Estimating Risk. Sukon Kanchanaraksa, PhD Johns Hopkins University

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1 This work is licensed under a Creative Commons Attribution-onCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this site. Copyright 2008, The Johns Hopkins University and Sukon Kanchanaraksa. All rights reserved. Use of these materials permitted only in accordance with license rights granted. Materials provided AS IS ; no representations or warranties provided. User assumes all responsibility for use, and all liability related thereto, and must independently review all materials for accuracy and efficacy. May contain materials owned by others. User is responsible for obtaining permissions for use from third parties as needed.

2 stimating Risk Sukon Kanchanaraksa, PhD Johns Hopkins University

3 Section A Relative Risk

4 Risk Incidence of Disease (Attack Rate) = Absolute Risk 4

5 Attack Rates from Food-Borne Outbreak xercise Attack Rate (%) Food (1) Ate (2) ot Ate gg salad Macaroni Cottage cheese Tuna salad Ice cream Other

6 Attack Rates from Food-Borne Outbreak xercise Attack Rate (%) Difference of Attack Rates Food (1) Ate (2) ot Ate (1) (2) gg salad Macaroni Cottage cheese Tuna salad Ice cream Other

7 Attack Rates from Food-Borne Outbreak xercise Attack Rate (%) Difference of Attack Rates Ratio of Attack Rates Food (1) Ate (2) ot Ate (1) (2) (1)/(2) gg salad Macaroni Cottage cheese Tuna salad Ice cream Other

8 Approaches to the Measurement of xcess Risk Ratio of risks Risk in exposed Risk in non exposed Differences in risks (Risk in exposed) (Risk in non-exposed) 8

9 Relative Risk or Risk Ratio Relative risk (RR) = Risk in exposed Risk in non-exposed 9

10 Cohort Study First, identify Then follow to see whether Disease develops Disease does not develop Calculate and compare Totals xposed a b a+b ot exposed c d c+d Incidence of disease a a+b c c+d a a+b = Incidence in exposed c c+d = Incidence in not exposed 10

11 Cohort Study First, identify Then follow to see whether Disease develops Disease does not develop Calculate and compare Totals xposed a b a+b ot exposed a = Incidence in exposed a+b c = Incidence in not exposed c+d c d c+d Relative Risk = Incidence of disease a a+b c c+d a a+b c c+d 11

12 Cohort Study Then follow to see whether calculate First select Smoke cigarettes Do not smoke cigarettes Develop CHD Do not develop CHD Totals Incidence of disease Relative Risk = = =

13 Interpreting Relative Risk of a Disease If RR = 1 Risk in exposed = Risk in non-exposed o association If RR > 1 Risk in exposed > Risk in non-exposed Positive association;? causal If RR < 1 Risk in exposed < Risk in non-exposed egative association;? protective 13

14 Cross-Tabulation Table (Food-Borne Outbreak xercise) Attack Rates of Sore Throat gg Salad Ate Did not eat Tuna Salad Ate Did not eat 46/53 (87%) 8/12 (67%) 3/10 (30%) 3/10 (30%) 14

15 Cross-Tabulation Table (Food-Borne Outbreak xercise) Relative Risk of Sore Throat gg Salad Ate Did not eat Tuna Salad Ate Did not eat The baseline group for comparison is the no exposure group i.e., those who did not eat tuna salad and did not eat egg salad 15

16 xposure-disease Tables xpanded from the Cross- Tabulation Table (Food-Borne Outbreak xercise) Sore Throat Sore Throat Both Tuna Salad and gg Salad Yes o Total Ate Did not eat either RR = (46/53)/(3/10) =2.9 Tuna Salad Only Yes o Total Ate Did not eat either RR = (3/10)/(3/10) =1.0 Sore Throat gg Salad Only Yes o Total Ate Did not eat either RR = (8/12)/(3/10) =2.2 16

17 Relative Risk by Food Items o tuna salad Ate tuna salad 2 Relative Risk 1 +Tuna +gg o gg Salad Ate gg Salad 17

18 Relative Risk for MI and CHD Death in Men Aged in Relation to Cigarette Smoking 5 Cholesterol Levels Low 5 Blood Pressure < 130 mmhg 4 High* mmhg Relative Risk on-smoker Smoker on-smoker Smoker * High > 220 mg/100 cc Source: Doyle et al,

