According to Wikipedia, absolute risk reduction is experimental event rate minus control event rate (EER-CER).
Attributable risk is total experimental events/total events minus total experimental non-events/total non-events [EE/(EE+CE)]-[EN/(EN+CN)].
These come out to different values, and I still do not understand what information they are trying to give.
For instance, lets say the study is looking at two groups of 100 people each. The experimental group was exposed to asbestos, the control group was not exposed to asbestos. 25/100 in the experimental group (asbestos-exposed) got cancer (EER=.25), while only 10/100 in the control group (asbestos non-exposed) got cancer (CER=.10).
Calculations:
Absolute risk increase = .25-.10 = .15 = 15%
Relative risk increase = (.25-.10)/.10 = 1.5 = 150%
Number needed to harm = 1/(.25-.10) = 6.67
Relative risk = .25/.10 = 2.5 = 250%
These calculations all seem right so far. Then Wikipedia gives this equation for attributable risk: AR=[EE/(EE+CE)]-[EN/(EN+CN)]
So, using my example above, EE=25, CE=10, EN=75, CN=90.
Attributable risk=(25/(25+10))-(75/(75+90))=.2597=25.97%
Is this equation wrong? Is the attributable risk really just the absolute risk increase or is it something else entirely?