# Confidence Intervals

## Confidence Intervals

Lesson 14
Confidence Intervals of
Odds Ratio and
Relative Risk

Lesson 14 Outline
Lesson 14 covers
 Confidence Interval of an Odds Ratio
Review of Odds Ratio
 Sampling distribution of OR on natural log scale
 95% Confidence Interval of OR example

Confidence Interval of Relative Risk
Review of Relative Risk
 Sampling distribution of RR on natural log scale
 95% Confidence Interval of RR example

PubH 6414 Lesson 13

2

Review: Odds Ratio and Relative
Ri k
Risk

Both Odds Ratio and Relative Risk are
measures of association (or relationship)
between two nominal variables
variables.
The Odds Ratio is typically estimated from
data collected in a Case
Case--Control study
study.
The Relative Risk can be estimated from
d t collected
data
ll t d iin a prospective
ti study.
t d

PubH 6414 Lesson 13

3

Associations between 2 nominal
variable
i bl

If there is no association between the two
variables,
i bl
th
the OR or RR = 1
An OR or RR > 1.0 or < 1.0 indicates a possible
statistical
t ti ti l relationship
l ti
hi ((or association)
i ti ) b
between
t
the two variables.
Hypothesis tests for the OR and RR are not used
to determine statistical significance of the
association
Instead, Confidence intervals of OR or RR are
constructed and used to determine whether or not
the association is statistically significant.
PubH 6414 Lesson 13

4

Confidence Interval
off Odd
Odds Ratio
R ti

Review: Odds Ratio

Odds of an event =
probability that the event occurs
probability that the event does not occur

Odds Ratio
odds of event for g
group
p1
odds of event for group 2
PubH 6414 Lesson 13

6

Review: Disease OR for ‘Exposed’
compared
d to
t ‘Not
‘N t Exposed’
E
d’
Exposed Group
Not Exposed
Group

Disease

No Disease

Total

a
c

b
d

a+b
c+d

Odds of Disease for Exposed = a/(a+b)  b/(a+b) = a/b
Odds of...