1. 3/2/2011Case-control studies1 Study designs: Case-control studies Victor J. Schoenbach, PhD home page Department of Epidemiology Gillings School of Global Public Health University of North Carolina at Chapel Hill www.unc.edu/epid600/ Principles of Epidemiology for Public Health (EPID600)

2. 10/7/2008Case-control studies2 From my uncle Are you the weakest link? Below are four (4) questions. You have to answer them instantly. You can't take your time, answer all of them immediately. OK? Let's find out just how clever you really are. Ready?

3. 10/7/2008Case-control studies3 Question 1 You are participating in a race. You overtake the second person. Question: What position are you in?

4. 10/7/2008Case-control studies4 Question 1 – answer If you answer that you are first, then you are absolutely wrong! Answer: If you overtake the second person and you take his place, you are second!

5. 10/7/2008Case-control studies5 On to question 2 Try not to screw up on the next question. To answer the second question, don't take as much time as you took for the first question.

6. 10/7/2008Case-control studies6 Question 2 Question: If you overtake the last person, then you are …?

7. 10/7/2008Case-control studies7 Question 2 – answer Answer: If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST person?! …? You're not very good at this are you?

8. 10/7/2008Case-control studies8 On to question 3 The third question is very tricky math! Note: This must be done in your head only. Do NOT use paper and pencil or a calculator. Try it.

9. 10/7/2008Case-control studies9 Question 3 – what is the total? Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10.

10. 10/7/2008Case-control studies10 Question 3 – answer Did you get 5,000? The correct answer is actually 4,100. Don't believe it? Check with your calculator!

11. 10/7/2008Case-control studies11 On to question 4 Today is definitely not your day. Maybe you will get the last question right?

12. 10/7/2008Case-control studies12 Question 4 Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, 4. Nono. Question: What is the name of the fifth daughter?

13. 10/7/2008Case-control studies13 Question 4 – answer Answer: Nunu? NO! Of course not. Her name is Mary. Read again. (“Mary's father has five daughters.…”) You ARE the WEAKEST LINK!!!!!! Good- bye!!! (With Love, Your Uncle)

14. 10/7/2008Case-control studies14 Plan for this lecture Confidence intervals and significance tests (read only) Incidence density and cumulative incidence (brief) Attributable risk (brief) Theoretical overview of case-control studies as a complement to the traditional perspective

15. 10/7/2008Case-control studies15 Confidence intervals & significance tests Everything you’ve been told so far about confidence intervals and statistical significance is probably misleading, including this statement. I am not licensed to teach statistics, so what I say on this topic mustn’t leave this room!

16. 10/7/2008Case-control studies16 Confidence intervals “a plausible range of values for the unknown population parameter” Michael Oakes, Statistical inference, p.52 Exact interpretation is problematic We are more confident that a 95% interval covers the parameter than a 90% interval, but the 95% interval is wider (provides a less precise estimate)

17. 10/7/2008Case-control studies17 Significance tests “It might be argued that the significance test, if properly understood, does no harm. This is, perhaps, fair comment, but anyone who appreciates the force of the case presented in this chapter will realize that equally, it does very little good.” Michael Oakes, Statistical inference, p.72

18. 10/7/2008Case-control studies18 Incidence rate and incidence proportion [incidence density and cumulative incidence]

19. 10/7/2008Case-control studies19 IR (ID) and IP in a closed cohort } CI } 1 – CI T0T0 T1T1

20. 10/7/2008Case-control studies20 Attributable risk

21. 10/7/2008Case-control studies21 Attributable risk Assume that we know a causal factor for a disease. Conceptually, the “attributable risk” for that factor is: 1. difference in risk or incidence between exposed and unexposed people or 2. difference in risk or incidence between total population and unexposed people

22. 10/7/2008Case-control studies22 Attributable risk Attributable risk can be presented as: 1. an “absolute” number, e.g., “80,000, or 20 per 100 cases/year of stroke are attributable to smoking” 2. a “relative” number, e.g., “20% of stroke cases are attributable to smoking”. (analogy: a wage increase in a part-time job: $ increase, % increase in wage, % increase in income)

23. 10/7/2008Case-control studies23 For relative measures, think of % of cases People Incidence rate or proportions

24. 10/7/2008Case-control studies24 For relative measures, think of % of cases Substitute population Caseload

25. 10/7/2008Case-control studies25 For relative measures, think of % of cases Caseload