19 Relationship between Serum Cholesterol Levels and Risk of Coronary Heart Disease by Age and Sex Serum Men Women Cholesterol mg/dl Aged Aged Aged Aged Incidence Rates (per 1,000) < Source: Doyle et al,

20 Incidence Rates and RR of CHD in Relation to Serum Cholesterol Levels by Age and Sex Serum Men Women Cholesterol mg/dl Aged Aged Aged Aged Incidence Rates (per 1,000) < Relative Risk* < * RR of 1.0 set at level for males yrs of age with cholesterol level < 190 mg/dl. 20

21 Incidence Rates and RR of CHD in Relation to Serum Cholesterol Levels by Age and Sex Serum Men Women Cholesterol mg/dl Aged Aged Aged Aged Incidence Rates (per 1,000) < Relative Risk* < * RR of 1.0 set at level for males yrs of age with cholesterol level < 190 mg/dl. 21

22 Section B Odds Ratio

23 Interpreting Odds Odds is often known as the ratio of money that may be won versus the amount of money bet In statistics, an odds of an event is the ratio of: The probability that the event WILL occur to the probability that the event will OT occur For example, in 100 births, the probability of a delivery being a boy is 51% and being a girl is 49% The odds of a delivery being a boy is 51/49 = 1.04 In simpler term, an odds of an event can be calculated as: umber of events divided by number of non-events 23

24 Calculating Risk in a Cohort Study Develop Disease Do ot Develop Disease xposed a b on-exposed c d The probability that an exposed person develops disease = a a + b The probability that a non-exposed person develops disease = c c + d 24

25 Applying Concept of Odds Let s borrow the concept of odds and apply it to disease and non-disease So, the odds of having the disease is the ratio of the probability that the disease will occur to the probability that the disease will not occur Or, the odds of having the disease can be calculated as the number of people with the disease divided by the number of people without the disease [ote: in the exposure-disease 2x2 table, the odds of having a disease in the exposed group is the same as the odds that an exposed person develops the disease] 25

26 Calculating Odds in a Cohort Study Develop Disease Do ot Develop Disease xposed a b on-exposed c d The odds that an exposed person develops disease = a b The odds that a non-exposed person develops disease = c d 26

27 Calculating Odds in a Cohort Study Odds ratio is the ratio of the odds of disease in the exposed to the odds of disease in the non-exposed OR = Develop Disease Do ot Develop Disease xposed a b on-exposed c d odds that an exposed person develops the disease odds that a non - exposed person develops the disease = a b c d 27

28 Disease Odds Ratio in a Cohort Study OR = a b c d = a b x d c = ad bc 28

29 Calculating Odds Ratio in a Case-Control Study History of xposure o History of xposure Case a c Control b d The odds that a case was exposed = The odds that a control was exposed = a c b d 29

30 Calculating Odds Ratio in a Case-Control Study History of xposure o History of xposure Case a c Control b d Odds ratio (OR) is the ratio of the odds that a case was exposed to the odds that a control was exposed a odds that a case was exposed OR = = c odds that a control was exposed b d 30

31 xposure Odds Ratio in a Case-Control Study OR = a c b d = a c x d b = ad bc 31

32 Odds Ratio versus Relative Risk Odds ratio can be calculated in a cohort study and in a casecontrol study The exposure odds ratio is equal to the disease odds ratio Relative risk can only be calculated in a cohort study 32

33 When Is Odds Ratio a Good stimate of Relative Risk? When the cases studied are representative of all people with the disease in the population from which the cases were drawn, with regards to history of the exposure When the controls studied are representative of all people without the disease in the population from which the cases were drawn, with regards to history of exposure When the disease being studied is not a frequent one 33

34 When Is Odds Ratio a Good stimate of Relative Risk? If the incidence of the disease is low, then: a+b ~ b c+d ~ d Therefore: RR = ~ a/(a+b) c/(c+ d) a/b c/d = ad bc = OR 34

35 Comparing OR to RR: Disease Is Infrequent Develop Disease Do not Develop Disease xposed ,000 on- xposed ,000 Relative Risk = Odds Ratio = 200/10, /10, x x 9800 = 2 =

