For First Time, AIDS Vaccine Shows Some Success in Trials
nytimes.com
nytimes.com
They also don't know how it works...
The confidence interval is determined by the number of people in the trial (N=16,400), not the number of people who get sick.
Besides, Dr Kim is quoted elsewhere as saying "the result could be due to chance" and the vaguely phrased "31.2 percent effective" is not encouraging. Add in the likely funding source of AIDS vaccine trials, the pressure to get results and the unknown mechanism and it doesn't look so great.
Confidence intervals get smaller as you include more people in an experiment, but they get smaller more slowly as more people are added. So it's fairly easy to go from a 2% to a 1% confidence interval by adding a couple thousand people, but it takes a lot more people to go from 1% to 0.5%. And of course, it's asymptotic -- you'll never get to zero.
That said, in this case, the point is academic. This study was large enough that the confidence interval is going to be well below 30%.
See my post below.
Also, of course the result could be due to chance. You could flip a fair coin 25 times in a row and come up with heads each time -- it's just pretty damn unlikely. Similarly, I'd bet what he's measured is really this: you have two equally sized groups, one treated, one untreated. In group one you get a rate of x, and in group two, you get a rate of y. How big does |y-x| and the size of the two groups have to be to conclude it was not just chance? As below, a t-test can help you answer that.
By increasing the number of vaccinated people, the number of exposed people becomes more equal between the two groups since a few "more exposed/risky people were assigned to group A" will have a less significant impact.
See the second use here: http://en.wikipedia.org/wiki/Student%27s_t-test