Measures of Association

1. Measures of Association

2. Objectives Define measures of association Discuss formulas and examples of association measures Describe the relationships between measures of association Discuss strengths and weaknesses of ratio measures Compare/contrast ratio and difference measures

3. Measures of Association (Effect) Used to determine whether an association exists between an outcome and a study factor Reflects the strength of the statistical relationship between the study factor and the disease Involves a direct comparison of frequency measures for different values or categories of the study factor Involves a comparison group which is arbitrary and set by the investigator (usually considered the unexposed or least exposed)

4. Important Note ! In this discussion (like your chapter) We assume: categorical variables The primary statistical tools used to handle continuous variables are the correlation coefficients, ANOVA and linear regression analysis only two levels of exposure no loss to follow-up

6. Types of Measures of Association Used in Analytic Epidemiologic Studies Based on Relative Differences (Ratio Measures) Cumulative Incidence Ratio ( CIR, Risk Ratio) Incidence Density Ratio (IDR, Rate Ratio) Odds Ratio (OR) Based on Absolute Differences 1. Attributable risk in the exposed (AR E, % AR E ) Population attributable risk (PAR, % PAR) Mean differences (continuous outcomes)

7. Usual application of Measures of Association Used in Analytic Epidemiologic Studies

8. Relative Differences

9. Types of measures base on relative differences Ratio Measures (Relative Risk) Cumulative Incidence Ratio (Risk Ratio) Incidence Density Ratio (Rate Ratio) Odds Ratio

10. Careful! In the epidemiology literature, the term �relative risk� is used often used. It can mean either one of the following: Risk ratio (CIR) Rate ratio (IDR) Odds ratio (OR) Other measures, such as prevalence ratio in a cross-sectional study. As the reader, it is important to know which measure is actually being calculated because they are not all interchangeable.

11. Cohort Study with Count Data A cohort study with dichotomous exposure categories and with all subjects followed for a fixed period of time: exposed unexposed cases a b pop at risk N1 N0

12. Cohort Study with Count Data - CIR The distribution of CIR, (0, +8), is not symmetric and not normal. A log transformation is usually applied to CIR. If Ln(CIR) has an approximately normal distribution, the mathematical characteristics of this distribution can be used to construct a confidence interval.

13. Calculating CIR: Cohort study with count data A comparison of risk estimates Generally calculated from cohort studies based on internal comparison of the cumulative incidence (risk) of the exposed and unexposed groups Formula: CIR = CIe = a CIe a + b c c + d

14. Example: CIR with count data What is the association between taking anti-malarial pills (E) and the development of malaria (D) among Peace Corps volunteers in Kenya, 1997? (1 year of follow-up, no losses, CI by the simple method)

15. Types of measures base on relative differences Ratio Measures (Relative Risk) Cumulative Incidence Ratio (Risk Ratio) Incidence Density Ratio (Rate Ratio) Odds Ratio

16. Cohort Study with Person-time Data exposed unexposed cases a b person-time at risk PT1 PT0

17. Cohort Study with Person time Data: IDR Ratio comparison of 2 average rates Typically calculated from a cohort study drawn from a single defined population, either fixed or dynamic An internal comparison of incidence densities (rates) of the exposed and unexposed groups Formula: IDR = IDe = Ae / Te IDe Ae / Te

18. Cohort Study with Person time Data: IDR Maternal alcohol consumption (E) and the development of fetal alcohol syndrome (D) in babies born in Oslo, Norway, 1990-1993

19. Cohort Study with Person time Data: IDR Maternal alcohol consumption (E) and the development of fetal alcohol syndrome (D) in babies born in Oslo, Norway, 1990-1993

20. If we assume the rates are constant for the study period,

21. Types of measures base on relative differences Ratio Measures (Relative Effect) Cumulative Incidence Ratio (Risk Ratio) Incidence Density Ratio (Rate Ratio) Odds Ratio

22. Odds Ratio Calculated primarily from case-control studies, but also used for cohort studies (because it�s easy to calculate with logistic regression) Same interpretation as CIR or IDR, with 1.0 being the null value Can calculate either the exposure odds ratio or the disease odds ratio � these are mathematically equivalent.** Some synonyms: probability relative odds, risk relative odds OR is a valid measure of association, but is often used to approximate the CIR/IDR in case-control studies We�ll cover this in greater detail in our lecture on case-control studies

