1. 1/25/2011Incidence and prevalence1 Epidemiologic measures: Incidence & prevalence Principles of Epidemiology for Public Health (EPID600) 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/

2. 5/20/2002Incidence and prevalence2 Quotations that demonstrate the value of humility about predicting the future (authenticity not established) Courtesy of Suzanne Cloutier, 11/17/1998 Famous last words

3. 5/20/2002Incidence and prevalence3 “ Louis Pasteur's theory of germs is ridiculous fiction.” - Pierre Pachet, Professor of Physiology at Toulouse, 1872 FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

4. 5/20/2002Incidence and prevalence4 “This `telephone´ has too many shortcomings to be seriously considered as a means of communication. The device is inherently of no value to us.” - Western Union internal memo, 1876 (Source: 2000 National Ernst & Young Entrepreneur of the Year Awards special insert in USA Today, 2/11/2000, p9B) FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

5. 5/20/2002Incidence and prevalence5 “Everything that can be invented has been invented.” - Charles H. Duell, Commissioner, US Patent Office, 1899 FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

6. 9/11/2005Incidence and prevalence6 “The wireless music box has no imaginable commercial value. Who would pay for a message sent to nobody in particular?” - David Sarnoff's associates in response to his urgings for investment in radio in the 1920s. FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

7. 1/25/2011Incidence and prevalence7 “My thesis in this lecture is that macroeconomics... has succeeded: Its central problem of depression-prevention has been solved, for all practical purposes, and has in fact been solved for many decades.” - Robert E. Lucas, Jr., American Economics Association Presidential Address, January 10, 2003 http://home.uchicago.edu/~sogrodow/homepage/paddress03.pdf FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

8. 1/25/2011Incidence and prevalence8 The population perspective requires measuring disease in populations Science is built on classification and measurement. Reality is infinitely detailed, infinitely complex. Classification and measurement seek to capture the essential attributes.

9. 1/25/2011Incidence and prevalence9 Deriving meaning from stimuli Vase or faces? Which line is longer?

10. 1/25/2011Incidence and prevalence10 Measurement “captures” the phenomenon Classification and measurement are based on: 1.Objective of the classification 2.Conceptual model (understanding of the phenomenon) 3.Availability of data (technology)

11. 5/20/2002Incidence and prevalence11 O O O O O O O         An example population (N=200)

12. 1/25/2011Incidence and prevalence12         O How can we quantify disease in populations?

13. 1/25/2011Incidence and prevalence13         O O How can we quantify disease in populations?

14. 5/20/2002Incidence and prevalence14         O O O How can we quantify disease in populations?

15. 5/20/2002Incidence and prevalence15         O O O O O How can we quantify disease in populations?

16. 5/20/2002Incidence and prevalence16         O O O O O O How can we quantify disease in populations?

17. 1/25/2011Incidence and prevalence17         O O O O O O How can we quantify the frequency?

18. 1/25/2011Incidence and prevalence18         O O O O O O Rate of occurrence of new cases per unit time (e.g., 1 per month)

19. 5/20/2002Incidence and prevalence19         O 1 new case in month 1

20. 5/20/2002Incidence and prevalence20         O O 1 new case in month 2

21. 5/20/2002Incidence and prevalence21         O O O 1 new case in month 3, for a total of 3 cases

22. 5/20/2002Incidence and prevalence22         O O O O O 2 new cases in month 4

23. 5/20/2002Incidence and prevalence23         O O O O O O 1 new case in month 5 (total=6)

24. 5/25/2011Incidence and prevalence24         O O O O O O O 1 case in month 6

25. 5/20/2002Incidence and prevalence25         O O O O O O O O 1 new case in month 7

26. 5/20/2002Incidence and prevalence26         O O O O O O O O O O 2 new cases in month 8

27. 5/20/2002Incidence and prevalence27         O O O O O O O O O O O O 2 cases in month 9

