Data Analysis Basics for Analytic Epidemiology

2. Data Analysis Basics for Analytic Epidemiology Session 3, Part 3

3. Learning ObjectivesSession 3, Part 3 • Interpret risk ratios and odds ratios • Describe how a statistical test is used

4. OverviewSession 3, Part 3 • Measures of association • Statistical tests

5. Measures of Association

6. 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)

7. 2 x 2 Tables Used to summarize counts of disease and exposure to calculate measures of association

8. 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 Outcome 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 Yes No Exposure

9. 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 Outcome Yes No Total Risk among the exposed Yes Exposure No a + b c + d Risk among the unexposed

10. Relative Risk Example a / (a + b) 23 / 33 RR = = = 6.67 c / (c + d) 7 / 67

11. 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

12. Odds Ratio Example a x d 130 x 135 OR = = = 1.27 b x c 115 x 120

13. Interpreting Risk and Odds Ratios

14. 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

15. Statistical Tests

16. 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”

17. 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

18. 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

19. 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

20. 95% CI Example: Infertility 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

21. 95% CI Example: Infertility 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

22. 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

23. P-value Example 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

24. 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

25. 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.

26. 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.