### a + b - UNC Center for Public Health Preparedness

```Session 3, Part 3
Data Analysis Basics for Analytic
Epidemiology
Learning Objectives
Session 3, Part 3
• Interpret risk ratios and odds ratios
• Describe how a statistical test is used
Overview
Session 3, Part 3
• Measures of association
• Statistical tests
Measures of Association
Measures of Association
• Show the strength of the relationship
between an exposure and outcome
• Indicate how more or less likely a group is to
develop disease as compared to another
group
• Two widely used measures:
– Relative risk (risk ratio, RR)
– Odds ratio (OR)
2 x 2 Tables
Used to summarize counts of disease and
exposure to calculate measures of association
Outcome
Exposure
Yes
No
Total
Yes
a
b
a+b
No
c
d
c+d
a+c
b+d
a+b+c+d
Total
2 x 2 Tables
a = number exposed with outcome
b = number exposed without outcome
c = number not exposed with outcome
d = number not exposed without outcome
Exposure
******************************
a + b = total number exposed
c + d = total number not exposed
a + c = total number with outcome
b + d = total number without outcome
a + b + c + d = total study population
Outcome
Yes No
Yes
a
b
No
c
d
Relative Risk
• Used for cohort study data
• Defined as the risk of disease in the exposed
group divided by the risk of disease in the nonexposed group
Outcome
Yes
No
Yes
Exposure
No
a
b
c
d
a
a+b
Total
a+b
c+d
Risk among
the exposed
Risk among
the unexposed
RR =
c
c+d
Relative Risk Example
Escherichia coli?
Pink
hamburger
Yes
Total
Yes
23
No
10
33
No
7
60
67
Total
30
70
100
RR =
a / (a + b)
c / (c + d)
=
23 / 33
7 / 67
= 6.67
Odds Ratio
• Used with case-control studies
• Population at risk is not known (selected
participants by disease status)
• Calculate odds instead of risks
axd
OR =
bxc
Odds Ratio Example
Increased Blood
Pressure
Caffeine
intake “high”?
Yes
Yes
130
No
115
245
No
120
135
255
Total
250
250
500
OR =
axd
bxc
Total
=
130 x 135
115 x 120
= 1.27
Interpreting Risk and Odds
Ratios
RR or OR
RR or OR
RR or OR
<1
=1
>1
• Exposure
associated
with
decreased
risk of
outcome
• No
association
between
exposure
and
outcome
• Exposure
associated
with
increased
risk of
outcome
Interpretation
• RR = 5
– People who were exposed are 5 times more likely to
have the outcome when compared with persons who
were not exposed
• RR = 0.5
– People who were exposed are half as likely to have
the outcome when compared with persons who were
not exposed
• RR = 1
– People who were exposed are no more or less likely
to have the outcome when compared to persons who
were not exposed
Statistical Tests
Statistical Tests
• Calculations performed to test a
hypothesis
• Estimate of how likely it is the result is due
to chance
• Pre-determined threshold for acceptable
level of “chance”
Tests of Significance
• Indicate reliability of the association that
was observed
• Answers the question “How likely is it that
the observed association may be due to
chance?”
