The Laws of Probability

Demonstrations

Drug Trials

Strong Stuff: How effective is Viagra?

Statistics tell us that it is likely more effective that its advertising claims it to be.

“VIAGRA has shown improvement in erectile function in 4 out of 5 men compared with 1 out of 4 for sugar tablets.”-Ad, Conde-Nast Traveler, June 2000

What do these statistics mean about the effectiveness of VIAGRA? (80-25=55%?)

Actually, 55% is considerably lower than the true success rate of Viagra.

A recent magazine ad for Viagra stated that 80% of those in an experiment who used Viagra reported improvement, as compared to 25% among those who had the placebo. The inclination is to subtract 25 from 80, and thus to estimate Viagra's true effectiveness as 55%. Such a calculation, however, is harsh on Viagra. Among the 80% of Viagra users who reported improvement, some physically benefited while the remainder improved for other reasons. If Q is the fraction of users directly helped by the drug, then Q could be approximated from the linear equation: Q + .25(1-Q) = .8 The idea here is that, like the users of the placebo, 25% of those who used Viagra but did not physically benefit from it nonetheless reported improvements. 25% of 20% = 5%

5% of users that reported Viagra was effective is the result of placebo effect. Hence 75% of Q plus 25% response as placebo effect equals the 80% that believed they were helped by Viagra. Q = .7333 ~= 73% The 80% of Viagra patients who reported gains included the 73% with physical benefits and about 1/4 of the remaining 27% without such benefits. Note that 73% is considerably higher than the 55% success rate that many readers might have inferred from subtracting 25% from 80%.

See a graphical explanation of the mathematics

Confused? Read the Frequently Asked Questions

Thus, Viagra users essentially fall into three categories:

73% who benefit physically
7% who benefit psychologically
20% who do not benefit

The Center for Experimental Pharmacology and Therapeutics, Harvard-MIT Division of Health Sciences and Technology is solely responsible for the content of this web course.