28. 1/9/2007Incidence and prevalence28         O O O O O O O O O O O O Rate of occurrence of new cases during 9 months: 1 case/month to 2 cases/month

29. 1/9/2007Incidence and prevalence29 Number of cases depends on length of interval Divide by length of time interval, so can compare across intervals Number of new cases Rate of new cases = ––––––––––––––––– Time interval = 12 cases / 9 months = 1.33 cases / month

30. 1/25/2011Incidence and prevalence30 Number of cases depends on population size So, divide by population and time: Number of new cases Incidence rate = –––––––––––––––––– Population-time

31. 1/25/2011Incidence and prevalence31 How to estimate population-time? Population at risk: the people eligible to become a case and to be counted as one. In this example that population declines as each case occurs. So estimate population-time as...

32. 1/25/2011Incidence and prevalence32 Population-time = Method 1: Add up the time that each person is at risk Method 2: Add up the population at risk during each time segment Method 3: Multiply the average size of the population at risk by the length of the time interval

33. 1/9/2007Incidence and prevalence33 Estimating population-time - method 2 Total population-time over 9 months = 200 + 199 + 198 + 197 + 195 + 194 + 193 + 192 + 190 = 1,758 person-months = 146.5 person-years However, cases are not at risk for a full month.

34. 1/9/2007Incidence and prevalence34 Estimating population-time - method 2 - better Total population-time over 9 months = 199.5 + 198.5 + 197.5 + 196 + 194.5 + 193.5 + 192.5 + 191 + 189 = 1,752 person-months = 146 person-years assuming that cases develop, on average, in the middle of the month

35. 1/9/2007Incidence and prevalence35 Estimating population-time - method 3 Average size of the population at risk during the 9 months = 195.3 (1,758 / 9) or approximately : (200 + 188) /2 = 194 Population-time = 195.3 x 9 months or (approximately) 194 x 9 months = 1,746 person-months = 145.5 person-years

36. 1/9/2007Incidence and prevalence36 Equivalent to - method 3 Take initial size of population at risk and reduce it for time the people were not at risk due to acquiring the disease: 200 - 12/2 = 194 (approximately) Population-time = 194 x 9 months = 1,746 person-months = 145.5 person-years

37. 1/25/2011Incidence and prevalence37 Incidence rate (“incidence density”) Number of new cases ––––––––––––––––––––––––––––––– Avg population at risk × Time interval Number of new cases = –––––––––––––––––––– Population-time

38. 1/25/2011Incidence and prevalence38 O O O O O O O         What proportion of the population at risk are affected after 5 months?

39. 1/30/2004Incidence and prevalence39         O What proportion of the population is affected after 1 month? (1/200)

40. 5/20/2002Incidence and prevalence40         O O What proportion of the population is affected after 2 months? (2/200)

41. 5/20/2002Incidence and prevalence41         O O O What proportion of the population is affected after 3 months? (3/200)

42. 5/20/2002Incidence and prevalence42         O O O O O What proportion of the population is affected after 4 months? (5/200)

43. 1/9/2007Incidence and prevalence43         O O O O O O 6 / 200 = 0.03 = 3% = 30 / 1,000 in 5 months

44. 1/25/2011Incidence and prevalence44 Incidence proportion (“cumulative incidence”) Number of new cases 5-month CI = ––––––––––––––––––– Population at risk Incidence proportion estimates risk.

45. 1/25/2011Incidence and prevalence45 Incidence rate versus incidence proportion Incidence rate measures how rapidly cases are occurring. Incidence proportion is cumulative. When care only about the “bottom line” (i.e., what has happened by the end of given period): incidence proportion (CI).

46. 1/25/2011Incidence and prevalence46 Incidence rate versus incidence proportion If risk period is long (e.g., cancer), we usually observe only a portion. To compare results from studies with different length of follow-up, use incidence rate (IR) If risk period is short, we usually observe all of it and can use incidence proportion.