26. 10/7/2008Case-control studies26 Case-control studies

27. 10/8/2001Case-control studies27 Case-control studies Traditional view: compare - people who get the disease - people who do not get the disease “Controls” a misnomer, derived from faulty analogy to controls in experiment Modern conceptualization: controls are a “window” into the “study base”

28. 10/7/2008Case-control studies28 Case-control studies

29. 10/7/2008Case-control studies29 Population at risk (N=200)        

30. 10/7/2008Case-control studies30         O Week 1 O

31. 10/7/2008Case-control studies31         O Week 2 O O O O

32. 10/7/2008Case-control studies32         O O O Week 3 O O O O

33. 10/7/2008Case-control studies33 Incidence rate (“incidence density”) Number of new cases IR = ––––––––––––––––––– Population time

34. 6/23/2002Case-control studies34 Incidence rate (“incidence density”) Number of new cases 7 IR = ––––––––––––––––––– = –––––– Population time ?

35. 6/23/2002Case-control studies35 Incidence rate (“incidence density”) Population time at risk: 200 people for 3 weeks = 600 person-wks But 2 people became cases in 1st week 3 people became cases in 2nd week 2 people became cases in 3rd week Only 193 people at risk for 3 weeks

36. 6/23/2002Case-control studies36 Incidence rate (“incidence density”) Assume that: 2 people who became cases in 1st week were at risk for 0.5 weeks each = 2 @ 0.5 = 1.0 3 people who became cases in 2nd week were at risk for 1.5 weeks each = 3 @ 1.5 = 4.5 2 people who became cases in 3rd week were at risk for 2.5 weeks each = 2 @ 2.5 = 5.0

37. 6/23/2002Case-control studies37 Incidence rate (“incidence density”) Total population-time = Cases occuring during week 1: 1.0 p-w Cases occuring during week 2: 4.5 p-w Cases occuring during week 3: 5.0 p-w Non-cases: 193 x 3 = 579.0 p-w 589.5 p-w

38. 6/23/2002Case-control studies38 Incidence rate (“incidence density”) 7 IR = –––––– = 0.0119 cases / person-wk 589.5 average over 3 weeks Number of new cases IR = ––––––––––––––––––– Population time

39. 3/2/2011Case-control studies39 Incidence proportion (“cumulative incidence”) Number of new cases CI = ––––––––––––––––––– Population at risk

40. 10/7/2008Case-control studies40 Incidence proportion (“cumulative incidence”) 7 3-week CI = –––– = 0.035 200 Number of new cases CI = ––––––––––––––––––– Population at risk

41. 10/7/2008Case-control studies41 Can estimate incidence in people who are “exposed”    O Week 1

42. 10/7/2008Case-control studies42 Can estimate incidence in people who are “exposed”    O Week 2 O O

43. 10/7/2008Case-control studies43 Can estimate incidence in people who are “exposed”    O Week 3 O O O

44. 10/7/2008Case-control studies44 Can estimate incidence in people who are “unexposed”      O Week 1

45. 10/7/2008Case-control studies45 Can estimate incidence in people who are “unexposed”      O Week 2 O

46. 10/7/2008Case-control studies46 Can estimate incidence in people who are “unexposed”      O Week 3 O O

47. 10/7/2008Case-control studies47 Entire population, week 1    O      O

48. 10/7/2008Case-control studies48 Entire population, week 2         O O O O O

49. 10/7/2008Case-control studies49 Entire population, week 3         O O O O O O O

50. 10/7/2008Case-control studies50 Incidence rate (“incidence density”) Number of new cases IR = ––––––––––––––––––– Population time

51. 10/7/2008Case-control studies51 Incidence rate in exposed during three weeks 4 4 IR = –––––––––––––– = –––– = 0.018 / wk 74.5 + 73 + 71.5 219 Number of new cases IR = ––––––––––––––––––– Population time

52. 10/7/2008Case-control studies52 Incidence rate in unexposed during three weeks 3 3 IR = –––––––––––––––––– = ––––– = 0.008 / wk 124.5 + 123.5 + 122.5 370.5 Number of new cases IR = ––––––––––––––––––– Population time

53. 10/7/2008Case-control studies53 Compare incidence rates in exposed and unexposed

54. 10/7/2008Case-control studies54 Difference between incidence rates in exposed and unexposed Incidence rate difference (IRD, IDD) = (0.018 – 0.008) / wk = 0.010 / week How to interpret?

55. 10/7/2008Case-control studies55 Difference in incidence rates Incidence rate difference (IRD) = (0.018 – 0.008) / wk = 0.010 / week “The rate in the exposed was 0.010 / week greater than the rate in the unexposed.”

