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# Measures of Comparison

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1. Measures of Comparison

2. Purpose • Summarize relationship between exposure and disease by comparing at least two measures of disease frequency • Overall rate of disease in an exposed group says nothing about whether exposure is a risk factor for or causes a disease. This can only be evaluated by comparing disease occurrence in an exposed group to another group that is usually not exposed. The latter group is usually called the comparison or reference group. • Comparison is the essence of epidemiology.

3. Two Main Options for Comparison 1. Calculate ratio of two measures of disease frequency ( a measure in exposed group and a measure in unexposed comparison group) 2. Calculate difference between two measures of disease frequency (a measure in exposed group and a measure in unexposed comparison group)

4. Data Set Up: Two by Two Table For cumulative incidence and prevalence Disease Exposure

5. For Incidence Rates Disease Exposure

6. Rate/Risk Ratio (also called Relative Risk) Comparing disease occurrence among exposed with disease occurrence among comparison group (usually unexposed) in a ratio measure.

7. Rate/Risk Ratio (also called Relative Risk) • RR= Rate or risk in exposed group (Rexp) / Rate or risk in unexposed group (Runexp) • For CI: CIexp/ CIunexp = a / (a+b) / c / (c+d) • For IR: IRexp/ IRunexp = a / PTexp / c / PTunexp

8. Rate/Risk Ratio (also called Relative Risk) Purpose: Gives information on the relative effect of the exposure on the disease. Tells you how many times higher or lower the disease risk is among the exposed as compared to the unexposed. Is commonly used in etiologic research

9. Rate/Risk Ratio • RR=1.0 -- no association between exposure and disease • RR=2.0 -- two times the risk of disease in the exposed compared to the unexposed

10. Rate/Risk Ratio (cont’d) • RR=1.6 -- 1.6 times the risk of disease in the exposed compared to the unexposed or 60% increased risk of disease in the exposed (1.6 - 1.0 = .60 = 60%) • RR = 0.5 -- 0.5 times or ½ the risk of disease in exposed compared to unexposed.

11. Example: Cohort study of hypertension and cardiovascular morbidity and mortality(Nurses Health Study) Non Fatal Heart Attack Hyper- tension

12. Example: Cohort study of hypertension and cardiovascular morbidity and mortality (Nurses Health Study) RR =CIexp/ CIunexp =117/13,422= .00872=7.5 125/106,541.00117 Interpretation: Women with hypertension have 7.5 times the risk of having a non-fatal heart attack compared to women without hypertension.

13. Example of an R x C Table in a Study of Magnetic Field Exposure and Leukemia Leukemia Magnetic Field Exposure Note: Low exposure group is the comparison group for both high and medium exposures. Interpretation: Children exposed to medium levels have a 23% increased risk of leukemia, and those exposed to high levels have a 33% increased risk as compared to children exposed to low magnetic field levels.

14. Difference Measures Comparing disease occurrence among the exposed with the disease occurrence among the unexposed comparison group by subtracting one from the other.

15. Risk/Rate Difference (also called Attributable Risk/Rate) RD=Rate or risk in exposed (Rexp)– Rate or risk in unexposed (Runexp) • For CI: CIexp - CIunexp = a / (a+b) - c / (c+d) • For IR: IRexp - IRunexp = a / PTexp - c / PTunexp • RD = 0 when there is no association

16. Risk/Rate Difference (continued) Purpose: Gives information on • the absolute effect of exposure on disease occurrence. • the excess disease risk in the exposed group compared to the unexposed group. • the public health impact of an exposure, that is, how much disease would be prevented if the exposure were removed. This assumes that the exposure causes the disease.

17. Non Fatal Heart Attack Hypertension RD = CIexp - CIunexp = 117 / 13,422 - 125 / 106,541 = .00872 - .00117 = .00755 or 755 / 100,000 Interpretation: The excess occurrence of non-fatal heart attack among these hypertensive women was 755 per 100,000. Or, if hypertension causes non-fatal heart attacks then 755 cases of non-fatal heart attack per 100,000 women could be eliminated if the hypertension were treated.

18. Comparison of RR and RD Annual Mortality Rate Per 100,000 Conclusion: Cigarette smoking is a much stronger risk factor for lung cancer but (assuming smoking is causally related to both diseases) the elimination of cigarettes would prevent far more deaths from coronary heart disease. Why is this so?