47. Incidence rate versus incidence proportion (rare disease, IR = 0.005 / month) 1/25/2011Incidence and prevalence47 (see spreadsheet at epidemiolog.net/studymat/)

48. Incidence rate versus incidence proportion (common disease, IR = 0.1 / month) 2/7/2012Incidence and prevalence48

49. 5/20/2002Incidence and prevalence49 Case fatality rate “Case fatality rate” (but it’s really a proportion) = proportion of cases who die (in a specified time interval) Like a “cumulative incidence of death” in cases [ “incidence rate of death” in cases = “termination rate” = 1/(average survival time)]

50. 1/30/2007Incidence and prevalence50 Mortality rate Number of deaths Mortality rate = –––––––––––––––––––––––––––– Population at risk × Time interval Number of deaths Annual mortality rate = –––––––––––––––––––––– Mid-year population (x 1 yr)

51. 6/6/2002Incidence and prevalence51 Mortality rate (more notes) Number of deaths Mortality rate = –––––––––––––––––––––––––––– Population at risk × Time interval Number of deaths Annual mortality rate = –––––––––––––––––– Mid-year population

52. 5/20/2002Incidence and prevalence52 Mortality rates versus incidence rates Mortality data are more generally available Fatality reflects many factors, so mortality rates may not be a good surrogate of incidence rates Death certificate cause of death not always accurate or useful

53. 1/9/2007Incidence and prevalence53 Prevalence – another important proportion Number of existing (and new) cases Prevalence = ––––––––––––––––––––––––––––––– Population at risk

54. 5/20/2002Incidence and prevalence54         O O O O O O O 1 new case, 1 death

55. 5/20/2002Incidence and prevalence55         O O O O O O O O 1 new case, 1 new death

56. 5/20/2002Incidence and prevalence56         O O O O O O O O O O 2 new cases, no deaths

57. 5/20/2002Incidence and prevalence57         O O O O O O O O O O O O 2 new cases, 1 new death

58. 5/20/2002Incidence and prevalence58         O O O O O O O O O O O O What is the prevalence? (9 / 197)

59. 5/20/2002Incidence and prevalence59 Fine points... Who is “at risk”? Endometrial cancer? Prostate cancer? Breast cancer? Only women who have not had a hysterectomy? “Could” develop the condition + “would” be counted.

60. 5/20/2002Incidence and prevalence60 More fine points Age? Immunity? Genetically susceptible?

61. 5/20/2002Incidence and prevalence61 More fine points... How do we measure time? Are 10 people followed for 10 years the same as 100 people followed for 1 year? Aging of the cohort? Secular changes?

62. 9/22/2005, 9/8/2008Incidence and prevalence62 Fine points... Importance of stating units and scaling unless they are clear from the context – e.g., 120 per 100,000 person-years = 10 per 100,000 person-months – Hazards from lack of clarity

63. 1/30/2004Incidence and prevalence63 “You can never, never take anything for granted.” Noel Hinners, vice president for flight systems at Lockheed Martin Astronautics in Denver, concerning the loss of the Martian Climate Orbiter due to the Lockheed Martin spacecraft team’s having reported measurements in English units whiles the orbiter’s navigation team at the Jet Propulsion Laboratory (JPL) in Pasadena, California assumed the measurements were in metric units.

64. 5/20/2002Incidence and prevalence64 Relation of incidence and prevalence Prevalence depends on incidence Higher incidence leads to higher prevalence if duration of cases does not change. Limitation of the bathtub analogy – flow rate needs to be expressed relative to the size of the source Introducing a new analogy...

65. 9/23/2002Incidence and prevalence65

66. 5/20/2002Incidence and prevalence66 Population at risk Existing cases Deaths, cures, etc.