23. Odds Ratio Ratio of the odds of developing disease OR disease = OR exposure OR exposure = odds of exposure among diseased / odds of exposure among the non-diseased. OR disease = odds of disease among the exposed / odds of disease among the non-exposed

24. The Calculation of OR Diseased Non-diseased Exposed a b Non-exposed c d Exposure odds ratio = odds of exposure in diseased/odds of exposure in non-diseased = (a:c)/(b:d) = ad/bc Disease odds ratio = (a:b)/(c:d) = ad/bc

25. OR: Example Case control study of the association between aspirin consumption (E) and the development of a stomach ulcer (D)

26. OR: Example Case control study of the association between aspirin consumption (E) and the development of a stomach ulcer (D)

27. Relationship between RR and OR

28. OR vs RR in a Cohort Study with Count Data OR is a valid measure of association, but is often used to approximate the CIR/IDR in case-control studies � Why? Because for many it�s easier to interpret Because it is impossible to calculate the RR with certain designs (case-control) It�s easy to adjust an OR for confounding and can be derived from modeling (logistic regression) OR (event) is the exact reciprocal of the OR (nonevent) Which is not the case with the RR

29. Odds ratio (event) is the exact reciprocal of the OR (nonevent) Example: OR of disease = (154/308) / (709/142)= 0.1 The OR of no disease would be the reciprocal = 1/0.1 = 10.0

30. OR ~ RR: The General Rule OR is a good approximation of the CIR/IDR when disease is rare in the population In a case-control study, if controls are selected to represent the total population (rather than just non-cases), then OR ~ CIR/IDR without regard for disease prevalence in the population. (Miettienen, 1976) Covered in case-control lecture Under certain sampling schemes, OR ~ CIR/IDR more directly, without regard for disease prevalence Covered in case-control lecture

31. OR ~ CIR, cont�d Odds Ratio is biased away from the null ( in both directions) Recall, OR = q+ RR = q+ 1- q+ q- q- 1- q- So, 1- q- / 1- q+ defines the built in bias between RR & OR When disease is rare, this bias is negligible

32. Cross-Tabulation of Exposure and Disease in a Cohort Study with Count Data

33. OR ~ CIR, cont�d Example (data from text tables 3-3 and 3-4): OR = RR x �built in bias� If, RR = 6.0 and CI UE = .0030 and CI E = .0180 OR = 6.0 x [(1-.0030) / (1-.0180)] = 6.09 If, RR= 6.09 and CI UE = .0705 and CI E = .2529 OR = 6.0 x [(1- .0705) / (1-.2529)] = 7.46 If, RR= 3.59 and CI UE = .0705 and CI E = .2529 OR = 3.59 x [(1- .0705) / (1-.2529)] = 4.46

34. Hypothetical Cohort Study of the 1-Year Incidence of MI in Individuals with and without Hypertension

36. Odds Ratio and Relative Risk Both compare the likelihood of an event between two groups. Example: Who�s more likely to die, men or women? Would you use OR or RR and are they the same?

37. Odds Ratio and Relative Risk Importance of structuring data in a 2x2 table Assume: E = Female, D = Dead RR = (154/462) / (709/851) = 0.4 Assume E = Male, D = Dead RR = (709/851) / (154/462) = 2.5 Assume E = Female, D = Alive RR = (308/462) / (142/851) = 3.99

38. Odds Ratio and Relative Risk OR = RR?? Assume E = Male, D = Dead OR = 10.0 Assume E = Dead, D = Male OR = 10.0 Recall, OR exp = OR dis Assume E = Female, D = Dead OR = 0.1

39. Strengths of Ratio Measures All ratio measures have the same reference point, a null value of 1.0 (no association) Comparisons across studies of different designs can be made, because OR ~ CIR/IDR IDR ~ CIR The strength of the association between a study factor and outcome is one element (an important one) used to assess causality

40. Limitations of Ratio Measures May be deceptive in addressing the impact of the risk factor in assessing an individual�s risk due to an exposure Example: Risk of lung cancer and CHD for smokers and non-smokers

41. Absolute Differences

42. Measures of Association: Absolute Differences (Difference Measures, Attributable Risk) These are measure of association between an exposure and outcome based on the absolute difference between two risk/rate estimates. Difference measures are calculated by subtracting the frequency estimates of the reference group from the comparable estimate of the exposure group. Terminology: etiologic fraction (when causation is established), excess fraction (no causation established)

43. Incidence of Reproductive Malignancies among Women in the Royal College of General Practitioners Oral Contraceptive Study

