Number Needed to treat is the number of patients you needed to treat, so that one patient can get the benifit of the drug. That is, if on experiments 1% got a better result from the drug than placebo (ARR=1%), if you elimenate the effect of chance, you need to treat a 100 patients so that one would get the benifit (be the 1%). This is obtained from 100/1, inverted ARR.
Number Needed to Treat for harm has the same concept, but instead of ARR, it is absolute harm increase, which's the incidence difference of an adverse effect between placebo and the those who took the drug.
So at least UW is more accurate, but limited to number needed to treat to benifit (NNTB, or NNT), I don't know what incidence Kaplan means, but maybe it's either ARR or absolute harm increase..
Both of them are right
One divided by the incidence (reciprocal) will give you the number needed to reach out in order to prevent the occurrence of disease. For example if the incidence of influenza in certain population is 5 in 1000 per year then you need to vaccinate (1000/5 = 200) people in order to prevent one influenza case per year.
However, that's not the most common way NNT is used in medical journals. It's usually the reciprocal of ARR. Which basically means how many cases you have to treat in order for the new intervention/therapeutic measure/drug ...etc can prevent/improve one case in the population of the study. For example, if the incidence of DM retinopathy is 20% in people treated with OHA and 15% in people treated with glitazones then you have prevented 5% (which is your ARR) and so you need to treat 20 patients to achieve that difference.
Please note that NNT should always be a sound number. If your calculation ended up 5.9 then you have to round it up to 6 because you cannot treat 5.9 individuals