67. 1/25/2011Incidence and prevalence67 Incidence, prevalence, duration of hospitalization Remote community of 101,000 people One hospital, patient census = 1,000 Steady state 500 admissions per week Prevalence = 1,000/101,000 = 9.9/1,000 IR = 500/100,000 = 5/1,000/week Duration Prevalence / IR = 2 weeks

68. 1/25/2011Incidence and prevalence68 Relation of incidence and prevalence Under somewhat special conditions, Prevalence odds = incidence × duration Prevalence incidence × duration (see spreadsheet at www.epidemiolog.net/studymat/)

69. 5/20/2002Incidence and prevalence69 Standardization When objective is comparability, need to adjust for different distributions of other determinants Strategy: Analyze within each subgroup (stratum) Take a weighted average across strata Use same weights for all populations (See the Evolving Text on www.epidemiolog.net)

70. 8/17/2009Incidence and prevalence70 Familiar example of weighted averages Liters of petrol per kilometer - differs for Interstate (0.050 LpK) and non-Interstate (0.100 LpK) driving. To compare different cars, can: Compare them for each type of driving separately (stratified analysis) Average for each car, using one set of weights (e.g., 80% Interstate, 20% non-Interstate) E.g. = 0.80 x 0.050 LpK + 0.20 x 0.100 LpK = 0.060 LpK

71. 8/17/2009Incidence and prevalence71 Comparing a Suburu and a Mazda Juan drives a Suburu 800 km on Interstate highways and 200 km on other roads. His car uses 0.050 LpK on Interstates and 0.100 LpK on other roads, for a total of 60 liters of petrol, an average of 0.060 LpK (60 L / 1000 km). His overall LpK can be expressed as a weighted average: (800/1000) x 0.050 LpK + (200/1000) x 0.100 LpK = 0.80 x 0.050 LpK + 0.20 x 0.100 LpK = 0.060 LpK

72. 8/17/2009Incidence and prevalence72 Comparing a Suburu and a Mazda Shizu drives her Mazda on a different route, with only 200 km on Interstate and 800 km on other roads. She uses 0.045 lpk on Interstate highways and 0.080 LpK on non-Interstate. She uses a total of 73 liters, or 0.073 LpK. Her overall LpK can be expressed as a weighted average: (200/1,000) x 0.045 LpK + (800/1,000) x 0.080 LpK = 0.20 x 0.045 LpK + 0.80 x 0.080 LpK =0.073 LpK

73. 8/17/2009Incidence and prevalence73 How can we compare their fuel efficiency?

74. 8/17/2009Incidence and prevalence74 Total fuel efficiency is not comparable because weights are different

75. 8/17/2009Incidence and prevalence75 By adopting a “standard” set of weights we can compare fairly

76. 8/17/2009Incidence and prevalence76 Comparing a Suburu and a Mazda Juan’s Suburu: = 0.60 x 0.050 LpK + 0.40 x 0.100 LpK =0.070 LpK Shizu’s Mazda: = 0.60 x 0.045 LpK + 0.40 x 0.080 LpK =0.059 LpK The choice of weights may often affect the results of the comparison.

77. 5/20/2002Incidence and prevalence77 “I'm just glad it'll be Clark Gable who's falling on his face and not Gary Cooper.” - Gary Cooper on his decision not to take the leading role in “Gone With The Wind” FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

78. 5/20/2002Incidence and prevalence78 “A cookie store is a bad idea. Besides, the market research reports say America likes crispy cookies, not soft and chewy cookies like you make.” - Response to Debbi Fields' idea of starting Mrs. Fields' Cookies. FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

79. 5/20/2002Incidence and prevalence79 “Computers in the future may weigh no more than 1.5 tons.” - Popular Mechanics, forecasting the relentless march of science, 1949 FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future

80. 5/20/2002Incidence and prevalence80 “I think there is a world market for maybe five computers.” -Thomas Watson, chairman of IBM, 1943 FAMOUS LAST WORDS: quotations that demonstrate the value of humility in predicting the future