2. ph250b.14 measures of association 1

1. Measures of association

2. Measures of association learning objectives 1. Define and understand the difference between the concepts of “effects” and “associations” 2. Use a contingency (2x2) table to organize information on disease occurrence in time 3. Understand the differences between the additive and multiplicative scales a. Identify the scale of each measure of association 4. Know how to calculate and interpret measures of association listed below (this includes knowing the formulas) a. Relative measures i. Cumulative incidence ratio ii. Incidence density ratio iii. Prevalence ratio iv. Odds ratio b. Absolute measures i. Attributable risk (aka risk difference) ii. Attributable risk percent iii. Population attributable risk iv. Population attributable risk percent c. Number needed to treat 5. Understand what the strength of an association captures 6. Understand what relative and absolute measures capture 7. Understand what attributable percentage measures capture

3. Measures of association outline – Big picture – Scales of measures – The 2x2 table – Measures of association • Relative measures • Absolute measures • Other measures – Summary

4. Big picture • In epidemiology, we often compare measures of disease frequency between different groups – Building on measures of disease module • Typically comparing disease frequency between groups with different exposures • The goal is to ascertain associations between exposures and outcomes and, ultimately, effects of exposures on outcomes

5. Big picture • Reminder on the distinction between associations and effects • An association tells us about probabilities of past events – Carrying matches is associated with lung cancer

6. Big picture • An effect is causal and it tells us how probabilities change if conditions change – If you remove matches from pockets in the population, does the rate of lung cancer decrease? ?

7. Big picture • Measures of association quantify the strength and direction of associations between exposures and outcomes • Strength of association: – Is exposure weakly related to outcome? Strongly?

8. Big picture • Direction of association: – Does exposure increase risk of disease (risk factor)? – Does exposure decrease risk (protective factor)? – Is there no association (null result)?

9. Big picture • Recall counterfactual framework illustrated by an “ideal experiment” • A hypothetical study which, if we could actually conduct it, would allow us to infer causality – Population experiences one exposure and observed for outcome over a given time period – Roll back the clock – Change the exposure but leave everything else the same, observe for outcome over the same time period – Compare the outcomes under both exposures: this is the causal effect

10. Big picture • In reality, the “ideal experiment” cannot be conducted • We evaluate the associations between exposures and outcomes by comparing outcomes between groups that experienced different exposures

11. Big picture • Measure of association does not necessarily (or even typically) quantify a causal effect • Associations may be explained by various sources: – Causal relation – Chance (random error) – Bias (systematic error)

12. Big picture • Throughout course will enumerate the methods for: – Designing studies to minimize error (systematic and random) – Assessing the roles of systematic and random error once a study is conducted (qualitatively and quantitatively) – Incorporating knowledge or assumptions about the causal process – Analytically removing or adjusting for error to the extent possible

13. Big picture • These are key steps to moving towards inferring causality from associations

14. Measures of association outline – Big picture – Scales of measures – The 2x2 table – Measures of association • Relative measures • Absolute measures • Other measures – Causal perspective on scales and measures – Summary

15. Scales of measures • There are different scales for measuring associations between variables • Analogy: if you wanted to measure weight changes you might measure: – Weight loss/gain in lbs – Weight loss/gain as a percentage of starting weight – Change in BMI percentile • Comparison of gain/loss between people would depend on measure used

16. Scales of measures • Similarly, there are different scales for quantifying the size or strength of association between an exposure and an outcome

17. Scales of measures • Measures of association can be calculated on two different scales: – Relative scale (ratios) – Absolute scale (differences) • Each scale has several defining characteristics: – Range of values that the measure of association can take – Null value: value at which there is no association (value consistent with the null hypothesis of no association)

18. Scales of measures • The scale of a measure of association is critical because measures on different scales capture different things • First focus on learning how the scales are different • We will discuss motivations for choosing relative versus absolute measures towards the end of this module

