Comparing groups using conditional probabilities

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Comparing groups using conditional probabilities

• Relative risk and related measures...

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Plaque Breaks and Heart Attacks
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The comparison
0.68/0.21 3.24
Men who died during strenuous activity were more
than 3 times as likely to have ruptured plaque
than men who engaged in normal activity.
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Relative risk
Relative Risk P(DiseasedExposed) P(Diseased
Unexposed)
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Example Gender and Tattoos
Rows gender Columns tattoo
N Y All
M 74 16 90
82.22 17.78 100.00
F 79 8 87 90.80
9.20 100.00 All 153 24 1
77 86.44 13.56 100.00 Cell Content
s -- Count
of Row
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The comparison
0.1778/0.0920 1.93
Males in Fall 1998 Stat 250 classes are almost
twice (2 times) as likely to have a tattoo than
females in Fall 1998 Stat 250 classes.

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Interpretation of relative risk
Relative risk of 1 means that each exposed
group is equally likely to have the disease.
10 of students who take Stat 250 appreciate
statistics 10 of students who dont take Stat 25
0 appreciate statistics RR of appreciating statis
tics 0.10 /0.10 1
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Alternatively
1.93 - 1.00 0.93 ? 100 93
Males in Fall 1998 Stat 250 classes are 93
percent more likely to have a tattoo than females
in Fall 1998 Stat 250 classes.
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Increased risk
Increased risk (Relative Risk - 1.00) ? 100
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Increased risk
Increased risk can be negative! If so, it is a
decreased risk.
IR (0.70 - 1.00) 100 -30
The researchers found that even occasional
exercisers, those who did less than the
equivalent of six brisk half-hour walks a month,
were 30 percent less likely to die than their
sedentary twins.
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Caution!

• Relative risk and increased risk by themselves
  are not sufficient. Critical that you also know
  the conditional probabilities.
  
• RR 0.005/0.001 5
• RR 0.5/0.1 5
• Relative risk of 5 is very different in each of
  these cases!
  

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Odds

• If P(event) is p, then odds in favor of event is
  p/(1-p) to 1.
  
• If m number with trait and n number without
  trait, then odds in favor of event is m/n to
  1.
  

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Interpreting odds
Odds 10 to 1 For every 10 students who didnt s
leep enough last night, Ill find 1 who did sleep
enough.
Odds 3 to 2 For every 3 students who do their h
omework daily, Ill find 2 students who dont do
their homework daily.
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Example Gender and Tattoos
Rows gender Columns tattoo
N Y All
M 74 16 90
82.22 17.78 100.00
F 79 8 87 90.80
9.20 100.00 All 153 24 1
77 86.44 13.56 100.00 Cell Content
s -- Count
of Row
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Odds of Not Having a Tattoo
For males 0.8222/0.1778 to 1 74/16 to 1 4.6 t
o 1 For every 4.6 males I find without a tattoo,
Ill find one male with a tattoo.
For females 0.9080/0.0920 to 1 79/8 to 1 9.9
to 1 For every 9.9 females I find without a tatto
o, Ill find one female with a tattoo.
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Odds ratio
The ratio of two odds, that is, the odds for one
group divided by the odds for another group.
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The comparison
Odds ratio (79/8)/(74/16) 9.9/4.6 2.15
The odds of finding a female without a tattoo is
2.15 times that of the odds of finding a male
without a tattoo.
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What to know?

• Calculation of RR, IR, odds, OR
• Interpretation of RR, IR, odds, OR
• Relationship between RR and IR
• Relationship between probability and odds
• Importance of knowing probabilities and not just
  RR and IR