Estimating the Size of the Treatment Effect

Outcome
Positive Effect Negative Effect Risk
Treated (y) a b Y=a/a+b
Control (x) c d X=c/c+d


The absolute risk reduction is the difference in risk between the control group (x) and the treated group (y):

ARR = X - Y


The relative risk, or risk ratio, is the ratio of risk in the treated group (y) to risk in the control group (x):

RR = Y/X


The relative risk reduction expresses the percent reduction in events in treated (y) compared to controls (x):

RRR = (1 - Y/X) x 100%

OR

RRR = [(X - Y)/X] x 100%


The number needed to treat is the inverse of the absolute risk reduction:

NNT = 1/ARR = 1/(X - Y)