19. Scales of measures Relative scale – ratio measures of association • The ratio of two measures of diseases is on the relative scale: – Example: (rate among the exposed)/(rate among the unexposed) – IDexposed / IDunexposed • Examples of relative measures include: Cumulative incidence ratio (CIR), incidence density ratio (IDR) • The CIR and IDR are often referred to as risk ratio or rate ratio respectively, and are abbreviated RR

20. Scales of measures Relative scale – ratio measures of association • Range: zero to positive infinity • Null value: 1 • CIR = 1 or IDR = 1 means the exposure is not associated with the outcome

21. Scales of measures Absolute scale – difference measures of association • The difference between two measures of disease is on the absolute scale: – Example: rate among the exposed – rate among the unexposed – IDexposed – IDunexposed • Examples of absolute measures include: attributable risk/rate (AR), population attributable risk/rate (PAR) • Note that “attributable risk” often used generically to include risks and rates

22. Scales of measures Absolute scale – difference measures of association • Range: negative infinity to positive infinity • Null value: 0 • AR = 0 means the exposure is not associated with the outcome

24. 2x2 table • Count data is typically organized with a 2x2 or contingency table • Example: with incidence data a/(a+b) = CIe • What is CI in the total population?

25. 2x2 table • Incidence density data is also organized with a 2x2 or contingency table • Example: a/PTe = IDe

26. 2x2 table • Note that Stata and the Kleinbaum text book present the table “backwards” with exposure on top and disease on the left • Pay attention to the orientation of the table before making calculations

27. 2x2 table Note on notation – PTexposed = PTe – PTunexposed = PTu – PTtotal = PTt – Will also see applied to measures of disease including CI, ID

29. Relative measures • Measures to be discussed – Risk/rate ratio – Prevalence ratio – Odds ratio

30. Relative measures • Risk/rate ratio (RR) – aka relative risk – “Risk” in relative risk used generically to include risk or rate • Provides information about relative association between an exposure and a disease • The risk/rate of disease in the exposed is compared to the same measure among the unexposed as a ratio • RR = Rexposed / Runexposed = Re / Ru • Where R indicates either risk or rate – (i.e., CI (cumulative incidence) or ID (incidence density))

31. Relative measures • RR can be used to refer generically to these relative measures • CIR is the specific term when cumulative incidence is used • IDR is the specific term when incidence density is used • Used to see term RR used generically for any relative measure (including OR, PR) but current trend is toward specific terms

32. Relative measures • Interpretations of RR: • Relative difference in the risk/rate of disease between the exposed and unexposed • Interpretation of RR=5: Risk/rate of disease in the exposed is 5 times the risk/rate in the unexposed • Interpretation of RR=0.5: Risk/rate of disease in the exposed is 0.5 times the risk/rate in the unexposed

33. Relative measures • Example: study of oral contraceptive (OC) use and bacteriuria among women 16-49 yrs over 1 year • RR = ? • What measures of disease incidence can we estimate from this data? • How do we compare them to estimate RR?

34. Relative measures • Can estimate CIs • Take ratio to estimate RR • RR = CIR = CIe /CIu = • RR = (27/482)/(77/1908) = 1.39 • Women who use OCs have 1.39 times the risk of bacteriuria (over 1 year) compared with women who do not use OCs • Note that as with CI, CIR is only interpretable with information on the time period over which it was calculated

35. Relative measures • Prevalence ratio (PR) • Provides information about relative association between an exposure and a disease, using prevalence as the measure of disease – Analogous to RR • PR = Prevexposed / Prevunexposed = Preve / Prevu

36. Relative measures • Interpretations of PR: • Relative difference in the prevalence of disease between the exposed and unexposed • Interpretation of PR=5: Prevalence of disease among the exposed is 5 times the prevalence in the unexposed • Interpretation of PR=0.5: Prevalence of disease in the exposed is 0.5 times the prevalence of disease in the unexposed