36 Comparing OR to RR: Disease Is OT Infrequent Develop Disease Do not Develop Disease xposed on- xposed Relative Risk = 50/75 50/25 50 x 75 Odds Ratio = 50 x 25 = 2 = 3 36

37 Interpreting Odds Ratio of a Disease If OR = 1 xposure is not related to disease o association; independent If OR > 1 xposure is positively related to disease Positive association;? causal If OR < 1 xposure is negatively related to disease egative association;? protective 37

38 Section C Odds Ratio in Unmatched and Matched Case-Control

39 Unmatched Case-Control Study: xample CAS COTROL Assume a study of 10 cases and 10 unmatched controls, with these findings = xposed = ot exposed 39

40 Unmatched Case-Control Study: xample CAS COTROL Thus, 6 of 10 cases were exposed, and 3 of 10 controls were exposed. In a 2x2 table, we have the following: Case Control xposed 6 3 ot xposed 4 7 = xposed = ot exposed 40

41 Unmatched Case-Control Study: xample CAS COTROL Case Control xposed 6 3 ot xposed 4 7 OR = ad bc = 6 x 7 3 x 4 = 3.5 = xposed = ot exposed 41

42 Quick Pause In a hypothetical 2x2 table with the following rows and columns, is the OR calculated correctly? Control Case xposed 8 3 ot xposed 4 7 OR = ad bc = 8 x 7 3 x 4 =

43 Quick Pause Control Case xposed 8 3 ot xposed 4 7 Incorrect! OR = ad bc = 8 x 7 3 x 4 = 4.7 Why? 43

44 Odds Ratio in a Case-Control Study OR = a c b d = a c x d b = ad bc = (# cases exposed) x (# controls not exposed) (# cases not exposed) x (# controls exposed) The numerator is the product of cases exposed and controls not exposed. 44

45 Case-Control Study: xample Cases CHD Controls (without disease) Smoked cigarettes Did not smoke cigarettes Total % Smoking cigarettes = 56% = 44% OR = ad bc = 112 x x 88 =

46 Matched Case-Control Study In a matched case-control study, one or more controls are selected to match to a case on certain characteristics, such as age, race, and gender When one control is matched to a case, the case and the matched control form a matched pair 46

47 Concordant and Discordant Pairs We can define two types of matched pairs by the similarity or difference of the exposure of the case and control in each pair Concordant pairs are: 1. Pairs in which both the case and the control were exposed, and 2. Pairs in which neither the case nor the control was exposed Discordant pairs are: 3. Pairs in which the case was exposed but the control was not, and 4. Pairs in which the control was exposed and the case was not 47

48 2x2 Table in a Matched Case-Control Study Discordant xposed Controls ot xposed Cases xposed ot xposed Concordant 48

49 2x2 Table in a Matched Case-Control Study aa = number of matched pairs 2 x aa subjects in this cell xposed Controls ot xposed Cases xposed aa bb ot xposed cc dd Total number of subjects = 2 x (aa+bb+cc+dd) 49

50 OR from 2x2 Table in a Matched Case-Control Study Odds ratio (matched) = bb cc xposed Controls ot xposed Cases xposed aa bb ot xposed cc dd ote: bb is not the product of b and b (not b x b); it is the number of pairs 50

51 Matched Case-Control Study: xample CAS COTROL Assume a study of 10 cases and 10 controls in which each control was matched to a case resulting in 10 pairs. = xposed = ot exposed 51

52 Matched Case-Control Study: xample CAS COTROL Cases xposed Controls ot xposed xposed 2 4 ot xposed 1 3 Matched OR = 4 1 = 4 = xposed = ot exposed 52

53 Review: Matched Case-Control Study Cases xposed Controls ot xposed xposed 2 4 ot xposed 1 3 Q1. How many pairs? Q2. How many subjects? Q3. What are the discordant pairs? Q4. Which is the bb cell? Q5. What is the bb cell? 53

54 Review: Unmatching a Matched 2x2 Table Matched CC Controls xposed ot xposed Cases xposed 2 4 ot xposed 1 3 Disease Unmatched Yes o 2x2 xposure xposed ot xposed 54

