How to Test a Vaccine

I have been making some calculations on the alternative ways of testing a vaccine, and unless I misunderstand something, the current procedure not only takes longer, it probably kills more people. Here are my calculations:

Method 1: Give the vaccine to N1 people. Wait a month. If none of them get the disease, conclude that the vaccine works. 

Method 2: Give the vaccine to N2 people. Deliberately expose all of them to the disease. If none of them get the disease, conclude that the vaccine works.

The following calculations assume:

A: We select N1 and N2 to reduce the chance of a false positive to no more than .05 .

B: Someone not already immune who is deliberately exposed has a .5 chance of catching the disease.

C: The probability that the vaccine works is .1, but if it works it works perfectly — probability of catching the disease zero.

D: The probability that the vaccine not only does not work but gives the recipient the disease is .01 .

In the U.S. at present, about one person in a thousand gets the disease each month, so with method 1, in the U.S., if the vaccine does not work each test subject has a .001 probability of getting the disease. So if it does not work, the probability that none of them get the disease is .999^N1. If we set N1=3000, that comes to about .05.

With method 2, if the vaccine does not work, the probability that nobody gets the disease is .5^N2. We set N2=5, giving us a probability of about .03.

With method 1, the expected number of people who get the disease because of the vaccination is .01xN1=30. The number who get it because because they are in the test and the vaccination doesn’t work is zero, since their exposure is the same as if they were not in the test. The number who avoid getting the disease as a result of being in the test and the vaccine working is .3 . Net increase in disease due to Method 1 is 29.7 .

With method 2, the expected number of people who get the disease because of the vaccination is .01xN2=.05. The number who get it because of the exposure (and the vaccine doesn’t work) is .9x.5xN2= 2.25 . The number who don’t get the disease as a result of being in the test and the vaccine working is .0005. So the net increase in disease due to Method 2 is 2.3.

For simplicity, I am calculating the number of people in the test who don’t get the disease as a result of the vaccine over a month in both cases. It’s small with Method 1, trivially small with Method 2. 

Adding all of this up, Method 1 results in 29.7 people getting the disease as a result of the vaccine trial, Method 2 results in 2.3 people getting the disease as a result of the vaccine trial. Method 2 also gives a somewhat lower chance of a false positive and produces a result about a month faster. 

This is obviously a simplified analysis — a vaccine doesn’t have to work perfectly to be worth using, and my particular numbers were invented. But given how much larger the first figure is than the second, the argument that we must use the first because the second is too dangerous looks implausible unless one believes that the chance the vaccine gives people the disease is lower than the chance that it prevents the disease by substantially more than an order of magnitude. 

Also, even if there is no chance that the vaccine causes the disease, the downside of Method 2 is tiny. A small number of people, two or three with my numbers, get the disease as a result of the test. Since you will be using healthy young adult volunteers, the chance of death for each is about one in a thousand. Getting a vaccine out a month sooner, on the other hand, saves about 20,000 lives in the U.S. alone. 

Am I missing anything? Is there any plausible set of assumptions under which Method 1 is better than Method 2? Alternatively, have I misunderstood what the methods are?