ODDS RATIO

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ODDS RATIO

• Kristine joy Ramos
• MSCN- biostatistics
• Philippine Womens University

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ODDS RATIO

• 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.

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• 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.

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• which can be simplified to
• Notice that if the odds are the same in each
  row, then the odds ratio is 1.

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INDICATION

• 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.

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• 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).
• Clearly, a male passenger on the Titanic was
  more likely to die than a female passenger.

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• The odds ratio compares the relative odds of
  death in each group.
• For males, the odds were 51 in favor of death
  (709X308 218,372).
• For females, the odds were exactly 21 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.

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• 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.

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• The odds of a man drinking wine are 60 to 40, or
  21
• the odds of a woman drinking wine are only 20 to
  80, or 12
• Now, (60X70 4200) for men
• and (30X40 1200 ) for women
• (4200/12003.5 )
• so the odds ratio is 4, showing that men are much
  more likely to drink wine than women.

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USED IN

• 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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THANK YOU!!