56. 10/7/2008Case-control studies56 Relative difference in incidence rates in exposed and unexposed Relative incidence rate difference 0.018 – 0.008 = –––––––––––– = 2.25 – 1 = 1.25 0.008 How to interpret?

57. 10/7/2008Case-control studies57 Relative difference in incidence rates Relative incidence rate difference 0.018 – 0.008 = –––––––––––– = 2.25 – 1 = 1.25 0.008 “The rate in the exposed was 125% greater than the rate in the unexposed.”

58. 10/7/2008Case-control studies58 Ratio of incidence rates in exposed and unexposed 0.018 Incidence rate ratio = –––––– = 2.25 (IRR, IDR) 0.008 How to interpret?

59. 10/7/2008Case-control studies59 Ratio of incidence rates 0.018 Incidence rate ratio = –––––– = 2.25 (IRR, IDR) 0.008 “The rate in the exposed was 2.25 times the rate in the unexposed.” [not “times greater”]

60. 6/23/2002Case-control studies60 Estimating IRR and CIR with the Odds Ratio

61. 2/28/2006Case-control studies61 Odds odds = probability / (1 – probability) odds = risk / (1 – risk) (most commonly)

62. 1/29/2007Case-control studies62 For small probability, odds ≈ probability Odds Small p

63. 1/29/2007Case-control studies63 Odds = probability / (1 – probability) Odds

64. 1/29/2007Case-control studies64 Odds Any ratio of two natural numbers can be regarded as an odds: Exposed: 20 Unexposed: 30 Total: 50 Odds of exposure: 20/50 divided by 30/50

65. 1/29/2007Case-control studies65 Incidence rate ratio (a.k.a. “incidence density ratio”) can be expressed as a ratio of odds

66. 10/7/2008Case-control studies66 Incidence rate ratio IR in exposed IR 1 IRR = ––––––––––––––– = –––– IR in unexposed IR 0

67. 1/29/2007Case-control studies67 Incidence rate ratio IR 1 Exposed cases / Exp PT IRR = –––– = ––––––––––––––––––––––––– IR 0 Unexposed cases / Unexp PT (PT = “population time”)

68. 10/7/2008Case-control studies68 Incidence density ratio is a ratio of exposed to unexposed cases... IR 1 Exposed cases / Exp PT IRR = –––– = –––––––––––––––––––––––– IR 0 Unexposed cases / Unexp PT Exposed cases / Unexposed cases = ––––––––––––––––––––––––––––– Exposed PT / Unexposed PT

69. 10/7/2008Case-control studies69... divided by a ratio of exposed to unexposed population-time IR 1 Exposed cases / Exp PT IRR = –––– = –––––––––––––––––––––––– IR 0 Unexposed cases / Unexp PT Exposed cases / Unexposed cases = –––––––––––––––––––––––––––– Exposed PT / Unexposed PT

70. 10/7/2008Case-control studies70 Ratio of exposed to unexposed cases = “exposure odds” in cases Exposed cases / Unexposed cases IRR = ––––––––––––––––––––––––––––––– Exp Person-time / Unexp Person-time “Exposure odds” in cases = –––––––––––––––––––––––––– “Exposure odds” in population

71. 10/7/2008Case-control studies71 Ratio of exposed to unexposed population-time = “exposure odds” Exposed cases / Unexposed cases IRR = –––––––––––––––––––––––––––––––– Exp Person-time / Unexp Person-time “Exposure odds” in cases = ––––––––––––––––––––––––––– “Exposure odds” in population

72. 10/7/2008Case-control studies72 Count exposed and unexposed cases         O O O O O O O

73. 10/7/2008Case-control studies73 From before: Exposed: 4 4 IR = –––––––––––––– = –––– = 0.018 / wk 74.5 + 73 + 71.5 219 Unexposed: 3 3 IR = –––––––––––––––––– = ––––– = 0.008 / wk 124.5 + 123.5 + 122.5 370.5

74. 2/28/2006Case-control studies74 Exposure odds in cases = Exposed cases / Unexposed cases = (4/7) / (3/7) = 4 / 3 = 1.33 The exposure odds in cases are 1.33

75. 10/7/2008Case-control studies75 From before: Exposed: 4 4 ID = –––––––––––––– = –––– = 0.018 / wk 74.5 + 73 + 71.5 219 Unexposed: 3 3 ID = –––––––––––––––––– = ––––– = 0.008 / wk 124.5 + 123.5 + 122.5 370.5