37. Relative measures • A brief aside on odds • Odds – two equivalent definitions – Odds = number of people with event / number of people without an event – Odds = probability of event occurring / probability of event not occurring = P / (1-P) • Example: – 10 people in a classroom of 50 have a cold – Probability of having a cold = 10/50 = 0.2 – Probability of not having a cold = 40/50 = 0.8 – Odds of having a cold = 10/40 = 0.2/0.8 = 0.25 • Odds range from 0 to positive infinity

38. Relative measures • Utility of odds will become apparent when we discuss study design and analysis of epidemiologic data – When a disease is rare, odds can be modeled in place of risks with similar results – In some study designs (case-control varieties) odds estimate pseudo-risks/rates (more in study design)

39. Relative measures • Odds ratio (OR) • Provides information about relative association between an exposure and a disease, using odds as the measure of disease – Analogous to RR • OR = (Pe /(1-Pe ))/(Pu /(1-Pu )) • OR = Odds(disease)e / Odds(disease)u JC: discuss (Disease Odds) vs. (Exposure Odds)

40. Relative measures • Interpretations of OR: • Relative difference in the odds of disease between the exposed and unexposed • Interpretation of OR=5: Odds of disease is in the exposed is 5 times the odds in the unexposed • Interpretation of OR=0.5: The odds of disease in the exposed is 0.5 times the odds of disease in the unexposed • Note: it is incorrect to interpret the odds ratio as the risk/rate ratio – Exception for particular case-control study designs (more in study design module)

41. Relative measures • OR always more extreme than RR (further from null) – When the disease is rare the values will be close – Note that this is not relevant for designs in which OR captures a risk/rate ratio directly (more in study design)

42. Relative measures • OR versus RR • Example: – Recall the example of students having a cold • P=0.2 • Odds=0.25 – Say we wanted to compare this classroom to an office – In the office, 10 out of 100 people have a cold. • P = 10/100 = 0.1 • Odds = 10/90 = 0.111 – Exposed are students, unexposed are office workers, outcome is cold – RR comparing students to workers: RR = 0.2 / 0.1 = 2 – OR comparing students to workers: OR = 0.25 / 0.111 = 2.25

43. Relative measures • OR = ? • OR = Odds(dis)exposed /Odds(dis)unexposed • OR = (a/b)/(c/d) = ad/bc • OR = (27x1831)/(77x455) = 1.41 • Women who use OCs have 1.41 times the odds of bacteriuria compared to women who do not use OCs JC: mention disease odds vs. exposure odds

44. Relative measures • Formula review – RR = Re / Ru – PR = Preve / Prevu – OR = (Pe /(1-Pe ))/(Pu /(1-Pu )) – OR = Odds(dis)e /Odds(dis)u

45. Relative measures • Exercise for home (discuss in lab) • Hypothetical RCT for injection drug users – Primary outcomes are cessation of drug use – HIV as a secondary outcome of interest

46. Relative measures • Exercise at home / in lab • 60 people randomized to a 12-month residential detoxification program – 49 tested HIV negative at the start of the trial – At the end of the trial, 5 participants tested positive for HIV who had been negative at the start of the trial • 60 people randomized to 12-months of outpatient treatment – 50 tested HIV negative at the start of the trial – At the end of the trial, 3 participants tested positive for HIV who had been negative at the start of the trial

47. Relative measures • Exercise at home / in lab • Calculate and interpret relative measures of association of potential interest from these trial results

49. Absolute measures • Measures to be discussed – Attributable risk (AR) – aka risk/rate difference (RD) – Attributable risk percent (AR%) – Population attributable risk (PAR) – Population attributable risk percent (PAR%)

50. Absolute measures • Attributable risk (AR) – aka risk/rate difference (RD) • “Risk” in attributable risk used generically to include risk or rate • Provides information about absolute association between an exposure and a disease, or the excess risk or rate of disease in the exposed • AR = Rexposed – Runexposed • Where R indicates either risk or rate – (i.e., CI (cumulative incidence) or ID (incidence density))

51. Absolute measures • Interpretations of AR: • Difference in risk/rate of disease between the exposed and unexposed • Excess risk/rate of disease in the exposed compared with the unexposed • AR has same units as the incidence measure used (risk (dimensionless) if CI; rate (1/time) if ID)

52. Absolute measures Szklo Figure 3-1

53. Absolute measures • Example: study of oral contraceptive (OC) use and bacteriuria among women 16-49 yrs over 1 year • AR = ? • How do we compare cumulative incidence to estimate AR?