44. Measures of Absolute Difference Types of difference measures: Attributable Risk (risk difference, excess fraction, etiologic fraction) Attributable Risk in Exposed ( called Incidence Density Difference if using rates) Percent Attributable Risk in the Exposed Levin�s Population Attributable Risk

45. A. Attributable Risk in the Exposed Difference between risk estimates of different exposure levels and a reference level The excess, above background, associated with the exposure under study Theoretically, the absolute excess incidence that would be prevented by eliminating the exposure. Formula: ARe = CIe - CIe or IDD = IDe - IDe ARexp has the same unit as the incidence measure (dimensionless if CI; time-1 if ID).

46. Attributable Risk in the Exposed

47. A. Attributable Risk in the Exposed, Example Excess risk of taking anti-malarial pills attributed to the development of malaria among Peace Corps volunteers in Kenya, 1997

48. Comparison of Relative Risk and Attributable Risk in Mortality from Lung Cancer and from Coronary Heart Disease for Heavy Smokers and Nonsmokers

49. Measures of Absolute Difference Types of difference measures: Attributable Risk (risk difference, excess fraction, etiologic fraction) Attributable Risk in Exposed Percent Attributable Risk in the Exposed Population Attributable Risk (% Pop AR) 2. Incidence Density Difference

50. B. Percent Attributable Risk in the Exposed The percent of the total risk in the exposed group attributable to the exposure, if causality has been established. Formulas: %ARexp = CIe - CIe x 100 CIe %ARexp = CIR* � 1.0 x 100 CIR* *Can use IDR or OR %ARexp = IDe - IDe x 100 IDe

51. Percent ARexp %ARexp is equivalent to percent efficacy when assessing an intervention such as a vaccine. The group receiving the intervention is considered �nonexposed�, which has a lower incidence of the disease that is targeted by the vaccine.

52. B. Percent Attributable Risk in the Exposed, Example What is the percent of the total risk of developing malaria among those who take anti-malarial medication attributable to the medication? (Peace Corp Volunteers, 1997)

53. Measures of Absolute Difference Types of difference measures: Attributable Risk (risk difference, excess fraction, etiologic fraction) Attributable Risk in Exposed Percent Attributable Risk in the Exposed Levin�s Population Attributable Risk 2. Incidence Density Difference

54. C. Population Attributable Risk % The excess risk in the total population attributable to the exposure if a causal relationship is assumed. Formulas: Pop AR% = CIpop - CIe x 100 CIpop PopAR% = pe(CIR* � 1) x 100 pe(CIR* � 1) + 1 pe: prevalence of exposure in the population * Can use IDR or OR

55. C. Population Attributable Risk% , Cont. Population attributable risk is a function of 2 parameters, prevalence of exposure in the population & the magnitude of the increase in incidence associated with the exposure. It is population specific, ? frequency of exposure is taken into account Cannot project the results from one population to another if the frequency of exposure differs between the populations When pe is low, CIpop ~ CIe When pe is high, CIpop ~ CIe ? Pop AR% ~ ARexp when pe is high

56. Pop AR and Population Prevalence of the Exposure (when exposure is rare)

57. C. % PAR: Example Given the following data, what is percent of the total risk of CHD in the population attributable to being a current smoker?

58. Pop AR %, cont�d Consider, Exposure A has a CIR of 10 for cancer and Exposure B has a CIR of 20 for cancer Assume the health department has resources to address only one exposure, which one should it be?

59. General Use of Difference Measures Reflect the excess number of cases attributable to the exposure Reflect the expected effect of changing the distribution of one or more risk factors in a particular population Useful from a public health perspective � when attributable risk is high, the risk factor is of importance to the health of the community

60. Which measure of association should you calculate from a study?

61. Ratio Versus Difference Measures Example: British Physician�s Cohort Study, Death rate per 100,000 person years

62. Relative versus Absolute Differences Relative differences are used most often when evaluating the determinants of disease because they represent the magnitude of the association. This information is critical in the determination of causality. Once causality is assumed, absolute differences are more important measures from the perspective of public health administration and policy.

63. Summary We have now covered the major types of epidemiologic quantitative measures: Measures of Disease Frequency Measures of Association Taken together, these measures serve as the basic tools for developing methods of epidemiologic research

64. An Example to Try at Home A cohort study is conducted examining the relationship between cigar smoking and stroke. The results were as follows: