Transcript Comparing groups using conditional probabilities

Comparing groups using
conditional probabilities
Relative risk and related measures...
Plaque Breaks and Heart Attacks
Plaque Burst?
Activity
Yes
Strenuous
P(Y|S) = 0.68
Normal
P(Y|N) = 0.21
Total
No
Total
146
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.”
Relative risk
Disease?
Exposed to
risk?
Yes
Exposed
P(D|E)
Unexposed
P(D|EC)
No
Total
Relative Risk
= P(Diseased|Exposed) ÷ P(Diseased|Unexposed)
Example: Gender and Tattoos
Rows: gender
N
M
74
82.22
F
All
79
90.80
Columns: tattoo
Y
All
16
90
17.78
100.00
8
9.20
87
100.00
153
24
177
86.44
13.56
100.00
Cell Contents -Count
% of Row
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.”
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 don’t take Stat 250 appreciate
statistics
RR of appreciating statistics = 0.10 /0.10 = 1
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.
Increased risk
Increased risk = (Relative Risk - 1.00)  100
Relative Risk
1.00
1.50
2.00
3.00
Equally
likely
1.5 times
more
2 times
more
3 times
more
Increased Risk
0%
50%
100%
200%
Equally
likely
50%
more
100%
more
200%
more
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.”
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!
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”.
Interpreting odds
Odds = 10 to 1
For every 10 students who didn’t sleep enough
last night, I’ll find 1 who did sleep enough.
Odds = 3 to 2
For every 3 students who do their homework
daily, I’ll find 2 students who don’t do their
homework daily.
Example: Gender and Tattoos
Rows: gender
N
M
74
82.22
F
All
79
90.80
Columns: tattoo
Y
All
16
90
17.78
100.00
8
9.20
87
100.00
153
24
177
86.44
13.56
100.00
Cell Contents -Count
% of Row
Odds of Not Having a Tattoo
For males
0.8222/0.1778 to 1 = 74/16 to 1 = 4.6 to 1
For every 4.6 males I find without a tattoo, I’ll 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 tattoo, I’ll find
one female with a tattoo.
Odds ratio
The ratio of two odds, that is, the odds for
one group divided by the odds for another
group.
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.
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