54. Absolute measures • Take difference to estimate AR • AR = CIe – CIu = • AR = (27/482)–(77/1908) = 0.01566 • Women who use OCs have 0.01566 higher risk of bacteriuria compared with women who do not use OCs over 1 year • Can multiply by a population size to facilitate interpretation: 0.01566x100,000 = 1566/100,000 • Among every 100,000 women who use OCs there are 1566 excess cases of bacteriuria compared with women who do not use OCs over 1 year

55. Absolute measures • Attributable risk percent (AR%) • Provides information about the excess incidence in the exposed (AR) as a percentage of incidence in the exposed population • AR% = (Rexposed – Runexposed ) / Rexposed x 100 • AR% = AR/ Rexposed x 100

56. Absolute measures • Interpretations of AR%: • Percentage of all disease incidence among the exposed that is associated with the exposure • Percentage of disease incidence in the exposed that is in excess of the incidence in the unexposed

57. Absolute measures Szklo Figure 3-1 100% of incidence in the exposed population AR% - percentage of disease incidence in the exposed that is in excess of the incidence in the unexposed

58. Absolute measures • AR% = ? • AR% = (CIe – CIu )/CIe x 100 • AR% = (27/482)–(77/1908)/(27/482) x 100 = 28% • Of the bacteriuria incidence among women who use OCs, 28% is in excess of the incidence in women who do not use OCs

59. Absolute measures • Attributable risk percent (AR%) is analogous to efficacy for an intervention (e.g., vaccine, other treatment) • The control group is considered “exposed” • The treatment group is considered “unexposed” • AR% = (Rexposed – Runexposed ) / Rexposed x 100 • Efficacy% = (Rcontrol – Rtreatment ) / Rcontrol x 100 • Percentage of disease incidence in the control group that is in excess of the incidence in the treatment group

60. Absolute measures • Population attributable risk (PAR) • Provides information about the excess risk or rate of disease in the entire population (not just among the exposed as with AR) – Sometimes the AR is called the “attributable risk among the exposed” to make this distinction clear • PAR = Rtotal – Runexposed • Alternative formulation: • PAR = (AR)(Pe ) – Pe = prevalence of the exposure in the total population – See extra slides for derivation • Alternative formulation useful if estimating PAR for a total population other than your study population for which you have an estimate of Pe

61. Absolute measures • Interpretations of PAR: • Excess risk/rate of disease in the total population compared with the unexposed • If association is believed to be causal, PAR can be used to estimate the impact of an exposure on the health of a population of interest • PAR will never be larger than AR in a given population • PAR has same units as the incidence measure used (risk (dimensionless) if CI; rate (1/time) if ID)

62. Absolute measures • PAR = ? • PAR = CIt – CIu = • PAR = (104/2390)–(77/1908) = 0.00316 • In the total population of women there is 0.00316 higher risk of bacteriuria compared with women who do not use OCs • Can multiply by a population size to facilitate interpretation: 0.00316x100,000 = 316/100,000 • There are 316 excess cases of bacteriuria for every 100,000 women in the total population compared with women who do not use OCs JC: review NNT

63. Absolute measures • Comparison of AR and PAR • AR = 1566/100,000 • PAR = 316/100,000 • PAR < AR • Why is this the case?