• Two main tests:
– 95% Confidence Intervals (CI)
– p-values
95% Confidence Interval (CI)
• Range of values of the measure of
association (RR or OR) that is likely to
contain the true RR or OR
• Interpreted as 95% “confident” that the
true measure of association falls within
this interval
Interpreting 95% Confidence
Intervals
• CI range that does not include 1.0
Indicates statistically significant
association
• CI range below 1
Suggests less risk of the outcome in the
exposed population
• CI range above 1
Suggests a higher risk of the outcome in the
exposed population
95% CI Example: Infertility
Exposure
Odds Ratio
95% CI
Gonorrhea
2.4
1.3 – 4.4
Trichomonas
1.9
1.3 – 2.8
Yeast
1.3
1.0 – 1.7
Other vaginitis
1.7
1.0 – 2.7
Herpes
0.9
0.5 – 1.8
Genital warts
0.4
0.2 – 1.0
Grodstein F, Goldman MB, Cramer DW. Relation of tubal infertility to history of sexually
transmitted diseases. Am J Epidemiol. 1993 Mar 1;137(5):577-84
95% CI Example: Infertility
Exposure
Odds Ratio
95% CI
Gonorrhea
2.4
1.3 – 4.4
Trichomonas
1.9
1.3 – 2.8
Yeast
1.3
1.0 – 1.7
Other vaginitis
1.7
1.0 – 2.7
Herpes
0.9
0.5 – 1.8
Genital warts
0.4
0.2 – 1.0
Grodstein F, Goldman MB, Cramer DW. Relation of tubal infertility to history of sexually
transmitted diseases. Am J Epidemiol. 1993 Mar 1;137(5):577-84
p-values
• A measure of how likely the observed association would occur
by chance alone, if there were no true association
• Very small p-value (<0.05)
– An unlikely result (RR or OR) if there was no true association
– Statistically significant
• A p-value of 0.05
– Indicates a 5% chance that the RR or OR was observed by
chance
• Large p-value (>0.05)
– A likely result (RR or OR) if there was no true association
– Not statistically significant
P-value Example
Exposure
Odds Ratio
95% CI
P-value
Gonorrhea
2.4
1.3 – 4.4
0.004
Trichomonas
1.9
1.3 – 2.8
0.001
Yeast
1.3
1.0 – 1.7
0.04
Other vaginitis
1.7
1.0 – 2.7
0.04
Herpes
0.9
0.5 – 1.8
0.80
Genital warts
0.4
0.2 – 1.0
0.05
Grodstein F, Goldman MB, Cramer DW. Relation of tubal infertility to history of sexually transmitted diseases. Am J
Epidemiol. 1993 Mar 1;137(5):577-84
Summary
• Measures of association are calculated to assess
the strength of association between an exposure
and an outcome in an epidemiologic study
• Risk ratios (RR) are the measure of association
used for cohort studies
• Odds ratios (OR) are the measure of association
used for case-control studies
• Confidence intervals give a range of values that are
likely for a given measure of association
• Confidence intervals and p-values can be used to
assess statistical significance of a measure of
association
References and Resources
•
•
•
•
•
Centers for Disease Control and Prevention. Principles of Epidemiology.
3rd ed. Atlanta, Ga: Epidemiology Program Office, Public Health Practice
Program Office; 1992.
Gordis L. Epidemiology. 2nd ed. Philadelphia, Pa: WB Saunders Company;
2000.
Gregg MB, ed. Field Epidemiology. 2nd ed. New York, NY: Oxford
University Press; 2002.
Hennekens CH, Buring JE. Epidemiology in Medicine. Philadelphia, Pa:
Lippincott Williams & Wilkins; 1987.
Cohort Studies. ERIC Notebook [serial online]. 1999:1(3). Department of
Epidemiology, University of North Carolina at Chapel Hill School of Public
Health / Epidemiologic Research & Information Center, Veterans
Administration Medical Center. Available at:
http://cphp.sph.unc.edu/trainingpackages/ERIC/issue3.htm. Accessed
March 1, 2012.
References and Resources
•
•
Case-Control Studies. ERIC Notebook [serial online]. 1999:1(5).
Department of Epidemiology, University of North Carolina at Chapel Hill
School of Public Health / Epidemiologic Research & Information Center,
Veterans Administration Medical Center. Available at:
http://cphp.sph.unc.edu/trainingpackages/ERIC/issue5.htm. Accessed
March 1, 2012.
Laboratory Instructor’s Guide: Analytic Study Designs. EPID 168 Lecture
Series. Department of Epidemiology, University of North Carolina at Chapel
Hill School of Public Health; August 2002. Available at:
http://www.epidemiolog.net/epid168/labs/AnalyticStudExerInstGuid2000.pdf
. Accessed March 1, 2012.
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