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.