64. Absolute measures • Population attributable risk percent (PAR%) • Provides information about the excess incidence in the total population (PAR) as a percentage of incidence in the total population • PAR% = (Rtotal – Runexposed ) / Rtotal x 100 • PAR% = (PAR / Rtotal ) x 100

65. Absolute measures • PAR% = ? • PAR% = (CIt – CIu )/CIt x 100 • PAR% = (104/2390)–(77/1908)/(104/2390) x 100 = 7.3% • Of the bacteriuria incidence in the total population of women, 7% is in excess of the incidence in women who do not use OCs

66. Absolute measures • Comparison of AR% and PAR% • AR% = 28% • PAR% = 7% • PAR% < AR% • Why is this the case?

67. Absolute measures Szklo Figure 3-2 Exposure uncommon in total population Exposure common in total population

68. Absolute measures • AR versus PAR – The AR depends only on the strength of the relation between the exposure and the disease – The PAR depends both on the strength of the relation and the prevalence of the exposure

69. Absolute measures • AR = Rexposed – Runexposed • PAR = Rtotal – Runexposed • Think of Rtotal (risk/rate in total population) as a weighted average of the risk/rate among the exposed and unexposed • Weighted by the prevalence of the exposure (Pe ): – Rt = (Pe )Re + (Pu )Ru – Rt = (Pe )Re + (1-Pe )Ru – When Pe is close to 1 (and 1- Pe is close to 0), Rt is close to Re and thus PAR is close to AR – When Pe is close to 0 (and 1- Pe is close to 1), Rt is close to Ru (not Re ) and thus PAR is much smaller than AR

70. Absolute measures Szklo Figure 3-2 Prevalence of exposure not depicted here, but reflected in different magnitudes of PAR Pe is close to 0, Rt is close to Ru (not Re ) and thus PAR is much smaller than AR Pe is close to 1, Rt is close to Re and thus PAR is close to AR

71. – An exposure with a large AR can have a low PAR if the exposure is uncommon – Example: extremely carcinogenic but rare chemical • Removing an exposure with a large AR but a small PAR would not improve the overall health of the population appreciably Absolute measures

72. Absolute measures • There are some study designs (case-control) for which measures of disease cannot be estimated – only the odds ratio (OR), a relative measure, can be calculated (more in study design) • For these studies, there are alternative formulas for the absolute measures that can be applied – they require making some assumptions and/or bringing in outside information

73. Absolute measures • Alternative formulation for AR% • Additional information/assumptions – OR estimates risk/rate ratio • AR% = [(OR – 1) / OR] x 100 • Alternative formula is a simple algebraic transformation of original formula – Dividing (Re – Ru ) / Re by Ru – ((Re /Ru )-(Ru /Ru )) / (Re /Ru ) – (RR-1)/RR – RR estimated by OR* – *How well OR estimates risk or rate ratio depends on design of case-control study and on how common disease is for cumulative case-control

74. Absolute measures • Alternative formulation for PAR% • Additional information/assumptions – OR estimates risk/rate ratio – Prevalence of exposure in the total population can be estimated as the proportion of non-diseased individuals exposed, or from another source: Pe – PAR% = [((Pe )(OR-1)) / ((Pe )(OR-1) + 1)] x 100 • Note Miettinen 1974 other formulation – PAR% = AR% x (proportion exposed among diseased) – Will provide a different estimate than formulation above

75. Absolute measures • Derivation of alternative formula for PAR% • Think of Rtotal (risk/rate in total population) as a weighted average of the risk/rate among the exposed and unexposed • Weighted by the prevalence of the exposure: – Rt = (Re )(Pe ) + (Ru )(1-Pe ) • Substitute into original equation – PAR% = (Rt – Ru )/ Rt – PAR% = ((Re )(Pe ) + (Ru )(1-Pe ) – Ru )/ (Re )(Pe ) + (Ru )(1-Pe ) – PAR% = ((Re )(Pe ) + (Ru )-(Ru Pe ) – Ru )/ (Re )(Pe ) + (Ru )-(Ru Pe )