76. 10/7/2008Case-control studies76 Exposure odds in population-time = Exp. person-time / Unexp. person-time = (74.5 + 73 + 71.5) / (124.5 + 123.5 + 122.5 ) = 219 / 370.5 = 0.59 The exposure odds in population-time are 0.59

77. 10/7/2008Case-control studies77 So incidence rate ratio can be expressed as a ratio of odds “Exposure odds” in cases IRR = ––––––––––––––––––––––––– “Exposure odds” in population 1.33 = –––––– = 2.25 (same as earlier) 0.59

78. 1/29/2007Case-control studies78         O O O O O O O Can we estimate exposure odds in the population by taking a sample?

79. 1/29/2007Case-control studies79 Take sample of “risk set” – “density controls” – week 1    O      O

80. 10/7/2008Case-control studies80 Take sample of “risk set” – “density controls” – week 2         O O O O O

81. 2/28/2006Case-control studies81 Take sample of “risk set” – “density controls” – week 3         O O O O O O O

82. 10/7/2008Case-control studies82 Now estimate incidence rate ratio using the “density controls” IR 1 Exposed cases / Unexposed cases IRR = –––– = ––––––––––––––––––––––––––– IR 0 Exposed PT / Unexposed PT

83. 10/7/2008Case-control studies83 Estimating the population odds with the odds in the control group Exposed cases / Unexposed cases IDR = ––––––––––––––––––––––––––––––– Exposed controls / Unexposed controls We call this the “exposure odds ratio” (OR).

84. 3/4/2002Case-control studies84 Exposure odds ratio = estimates incidence rate ratio (a.k.a. IDR) 1.33 1.33 OR = ––––– = ––––– = 2.22 6 / 10 0.60

85. 1/29/2007Case-control studies85 Odds ratio from a 2 x 2 table

86. 3/4/2002Case-control studies86 Odds ratio from a 2 x 2 table

87. 10/7/2008Case-control studies87 What about incidence proportion in a cohort? (“cumulative incidence”) Number of new cases 3-week CI = ––––––––––––––––––– Population at risk

88. 10/7/2008Case-control studies88 Population at risk – baseline        

89. 10/7/2008Case-control studies89 Entire population, week 3         O O O O O O O

90. 10/7/2008Case-control studies90 Cumulative incidence in exposed Number of new exposed cases 3-week CI = ––––––––––––––––––––––––––– Exposed population at risk 4 3-week CI = –––– = 0.053 75

91. 10/7/2008Case-control studies91 Cumulative incidence in unexposed Number of new unexposed cases 3-week CI = –––––––––––––––––––––––––––– Unexposed population at risk 3 3-week CI = –––– = 0.024 125

92. 10/7/2008Case-control studies92 Compare incidence proportions in exposed and unexposed

93. 10/7/2008Case-control studies93 Difference in incidence proportions between exposed and unexposed 3-wk cumulative incidence difference (CID) = (0.053 – 0.024) = 0.029 How to interpret?

94. 10/7/2008Case-control studies94 Difference in incidence proportions 3-wk cumulative incidence difference (CID) = (0.053 – 0.024) = 0.029 “The 3-week cumulative incidence in the exposed was 0.029 greater than in the unexposed.”

95. 10/7/2008Case-control studies95 Relative difference in incidence proportions for exposed and unexposed 3-wk cumulative incidence relative difference (0.053 – 0.024) 0.029 = –––––––––––––– = –––––– = 1.22 0.024 0.024 How to interpret?

96. 10/7/2008Case-control studies96 Relative difference in incidence proportions 3-wk cumulative incidence relative difference (0.053 – 0.024) 0.029 = –––––––––––––– = –––––– = 1.22 0.024 0.024 “The 3-week CI in the exposed was 122% greater than in the unexposed.”

97. 1/29/2007Case-control studies97 Ratio of incidence proportions for exposed and unexposed 3-week cumulative incidence ratio (CIR) = (0.053 / 0.024) = 2.22 How to interpret?