19. Population Risk/Rate Difference (PRD) Purpose: Measures excess disease occurrence among the total population that is associated with the exposure. Helps to evaluate which exposures are most relevant to the health of a target population.

20. Population Risk/Rate Difference (PRD) • Two formulas for PRD: • PRD = (RD) (Pexp) where Pexp = proportion of population that is exposed, and RD is the risk or rate difference • PRD = Rtotal - Runexp where Rtotal = risk/rate in total population and Runexp = risk/rate among unexposed

21. Non-fatal Heart Attack Population Risk/Rate Difference Hypertension PRD = [(117/13,422) - (125/106,541)] x (13,422/119,693) = (.00755) x (.112) = .00085 or PRD = 242/119,963 - 125/106,541 = .00202 - .00117 = .00085 or 85/100,000 Interpretation: Hypertension results in an excess incidence of 8.5/10,000 non-fatal heart attacks in the total study population. Or, if hypertension were eliminated, 8.5/10,000 cases of non-fatal heart attacks could be eliminated among the total study population.(Assumes that hypertension causes heart attacks.)

22. Population Risk/Rate Difference Note the dependence of PRD on prevalence of exposure. What would the excess of non-fatal heart attack due to hypertension be if the prevalence of hypertension were 1% rather than 11.2%? A relatively weak risk factor (in terms of relative risk) that is quite prevalent could account for more of disease incidence in a population than a stronger risk factor that is rarely present.

23. Calculating Measures of Comparison for Cigarette Smoking and Lung Cancer* Simple Rates • Death rate from lung cancer in smokers 0.96 / 1,000 / year • Death rate from lung cancer in non-smokers: 0.07 / 1,000 / year • Prevalence of smoking in population: 56% * Estimated data from Doll and Hill. Br J Med 1:1399-1410, 1964.

24. Calculating Measures of Comparison for Cigarette Smoking and Lung Cancer* Compared Rates • Rate Ratio: 0.96 / 1,000 / year / 0.07 / 1,000 / year = 13.7 • Rate Difference: 0.96 / 1,000 / year – 0.07 / 1,000 / year = 0.89 / 1,000 / year • Population Rate Difference: 0.89 / 1,000 / year x 0.56 =0.50 / 1,000 / year * Estimated data from Doll and Hill. Br J Med 1:1399-1410, 1964.

25. Exercise to Practice Measures of Comparison The 58th annual convention of the American Legion was held in Philadelphia from July 21 until July 24, 1976. People at the convention included American Legion delegates, their families, and other legionnaires who were not official delegates. Between July 20th and August 30th, some of those who were or had been present became ill with a type of pneumonia subsequently named Legionnaire's Disease. No one attending the convention developed the disease after august 30th. Following are the numbers of delegates and non-delegates who developed Legionnaire's Disease during the period July 20 to August 30 (41 day period).

26. Exercise to Practice Measures of Comparison Developed Legionnaire’s Disease Convention Status

27. Exercise to Practice Measures of Comparison 1. Compute the "rate" of Legionnaires' Disease among the delegates and non-delegates. What type of measure of disease frequency is this "rate"? CI Del 125/1849 = .068 in 41 Days CI No 3/762 = .004 in 41 Days

28. Exercise to Practice Measures of Comparison 2. Calculate the "rate" ratio of Legionnaires' Disease among delegates compared to non-delegates. State in words the meaning of this “rate” ratio. RR .068 / .004 = 17

29. Exercise to Practice Measures of Comparison 3. Calculate the "rate" difference of Legionnaires' Disease for delegates. State in words the meaning of this”rate” difference. AR = .068 - .004 = .064 or 64/1000

30. Further Analysis of Convention Delegates Developed Legionnaire’s Disease Hotel of Residence Cumulative incidence among Hotel A residents: 62 / 690 = 9.0 / 100 or 9.0% Cumulative incidence among other hotel residents: 63 / 1,161 = 5.4 / 100 or 5.4% RR= 9.0 / 5.4 = 1.7 RD = 9.0 %- 5.4% = 3.4%

31. Epidemiology In the News

32. Epidemiology In the News • What is the exposure under study? • How is it defined? • What are the diseases under study? • Find the measures of disease frequency. • Find the measures of association. • What did the investigators do to ensure that the comparisons were “fair?”