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.