data analysis basics for analytic epidemiology
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Data Analysis Basics for Analytic Epidemiology
Session 3, Part 3
Learning ObjectivesSession 3, Part 3
• Interpret risk ratios and odds ratios
• Describe how a statistical test is used
OverviewSession 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 TablesUsed 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
Total a + c b + d a + b + c + d
2 x 2 Tables
a = number exposed with outcomeb = number exposed without outcomec = number not exposed with outcomed = number not exposed without outcome
******************************a + b = total number exposedc + d = total number not exposeda + c = total number with outcomeb + d = total number without outcomea + b + c + d = total study population
a bc d
OutcomeYes No
Exposure YesNo
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
a a + b
RR = c
c + d
a bc d
OutcomeYes No Total
YesExposure
No
a + bc + d
Risk among the exposedRisk amongthe unexposed
Relative Risk Example
Escherichia coli?Pink hamburger Yes No
Total
Yes 23 10 33
No 7 60 67
Total 30 70 100
a / (a + b) 23 / 33RR = = = 6.67
c / (c + d) 7 / 67
Odds Ratio• Used with case-control studies
• Population at risk is not known (selected participants by disease status)
• Calculate odds instead of risks a x d
OR = b x c
Odds Ratio Example
Increased Blood Pressure
Caffeine intake “high”? Yes No
Total
Yes 130 115 245
No 120 135 255
Total 250 250 500
a x d 130 x 135OR = = = 1.27
b x c 115 x 120
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 1.0Indicates 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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