HED 343 Odds Ratio & Relative Risk

# HED 343 Odds Ratio & Relative Risk - Journal of...

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533 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:[email protected]). 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

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## This note was uploaded on 04/12/2009 for the course HED 10520 taught by Professor Edmundson during the Spring '08 term at University of Texas.

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HED 343 Odds Ratio & Relative Risk - Journal of...

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