# ODDS RATIO

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```					 It is defined as the ratio of the odds of an event
occurring in one group to the odds of it occurring
in another group, or to a sample-based estimate of
that ratio.
 The odds ratio compares the relative odds in each
group
 One advantage of the odds ratio is that it is not
dependent on whether we focus on the event's
occurrence or its failure to occur. If the odds ratio
for an event deviates substantially from 1.0, the
odds ratio for the event's failure to occur will also
deviate substantially from 1.0, though in the
opposite direction.
Shown below is the typical 2 by 2 table.

You can understand the odds ratio by first noticing
what the odds are in each row of the table. The
odds for row Y- are a/b. The odds for row Y+ are
c/d. The odds ratio (OR) is simply the ratio of the
two odds.
which can be simplified to

Notice that if the odds are the same in
each row, then the odds ratio is 1.
   An odds ratio of 1 indicates that the condition or
event under study is equally likely in both groups.
An odds ratio greater than 1 indicates that the
condition or event is more likely in the first group.
And an odds ratio less than 1 indicates that the
condition or event is less likely in the first group.
Consider the following data on survival of
passengers on the Titanic. There were 462 female
passengers: 308 survived and 154 died. There were
851 male passengers: 142 survived and 709 died
(see table below).

MALE      709       142       851

FEMALE    154       308       462

TOTAL     863       450       1,313

Clearly, a male passenger on the Titanic was more
likely to die than a female passenger.
   The odds ratio compares the relative odds of
death in each group.
   For males, the odds were 5:1 in favor of death
(709X308= 218,372).
   For females, the odds were exactly 2:1 against
dying (154X142= 21,868)
   The odds ratio (218,372/21,868= 9.986 ). There is a
ten fold greater odds of death for males than for
females.
   EXAMPLE
suppose that in a sample of 100 men, 60 have
drunk wine in the previous week, while in a sample
of 100 women only 20 have drunk wine in the same
period.

WHO       WHO DIDN’T    TOTAL
DRUNK     DRUNK
WINE      WINE
MEN       60        40           100
WOMEN     30        70           100
TOTAL     90        110          200
   The odds of a man drinking wine are 60 to 40, or 2:1
   the odds of a woman drinking wine are only 20 to
80, or 1:2
   Now, (60X70 =4200) for men
    and (30X40 = 1200 ) for women
   (4200/1200=3.5 )
   so the odds ratio is 4, showing that men are much
more likely to drink wine than women.
   the odds ratio is commonly used as a means of
expressing the results in some forms of clinical trials,
in survey research, and in epidemiology, such as in
case-control studies.

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 views: 102 posted: 9/7/2010 language: English pages: 11