76. Absolute measures • Divide numerator and denominator by Ru – PAR% = ((Re )(Pe )/Ru + 1 - Pe –1)/ (Re )(Pe )/Ru + 1-Pe – PAR% = ((Re )(Pe )/Ru - Pe )/ (Re )(Pe )/Ru - Pe + 1 – PAR% = (Pe (Re /Ru - 1)/ Pe (Re /Ru – 1) + 1 • Note that RR = Re / Ru therefore if OR estimates RR – PAR% = [(Pe )(OR-1)] / [(Pe )(OR-1) + 1]

77. Absolute measures • Alternative formulation for AR, PAR • Additional information/assumptions – OR estimates risk/rate ratio – Prevalence of exposure in the total population can be estimated as the proportion of non-diseased individuals exposed, or from an outside source: Pe – Risk/rate for the total population can be estimated, usually from an outside source: Rt • Ru = (Rt ) / ((OR)(Pe ) + (1- Pe )) • Re = (OR)(Ru ) • AR = Re -Ru • PAR = Rt -Ru

78. Absolute measures • Derivation of alternative formulas for AR and PAR • Think of Rtotal (risk/rate in total population) as a weighted average of the risk/rate among the exposed and unexposed • Weighted by the prevalence of the exposure: – Rt = (Re )(Pe ) + (Ru )(1- Pe ) • Note that RR = Re / Ru therefore if OR estimates RR – Re = (OR)(Ru ) – Rt = (OR)(Ru )(Pe ) + (Ru )(1- Pe ) • Solve for Ru – Ru = (Rt ) / ((OR)(Pe ) + (1- Pe )) – Re = (OR)(Ru )

79. Absolute measures • Formula review – AR = Rexposed – Runexposed – AR% = [(Rexposed – Runexposed ) / Rexposed ] x 100 – PAR = Rtotal – Runexposed – PAR = (AR)(Pe ) – PAR% = [(Rtotal – Runexposed ) / Rtotal ] x 100 – AR% = [(OR – 1) / OR] x 100 – PAR% = [((Pe )(OR-1)) / ((Pe )(OR-1) + 1)] x 100 – AR = (OR)(Ru ) - (Rt / [(OR)(Pe ) + (1- Pe )]) – PAR = Rt - [(Rt )/ ((OR)(Pe ) + (1- Pe ))]

80. Properties of scales • Absolute measures are symmetrical around 0 – Exposure associated with higher risk/rate is indicated by a positive value (e.g., AR = 0.01) – Exposure associated with lower risk/rate is indicated by a negative value (e.g., AR = -0.01) – Magnitudes of negative and positive ARs with same numeric value are equivalent but in opposite directions (e.g., AR = 0.01 same magnitude as AR = -0.01)

81. Properties of scales • Relative measures are asymmetrical around 1 – Exposure associated with higher risk/rate is indicated by a value >1 (e.g., RR = 2) – Exposure associated with lower risk/rate is indicated by a value 0-1 (e.g., RR = 0.5) – To calculate a relative measure’s equivalent on the other side of the null you have to take its inverse (1/RR) • RR = 2 is of equivalent strength to a protective factor with RR = 1/2 = 0. 5

82. Properties of scales • Relative measures – on arithmetic and log scales

83. Properties of scales • Due to the asymmetry of relative measures – Log-transformed (natural log) axes are often used to graphically present relative measures – Variances of relative measures are calculated on the log scale, and any calculations based on the variance (e.g., confidence intervals) are completed on the log scale before returning to the relative measure scale

84. Variance estimates • Approximate variance estimates for measures of association (some are in Szklo appendix A) • Variance of: – ln(IDR) = (1/a) + (1/b) – ln(CIR) = (b / a(a+b)) + (d / c(c+d)) – ln(OR) = (1/a) + (1/b) + (1/c) + (1/d) • Small cells inflate variance

85. Other measures • Number needed to treat (NNT) – Related to attributable risk • Provides information about the number of people you would have to remove exposure from to prevent one case of disease • NNT = 1 / AR – The number (of exposed persons) needed to treat is the reciprocal of the attributable risk • Not appropriate unless you believe the relation is causal

