If we only tested people who are hospitalized with flu-like symptoms, the mortality rate jumps 75-fold. Similarly with the coronavirus, testing only sick and symptomatic people will result in an overestimate of mortality, which would heighten fear and anxiety and worsen their economic effects.
The way to learn the truth is to test a random sample of the population in major cities with an outbreak. Random testing would reveal the true mortality rate and also how many people have the virus, an important factor in determining its infectivity. Authorities need to start conducting random testing now, with statisticians in the coronavirus command center guiding the design. If the infectivity and mortality rates turn out to be similar to those of the flu, this approach could avert billions of dollars in economic loss and calm public fears.
The second purpose of testing is to avert spread by isolating those who are infected. In this regard, it is unclear that relying exclusively on people who are volunteering for the tests makes sense. These are probably people who are exhibiting symptoms and heeding public-health messages to isolate themselves at home, as they would do for seasonal flu. A study of flu-vaccine strategies (of which I am a co-author) shows that self-selection doesn’t get at the high-risk populations.