98. 10/7/2008Case-control studies98 Ratio of incidence proportions (“relative risk”, “risk ratio”) 3-week cumulative incidence ratio (CIR) = (0.053 / 0.024) = 2.22 “The 3-week CI in the exposed was 2.2 times that in the unexposed.” [not “times greater than”]

99. 10/7/2008Case-control studies99 Ratio of incidence proportions, a.k.a. cumulative incidence ratio CI 1 Exposed cases / Exp PAR CIR = –––– = –––––––––––––––––––––––––– CI 0 Unexposed cases / Unexp PAR

100. 10/7/2008Case-control studies100 Cumulative incidence ratio can also be expressed as a ratio of odds of exposure in cases divided by... CI 1 Exposed cases / Exp PAR CIR = –––– = –––––––––––––––––––––––––– CI 0 Unexposed cases / Unexp PAR Exposed cases / Unexposed cases = ––––––––––––––––––––––––––––– Exp PAR / Unexp PAR

101. 10/7/2008Case-control studies101... an odds of exposure in the population at risk (PAR) CI 1 Exposed cases / Exp PAR CIR = –––– = –––––––––––––––––––––––––– CI 0 Unexposed cases / Unexp PAR Exposed cases / Unexposed cases = ––––––––––––––––––––––––––––– Exp PAR / Unexp PAR

102. 10/7/2008Case-control studies102 So cumulative incidence ratio is also an odds ratio CI 1 Exposed cases / Unexposed cases CIR = ––– = ––––––––––––––––––––––––––– CI 0 Exp PAR / Unexp PAR Exposure odds in cases = ––––––––––––––––––––––––––––––– Exposure odds in population at risk

103. 10/7/2008Case-control studies103 Exposure odds in cases = Exposed cases / Unexposed cases = 4 / 3 = 1.33 (same as for incidence density ratio)

104. 10/7/2008Case-control studies104 Population at risk (before cases occur)        

105. 1/29/2007Case-control studies105 Exposure odds in population at risk (before cases occur) = Exposed PAR / Unexposed PAR = 75 / 125 = 0.60 (slightly different from odds of exposure for person-time)

106. 10/7/2008Case-control studies106 So cumulative incidence ratio is also an odds ratio CI 1 Exposure odds in cases CIR = –––– = –––––––––––––––––––––––– CI 0 Exposure odds in pop. at risk 1.33 3-week CIR = ––––– = 2.22 0.60

107. 10/7/2008Case-control studies107 So if can estimate exposure odds in PAR, may not need to analyze entire cohort “Case-cohort” or “case-base” design Can be very advantageous if, for example, one wants to analyze specimens stored at baseline.

108. 10/7/2008Case-control studies108 Sample from population at risk (before cases occur)        

109. 10/7/2008Case-control studies109 Exposure odds in controls = Exp. controls / Unexp. controls = 6 / 10 = 0.60 (expected value for the estimated odds)

110. 10/7/2008Case-control studies110 Cumulative incidence ratio CI 1 Exposed odds in cases CIR = ––– = ––––––––––––––––––––––– CI 0 Exposure odds in population 1.33 3-wk CIR = exposure OR = ––––– = 2.22 0.6

111. 10/7/2008Case-control studies111 What if cannot sample population at risk? Draw controls from noncases at end of follow-up period

112. 10/7/2008Case-control studies112 Non-cases at end of follow-up         O O O O O O O 71 122

113. 10/7/2008Case-control studies113 Exposure odds in population at risk (after cases occur) = Exposed noncases / Unexp. noncases = 71 / 122 = 0.58 (slightly different from ratio of person-time and ratio of population at risk)

114. 10/7/2008Case-control studies114 Odds ratio Exposed odds in cases OR = –––––––––––––––––––––––– Exposure odds in population 1.33 = ––––– = 2.29 0.58 (slightly larger than CIR)

115. 1/29/2007Case-control studies115 Draw controls from noncases         O O O O O O O 5 9

116. 10/7/2008Case-control studies116 Exposure odds in “cumulative” controls = Exposed noncases / Unexp. noncases = 5 / 9 (about) = 0.58 (Note: 5/9=0.555, but a larger “sample” would produce 0.58)

117. 10/7/2008Case-control studies117 Odds ratio Exposed odds in cases OR = –––––––––––––––––––––––– Exposure odds in population 1.33 = ––––– = 2.29 0.58 (slightly larger than CIR)

118. 1/29/2007Case-control studies118 Case-control design is an efficient sampling technique Much more efficient, especially for rare outcomes Validity depends upon whether controls provide a clear view of population from which cases arise Susceptible to various sources of bias

119. 10/7/2008Case-control studies119 New Software for Psychics “Notice to user: By breaking the seal of this envelope, you accept the terms of the enclosed license agreement.” – Adobe Font Pack for Windows Source: Willmott, Don, Abort, Retry, Fail? PC Magazine, June 14, 1994, 482.