Transcript 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 Exposure Yes No Total Yes
a c a + c
Outcome No
b d b + d
Total
a + b c + d a + b + c + d
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 Yes No
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
a c b 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 non exposed group
Yes Exposure No Outcome Yes No Total
a c b d a + b c + d
Risk among the exposed Risk among the unexposed
RR =
a a + b c c + d
Relative Risk Example
Escherichia coli
?
Pink hamburger Yes No Total Yes
23 7
30 No
10 60
70 RR =
a
/ (
a + b
)
c
/ (
c + d
) = 23 / 33 7 / 67 = 6.67
Total 33 67 100
Odds Ratio
• Used with
case-control
studies • Population at risk is not known (selected participants by disease status) • Calculate odds instead of risks OR = a x d b x c
Odds Ratio Example
Caffeine intake “high”?
Yes No Total OR =
a x d b x c
Increased Blood Pressure Total Yes 130 120 250 No 115 135 250 = 130 x 135 115 x 120 = 1.27
245 255 500
Interpreting Risk and Odds Ratios
RR or OR < 1 • Exposure associated with decreased risk of outcome RR or OR = 1 • No association between exposure and outcome RR or OR > 1 • 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
Gonorrhea Trichomonas Yeast Other vaginitis Herpes Genital warts
Odds Ratio
2.4
1.9
1.3
1.7
0.9
0.4
95% CI
1.3 – 4.4
1.3 – 2.8
1.0 – 1.7
1.0 – 2.7
0.5 – 1.8
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
Gonorrhea Trichomonas Yeast Other vaginitis Herpes Genital warts
Odds Ratio
2.4
1.9
1.3
1.7
0.9
0.4
95% CI
1.3 – 4.4
1.3 – 2.8
1.0 – 1.7
1.0 – 2.7
0.5 – 1.8
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
Gonorrhea Trichomonas Yeast Other vaginitis Herpes Genital warts
Odds Ratio
2.4
1.9
1.3
1.7
0.9
0.4
95% CI
1.3 – 4.4
1.3 – 2.8
1.0 – 1.7
1.0 – 2.7
0.5 – 1.8
0.2 – 1.0
P-value
0.004
0.001
0.04
0.04
0.80
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.