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Journal of Andrology, Vol. 22, No. 4, July/August 2001
Copyright
q
American Society of Andrology
Andrology Lab Corner
Understanding the Odds Ratio
and the Relative Risk
STEPHEN D. SIMON
From the Office of Medical Research, Children’s Mercy
Hospital, Kansas City, Missouri.
The simplest of all possible statistical problems ought to
be exploring the relationship between binary variables.
But binary variables are tricky. Binary, of course, means
two possible levels. You might be interested in how a
binary outcome variable such as live/dead, pregnant/not
pregnant, diseased/healthy, etc, is related to another bi-
nary variable such as treatment/control or exposed/unex-
posed.
Two common measures you might see in such a situ-
ation are the odds ratio and the relative risk. For example,
Bracken et al (1990) showed a strong relationship be-
tween cocaine usage in the last 2 years (yes/no) and sperm
counts (above/below 20
3
10
6
mL) by reporting an odds
ratio of 2.1. Lin et al (1996) showed a strong relationship
between lead exposure (workers with at least 5 years of
lead exposure/professional bus drivers) and fathering a
child during the years 1981–1992 (yes/no) by reporting a
relative risk of 0.38. What do these numbers mean, and
why would you use one instead of the other?
Consider the following data on survival of passengers
on the Titanic. There were 462 women: 308 survived and
154 died. There were 851 men: 142 survived and 709
died.
Clearly, a man on the Titanic was more likely to die
than a woman. But how much more likely? You can com-
pute either the odds ratio or the relative risk to answer
this question.
The odds ratio compares the relative odds of death in
each group. For women, the odds were exactly 2 to 1
against dying (154/308
5
0.5). For men, the odds were
almost 5 to 1 in favor of death (709/142
5
4.993). The
odds ratio is 9.986 (4.993/0.5). There is a 10-fold greater
odds of death for men than for women.
The relative risk (sometimes called the risk ratio) com-
pares the probability of death in each group rather than
the odds. For women, the probability of death is 33%
(154/462
5
0.3333). For men the probability is 83% (709/
Correspondence to: Stephen D Simon, PhD, Research Biostatistician,
Office of Medical Research, Children’s Mercy Hospital, Room HHC-600,
2401 Gillham Road, Kansas City, MO 64108 (e-mail:ssimon@cmh.edu).
Received for publication February 15, 2001; accepted for publication
February 15, 2001.
851
5
0.8331). The relative risk of death is 2.5 (0.8331/
0.3333). There was 2.5 times as much probability for
death among the men than among the women.
Both measurements show that men were more likely to
die. But the odds ratio implies that men were a lot worse
off than the relative risk would imply. Which number is
a fairer comparison?
There are three issues here. The relative risk measures