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Data Analysis Basics for Analytic Epidemiology Session 3, Part 3

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Learning Objectives Session 3, Part 3 Interpret risk ratios and odds ratios Describe how a statistical test is used

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Overview Session 3, Part 3 Measures of association Statistical tests

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Measures of Association

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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)

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2 x 2 Tables Used to summarize counts of disease and exposure to calculate measures of association Outcome ExposureYesNoTotal Yesaba + b Nocdc + d Totala + cb + da + b + c + d

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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 ****************************** 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 ab cd Outcome Yes No Exposure Yes No

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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 ab cd Outcome Yes No Total Yes Exposure No a + b c + d Risk among the exposed Risk among the unexposed

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Relative Risk Example Escherichia coli? Pink hamburgerYesNo Total Yes231033 No76067 Total3070100 a / (a + b) 23 / 33 RR = == 6.67 c / (c + d) 7 / 67

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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

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Odds Ratio Example Increased Blood Pressure Caffeine intake “high”?YesNo Total Yes130115245 No120135255 Total250 500 a x d 130 x 135 OR = == 1.27 b x c 115 x 120

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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

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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

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Statistical Tests

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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”

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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

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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

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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

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95% CI Example: Infertility ExposureOdds Ratio95% CI Gonorrhea2.41.3 – 4.4 Trichomonas1.91.3 – 2.8 Yeast1.31.0 – 1.7 Other vaginitis1.71.0 – 2.7 Herpes0.90.5 – 1.8 Genital warts0.40.2 – 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

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95% CI Example: Infertility ExposureOdds Ratio95% CI Gonorrhea2.41.3 – 4.4 Trichomonas1.91.3 – 2.8 Yeast1.31.0 – 1.7 Other vaginitis1.71.0 – 2.7 Herpes0.90.5 – 1.8 Genital warts0.40.2 – 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

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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

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P-value Example ExposureOdds Ratio95% CIP-value Gonorrhea2.41.3 – 4.40.004 Trichomonas1.91.3 – 2.80.001 Yeast1.31.0 – 1.70.04 Other vaginitis1.71.0 – 2.70.04 Herpes0.90.5 – 1.80.80 Genital warts0.40.2 – 1.00.05 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

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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

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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. http://cphp.sph.unc.edu/trainingpackages/ERIC/issue3.htm

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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. http://cphp.sph.unc.edu/trainingpackages/ERIC/issue5.htm 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. http://www.epidemiolog.net/epid168/labs/AnalyticStudExerInstGuid2000.pdf

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