Which formula correctly computes the risk ratio from a 2x2 table?

• A. RR = [a/(a+b)] / [c/(c+d)]
• B. RR = [a/c] / [b/d]
• C. RR = (a+d)/(b+c)
• D. RR = a/(a+b) * c/(c+d)

Answer: (A)

Relative risk measures how much more (or less) likely the outcome is in the exposed group compared with the unexposed group. In a 2x2 table, a is the number of exposed with the outcome, b is exposed without the outcome, c is unexposed with the outcome, and d is unexposed without the outcome. The risk in the exposed group is a/(a+b), since that’s the proportion of exposed individuals who have the outcome. The risk in the unexposed group is c/(c+d). The relative risk is the ratio of these two risks, so it is a/(a+b) divided by c/(c+d).

Using numbers helps see it clearly: if a=20, b=80, c=10, d=90, then exposed risk = 20/100 = 0.20, unexposed risk = 10/100 = 0.10, and RR = 0.20/0.10 = 2.0.

Other expressions don’t compute RR. The form (a/c) ÷ (b/d) equals ad/(bc), which is the odds ratio, not the relative risk. The form (a+d)/(b+c) uses totals across columns or rows and doesn’t compare the two group risks. The product a/(a+b) × c/(c+d) multiplies the two risks instead of taking their ratio.