The Hong Kong Government claims the death rate of SARS to be 6%. The formula that leads to this number is based on a wrong assumption. Upon fixing it, we found the true death rate of SARS to be 17.7% instead.

How they get 6%:

Naturally, one might think, the death rate is simply the number of dead divided by the total number of cases, right? Well, that is how they get the 6%. As of April 20, the total number of people who died of SARS is 88, and the total number of SARS cases is 1380. So the 'death rate' is 88 / 1380 = 6%.

Here is a simple explanation of what went wrong in the government's calculation. The death rate is defined to be the probability that you will die if you get the disease. So it is natural to calculate it by the number of people who died of the disease divided by the number of people who survived and recovered from the disease plus the people who died.

Using the total number of people who died as the numerator is correct, but using the total number of cases as the denominator assumes that all the people who got the disease but are now in the hospital will eventually recover. This assumption is questionable and is where the argument went wrong.

How we get 17.7%:

We can divide the people who got the disease into 3 groups. Group 1 is the people who got the disease and recovered from it. Group 2 is the people who got the disease and died. Group 3 is the people who got the disease and are now in the hospital.

Let there are A individuals in group 1, B individuals in group 2, C individuals in group 3. Let the death rate be p.

The expected number of people who will die in Group 3 is C*p. So the expected dead toll among all the people who got the disease is

B + C * p.

But the death rate = Expected dead toll / Total number of people who got the disease

So we have p = (B + C * p) / (A + B + C)

Solving for p, we get p = B / (A + B)

As of April 20, B = 88, A + B = 409, so p = 17.7%

For those who still don't get it, say there are 100 people who got the disease, 10 have died, and 20 have recovered, and the remaining 70 is unknown. The death rate so far is 10 / (10 + 20) = 1 / 3 but not 1 / 10.

Conclusions:

Wear a mask!! Take extra precautions. Wash your hands. If you have SARS, one in five chance you will die.

Here is some statistics about SARS in Hong Kong.

Here is a description of our statistical model to come up with the estimation 17.7%.