## COVID-19 Hospitalization Rates

*DISCLAIMER: I am not a doctor and this is not medical advice.*

### Results

Here is the calculated likelihood of having a severe infection (requiring hospitalization) if you contract SARS-CoV-2:

Age | Hospitalization Rate (Overall) |
Hospitalization Rate (No Pre-Existing Conditions) |
---|---|---|

0-17 | 0.13% | 0.01% |

18-44 | 1.17% | 0.07% |

45-64 | 4.24% | 0.26% |

65-74 | 8.22% | 0.50% |

75+ | 13.05% | 0.80% |

Overall | 3.07% | 0.19% |

In other words: a healthy 18-44yo has a 0.07% chance of being hospitalized if he/she gets the virus. That’s a 1 in 1400 chance.

To put that number in perspective, you are ten times more likely to be audited by the IRS (0.6% chance) than to need hospitalization for COVID-19. Having a severe reaction to COVID as a healthy young person is about as likely as getting selected to be an astronaut (1 in 1500).

### Methods

Start with some obvious claims:

(1) % hospitalized in age group = hospitalizations due to infection / number of infections

(2) number of infections = population * infection rate

Putting these together, we get:

(3) % hospitalized in age group = hospitalizations due to infection / (population * infection rate)

But NYC hasn’t published total hospitalizations by age group. They only publish
hospitalization rate *per 100k
people*
per age group. That’s much less useful.
Fortunately, though, we can use that to get what we want without much
difficulty. After all:

(4) hospitalizations = (hospitalizations per 100k * 1/100k * population)

Substituting this in (3) we get:

(5) % hospitalized in age group = (hospitalizations per 100k * 1/100k * population) / (population * infection rate)

Which immediately allows us to cancel out *population*:

(6) % hospitalized in age group = (hospitalizations per 100k * 1/100k) / infection rate

That leaves just infection rate, which we can estimate from the antibody tests that were done on 15k random NY residents. The breakdown by region can be seen here, but the result was that 19.9% of NYC residents tested had antibodies for the virus. The presence of antibodies is very strong evidence that these people had COVID-19. And, given that the sample was random, we can reasonably extrapolate that 19.9% of the NYC population at large had the virus by the time of the study.

Plugging this infection rate into formula (6) we obtain:

(7) % hospitalized in age group = (hospitalizations per 100k * 1/100k) / 19.9%

But that just gives us the *overall* infection rate for a given age group. It
does not differentiate between those who were healthy and those who had
underlying conditions. This is significant because an overwhelming number
(93.9%) of
people hospitalized for COVID-19 had pre-existing conditions in NYC, most commonly
diabetes, hypertension, and/or
obesity. This means that only 6.1% of hospitalized patients were
healthy at the time of infection.

With this, we can easily refine our formula to give us the rate at which healthy people are hospitalized with COVID-19. First note that:

(8) healthy hospitalization rate for age group = % healthy in hospital x % hospitalized in age group

Combining this with (7) we get:

(9) healthy hospitalization rate for age group = % healthy in hospital x (hospitalizations per 100k * 1/100k) / 19.9%

Since we know that 1 - 93.9% = 6.1% of hospitalized COVID patients did not have underlying conditions, we get:

(10) healthy hospitalization rate for age group = 6.1% x (hospitalizations per 100k * 1/100k) / 19.9%

Using (10) and the hospitalization rates per 100k people per age group published by NYC, we get the following results:

Age | Hospitalizations (per 100k) | Overall Infection Hospitalization Rate | Healthy Infection Hospitalization Rate |
---|---|---|---|

0-17 | 26.46 | 0.13% | 0.01% |

18-44 | 232.63 | 1.17% | 0.07% |

45-64 | 844.19 | 4.24% | 0.26% |

65-74 | 1635.06 | 8.22% | 0.50% |

75+ | 2596.28 | 13.05% | 0.80% |

Overall | 610.65 | 3.07% | 0.19% |

### Objections

**1. But the infection rate near me hasn’t been nearly as high as it was in NYC**

That’s great! But it doesn’t matter to the calculations. If the virus puts 1 in 1400 infected healthy people in the hospital in NYC, it should do the same in Timbuktu, even if Timbuktu only has 5 infected healthy people.

Put another way: the calculation doesn’t consider your odds of getting the virus – only your odds of being hospitalized if you do get the virus.

**2. It seems wrong to apply the 93.9% rate of hospitalization
uniformly across age groups. Very likely that rate was
different for each age group.**

I’m sure there were differences between the age groups, but the paper doesn’t list them. I have requested the information from the corresponding author of the study. But I doubt they were significantly different from the 93.9% overall figure. Think about it: if the virus were disproportionately affecting healthy people in a given age group that would be exceptionally interesting and the authors almost certainly would have noted it. But they didn’t note anything like it. Hence, I think it’s safe to assume the data were comparable.

In either case, there is an upper bound to the error here. 350 of the 5700 hospitalized
patients in the
study had no comorbidities (see table 1). Now, for example, there were 660
patients between 20-49 yo in the study (see table 4). So, even if we assume that
*all* patients without underlying symptoms were in the 20-49 yo range, we still
end up with 53% of patients admitted in the 20-49 yo range had no underlying
symptoms. So you still end up with 1 in 700 odds of hospitalization for healthy
individuals in that age range.

**3. But I thought anitbody tests had high false positive rates**

That’s true for all I know – though I’ve not seen any studies backing this up. I’ve seen some sources claiming that as many as 50% of positives are false. So, again, if this concerns you, you can conservatively cut the numbers in half.