86. Other measures • Example of OCs and bacteriuria • AR = 0.01566 • NNT = 1/AR = 1/0.01566 = 64 • 64 OC users need to stop using OCs to eliminate one case of bacteriuria

87. Absolute measures • Exercise • Recall our hypothetical RCT • 60 people randomized to a 12-month residential detoxification program – 49 tested HIV negative at the start of the trial – At the end of the trial, 5 participants tested positive for HIV who had been negative at the start of the trial • 60 people randomized to 12-months of outpatient treatment – 50 tested HIV negative at the start of the trial – At the end of the trial, 3 participants tested positive for HIV who had been negative at the start of the trial

90. Summary • Measures of disease among groups with different exposures are compared in observational epidemiology • These comparisons are made with measures of association between exposures and diseases • Introduced to a variety of measures of association broadly classified as relative or additive Re /Ru Re -Ru

91. Summary • While the relative have been more commonly used, the additive have been argued to be better for purposes of identifying etiology and estimating public health impact • Insights from two of the theoretical causal models elucidate why this argument has been made, and elucidate what relative and absolute measures estimate

92. Summary Variety of terms used for measures of association discussed today • “Risk” often used generically to include rates (ID), risks (CI) and even prevalence

93. Summary Relative measures • Cumulative incidence ratio (CIR) • Incidence density ratio (IDR) • Prevalence ratio (PR) • Rate/risk ratio = Relative risk (RR) • Odds ratio (OR)

94. Summary Absolute measures • Attributable risk (AR) = Risk/rate difference = Excess risk • Population attributable risk (PAR) = Population risk/rate difference • Attributable risk percent (AR%) = Etiologic fraction = Attributable proportion among the exposed • Population attributable risk percent (PAR%) = Attributable proportion in the total population

95. Summary • Have only examined what are called “crude” measures of association – Compared exposed and unexposed populations without considering other variables that may differ between the populations – Later in the course we will discuss how to deal analytically with other variables that may be different between the exposed and unexposed and that thus make the populations not exchangeable (to be discussed in confounding)

96. Extra slides

97. Absolute measures • Alternative formulation: • PAR = (AR)(Pe ) • Where does this come from? • PAR = Rt – Ru • PAR = [(Pe )Re + (1-Pe )Ru ] - Ru • PAR = (Pe )Re + Ru - (Pe )Ru - Ru • PAR = (Pe )Re - (Pe )Ru • PAR = (Re - Ru )(Pe ) • PAR = (AR)(Pe )

98. Causal perspective • When we estimate AR, PAR, AR% or PAR% (whether with counterfactual populations or in observational data) they will only provide a lower bound of the true incidence or fraction of incidence due to the exposure mechanistically (think of the pies) – unless exposure acts independent of background causes

99. Causal perspective Szklo Figure 3-1 Incidence caused by mechanism including exposure In absence of exposure, another causal mechanism (background cause) was completed within study time frame

100. Causal perspective Population unexposed for a given time period, population exposed over same period Rates/risks compared are causal p1+p3 p1+p2 Counterfactual Counterfactual

101. Causal perspective • Extreme example – mechanism including your exposure causes disease 1 day earlier than would have occurred otherwise from background causes • In the exposed, your exposure mechanistically caused 100% of disease • In your data the rate of disease appears the same in the exposed and unexposed and you infer 0% of disease caused by your exposure (ME3 p63, 297 for elaborated discussion) • Type 2 (slide 74) individuals (in this example 100% of them) had disease caused by exposure when exposed, but caused by another mechanism when not exposed • Thus incidence due to specific causal mechanisms cannot be estimated from epidemiologic data

102. Relative measures • OR – exposure OR vs disease OR – Exposure OR = odds(E|D)/odds(E|Dnot) – EOR = (a/c)/(b/d) = ad/bc – Disease OR = odd(D|E)/odds(D|Enot) – DOR = (a/b)/(c/d) = ad/bc – Exposure OR = disease OR

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