55 Section D Attributable Risk

56 Attributable Risk Attributable risk (AR) is a measure of excess risk that is attributed to the exposure Attributable risk in the exposed group equals the difference between the incidence in the exposed group and the incidence in the non-exposed (baseline) group 56

57 Attack Rates from Food-Borne Outbreak xercise Attack Rate (%) Difference of Attack Rates Food (1) Ate (2) ot Ate (1) (2) gg salad Macaroni Cottage cheese Tuna salad Ice cream Other

58 Risk in xposed and on-xposed Groups Background Risk xposed group on-exposed group 58

59 Risk in xposed and on-xposed Groups Incidence due to exposure Attributable risk Incidence not due to exposure Background Risk xposed group on-exposed group 59

60 Risk in xposed and on-xposed Groups 1. Incidence attributable to exposure (attributable risk) = ( Incidence in ) ( Incidence in ) exposed group non-exposed group 60

61 Risk in xposed and on-xposed Groups 1. Incidence attributable to exposure (attributable risk) = ( Incidence in ) ( Incidence in ) exposed group non-exposed group 2. Proportion of incidence attributable to exposure (proportional attributable risk) = ( Incidence in ) ( Incidence in ) exposed group non-exposed group Incidence in exposed group 61

62 xample: Cohort Study Develop CHD Do not develop CHD Totals Incidence of disease Smoke cigarettes Do not smoke cigarettes per 1, per 1,000 62

63 Attributable Risk in Smokers 1. The incidence in smokers which is attributable to their smoking = ( Incidence in ) ( Incidence in ) smokers non-smokers = = 10.6/1,000/year 63

64 Proportion Attributable Risk in Smokers 2. The proportion of the total incidence in the smokers which is attributable to their smoking = ( Incidence in ) ( Incidence in ) smokers non-smokers Incidence in smokers = = = = 37.9% 64

65 Risk in the Total Population Population is a mix of exposed and non-exposed groups 65

66 Attributable Risk in the Total Population 3. Incidence attributable to exposure = ( Incidence in ) ( Incidence in ) total population non-exposed group 66

67 Attributable Risk in the Total Population 3. Incidence attributable to exposure =( Incidence in ) ( Incidence in ) total population non-exposed group 4. Proportion of incidence attributable to exposure = ( Incidence in ) ( Incidence in ) total population non-exposed group Incidence in total population 67

68 Attributable Risk in the Total Population 3. Incidence attributable to smoking in the total population = ( Incidence in ) ( Incidence in ) total population non-exposed group 68

69 Attributable Risk in the Total Population If the incidence in the total population is unknown, it can be calculated if we know: Incidence among smokers Incidence among nonsmokers Proportion of the total population that smokes 69

70 Attributable Risk in the Total Population We know that: The incidence in smokers = 28.0/1,000/year The incidence in nonsmokers = 17.4/1,000/year From another source, we learn that: The proportion of smokers in the population is 44% So, we know that: The proportion of nonsmokers in the population is 56% 70

71 Attributable Risk in the Total Population Incidence in total population = ( Incidence) Percent smokers in in smokers population ( ) ( )+ Incidence in nonsmokers Percent non-smokers in population ( ) (28.0/1000) (.44) + (17.4/1000) (.56) = 22.1/1000/year 71

72 Attributable Risk in the Total Population 3. Incidence attributable to smoking = ( Incidence in total population ) ( Incidence in ) non-smokers (22.1/1000/year) (17.4/1000/year) = 4.7/1000/year 72

73 Attributable Risk in the Total Population 4. Proportion of incidence attributable to exposure =( Incidence in ) ( Incidence in ) total population non-smokers Incidence in total population = 21.3% 73

74 Lung Cancer, CHD Mortality in Male British Physicians Age-Adjusted Death Rates/100,000 Smokers on-smokers RR AR %AR Lung cancer % CHD % %AR = Proportion attributable risk Source: Doll and Peto (1976). BMJ, 2:

75 Lung Cancer, CHD Mortality in Male British Physicians Age-Adjusted Death Rates/100,000 Smokers on-smokers RR AR %AR Lung cancer % CHD % %AR = Proportion attributable risk Source: Doll and Peto (1976). BMJ, 2:

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