# Role of Prevalence in Estimating Coronavirus Mortality

Let there be a sample of 10,000 people.

100 of them have a fever. You test them for COVID19 and they all come out positive. 5 of them die, 9 of them end up in intensive care. The estimated mortality is 5%, and estimated intensive care rate is 9%. What about the 9,900 asymptomatic people who did no get tested?

Scenario A: All 9,900 asymptomatic people would test negative for COVID19. Scenario B: All 9,900 asymptomatic people would test positive for COVID19 because of a combination of high rate of asymptomatic carriers and high false positive rate. End result:

Scenario A: true mortality rate is 5% and true intensive care rate is 9%. Scenario B: true mortality rate is 0.05% and true intensive care rate is 0.09%. the numbers are fictitious, but the point is simple - we can't estimate mortality without knowing the prevalence

Question:

Where are we right now between scenario A and scenario B? Or put another way, are there any ongoing studies/reports which take into account this factor?

• Update, using real numbers: Italy has a 250 cases/1mil pop (0.025% of the population tested positive) That’s 15k cases, and 1k deaths (7%). Scenario A - the remaining 99.975% are 100% Covid-free: Mortality is 7%. => If 100% of the planet is infected, 490mil die. Scenario B - the remaining 99.975% are asymptomatic, but positive Covids: Mortality rate is 0.0001%. => If 100% of the planet is infected, 7k die. – Tib Mar 13 '20 at 21:04

I think you're talking (setting aside false-positive/low-specificity testing problems for the moment) about the difference between infection fatality ratio (IFR, fraction of infected people who die from disease) and the case fatality ratio (CFR, fraction of clinically defined "cases" who die from disease). The difference between these two depends completely, as you suggest, on the difference between the population that gets infected and the population that is defined as a "case" (which could vary a lot: is it people who have a cough? fever & cough? request testing? are admitted to the hospital? are admitted to the ICU?).

Because most of the people aboard the Diamond Princess cruise ship were tested (3063/3711), we can have a reasonably good idea of the fraction infected (unlike the usual scenario where most asymptomatic cases are never noticed). The authors of this (not yet peer-reviewed) study concluded that:

the all-age cIFR on the Diamond Princess was 1.2% (0.38–2.7%) and the cCFR was 2.3% (0.75–5.3%)

(where 'c' in cIFR and cCFR stands for 'corrected'; these are estimates that account for the fact that we don't yet know the outcome for all patients).

Other issues to think about:

• sensitivity and specificity of testing (false positive/negative rates)
• variation with/adjustment for age (discussed in the paper)
• variation by medical/social context (e.g. Wuhan vs Iran vs places where cases are caught early and the medical infrastructure isn't overwhelmed)

Russell et al., "Estimating the infection and case fatality ratio for COVID-19 using age-adjusted data from the outbreak on the Diamond Princess cruise ship". https://cmmid.github.io/topics/covid19/severity/diamond_cruise_cfr_estimates.html