1. Measuring the Frequency of Health Events

2. The mayor of your town was startled to learn that there are 3 people who were recently diagnosed as HIV+ in his neighborhood. He is concerned that this may just be the tip of the iceberg, and he is wondering if this signals an epidemic. He wants your help in assessing the magnitude of the problem. What information (data) do you need in order to assess:  How big the problem is in town,  Whether there is an epidemic starting.  How the problem in your town compares to that of neighboring towns.

3. Population Examples: Residents of Boston Members of Blue Cross/Blue Shield Postmenopausal women in Massachusetts Coal miners in Pennsylvania Adolescents in U.S. A group of people with some common characteristic (age, race, gender, place of residence). Residents of Marshfield Residents of Marshfield Sample : 19 who got hepatitis 38 who did not

4. Fixed population: Membership is relatively permanent, and perhaps defined by some event. Examples: Responders to 911 terrorist attack Attendees of a luncheon (Salmonella outbreak) Dynamic Population: Membership can be transient. Examples: Homeless population of Boston Residents of MA Members of an HMO Dynamic & Fixed Populations

5. Basic Concepts  Ratio  Proportion  Rate

6. A number obtained by dividing one number by another. Ratio Example: the ratio of women to men in a class # women 120 # men 15 A ratio doesn’t have any dimensions or units. It just indicates the relative magnitude of the two entities. Women = Men = Women Men

7. A type of ratio that relates a part to a whole; often expressed as a percentage (%). Proportion Example: proportion of women in a class # women = 120 = 88.9% total # students 135 Men Women

8. A type of ratio that relates a part to a whole; often expressed as a percentage (%). Proportion Example: The proportion of students who developed a respiratory infection during the semester. # with colds 45 33.3% total # students 135 ==

9. Rate A type of ratio in which the denominator also takes into account the dimension of time. Example: 120 miles in 2 hours 120 miles = 60 miles per hr. 2 hours Example: 60 gallons in 3 hours 60 gal. = 20 gal. per hr. 3 hours

10. Rate A type of ratio in which the denominator also takes into account the dimension of time. Example: the incidence rate of myocardial infarctions (heart attacks) in a group taking low dose aspirin. 254.8 per 100,000 person-years

11. If events aren’t recorded, there is no way to detect trends. Measures of Disease Frequency

12. Causes of Death Abortive, and Stillborn445Grief11 Affrighted1Jaundies43 Aged628Jawfaln8 Ague43Impostume74 Apoplex, and Meagrom17Kil'd by accidents46 Bit with a mad dog1King's Evil38 Quinsie7Lethargie2 Bloody flux, scowring, and flux348Livergrown87 Brused, Issues, sores, and ulcers,28Lunatique5 Burnt, and Scalded5Made away themselves15 Burst, and Rupture 9Rising of the Lights98 Cancer, and Wolf10Murthered7 Canker1Over- laid, and starved at nurse7 Childbed171Palsie25 Chrisomes, and Infants2268Piles1 Cold, and Cough55Plague8 Colick, Stone, and Strangury56Planet13 Consumption1797Pleurisie, and Spleen36 Convulsion241Purples, and spotted Feaver38 Cut of the Stone5Quinsie7 Dead in the street, and starved6Rising of the Lights98 Dropsie, and Swelling267Sciatica1 Drowned34Scurvey, and Itch9 Executed, and prest to death18Suddenly62 Falling Sickness7Surfet86 Fever1108Swine Pox6 Fistula13Teeth470 Flocks, and small Pox531Thrush, and Sore mouth40 French Pox12Tympany13 Gangrene5Tissick34 Gout4Vomiting1 Worms27 England: Records of burials and christenings were kept intermittently from 1592-1603, then steadily from 1603. In 1839 William Farr established a system for routinely recording cause of death in England and Wales. Abscess Scrofula Lock jaw Croup Infected tonsils

13. The simple count of hepatitis A cases provides the basis for significant discussions among city officials and health care providers. Hepatitis A in our town 1998 5 1999 0 2000 2 2001 3 2002 1 2003 19 Counts of Disease Simple counts are essential to public health planners and policy makers by providing a direct measure of the need for resources for specific problems.

14. Hepatitis Is hepatitis A more of a problem in our town? But just counting diseased people isn’t enough. Our Town 19 Next Town 5 New Cases Population Size Incidence Our Town1930,0006.3/10,000 Next Town 57,0007.1/10,000 Converting to a standard population size (per 10,000) facilitates comparison.

15. Measures of Disease Frequency Prevalence (a proportion) Incidence  Cumulative incidence (a proportion)  (Incidence rate) Estimates the burden of disease at a given point in time. An estimate of the rate at which new cases are added; an estimate of risk.

16. The focus is on existing disease at a specific time, not the development of new cases. The proportion of a population that has disease at a given time. Prevalence Imagine you took a snapshot of a class and labeled those who had a COLD with a red “C”. C C C C C What proportion of the group has a cold at this point in time?

17. The focus is on existing disease at a specific point in time, not the development of new cases. The “point” can be a specific calendar time, or... The “point” can be a lifetime “event” (e.g., birth, death, entry into the military). The proportion of a population that has disease at a “point” in time (although the ‘point’ might be broad, e.g. a year.) “Point” Prevalence

18. The proportion of a population that has disease during a given period of time. 198019811979 Prevalence = 310 (cataracts) 2,477 (total) =.125 = 12.5% ‘Period’ Prevalence 310 had cataracts 310 had cataracts Eye exam survey of 2,477 people x x xx x x x xxx x x

19. 8,263 HIV+ Total MA population = 5.7 million in 2003 = 0.00145 = 0.145% = 145 per 100,000 Time 2003 Need to know: # HIV+ people living in MA in 2003 Population size in 2003 Prevalence of HIV in MA in 2003 The ‘burden of disease’ on the population.

20. 0.00145 per 1 person. 0.0145 per 10 persons 0.145 per 100 persons [%] 1.45 per 1,000 persons 14.5 per 10,000 persons 145 per 100,000 persons Each time you move the decimal to the right, you increase the number by a factor of 10. These Are All Equivalent Express the result in a way that provides a reasonable number of people, not a fraction.

21. www.cdc.gov Prevalence is the % with the condition at a point in time, but one can assess that repeatedly over time to get a sense of trends...

22. http://www.dizziness-and-balance.com/ Or differences based on personal characteristics such as gender and age.

23. Differences in disease frequency: over time or from place to place or among people with different personal characteristics … and invite us to speculate about explanations for differences in disease frequency. Describe disease patterns so we can see trends, …

24. Incidence

25. Numerator: # new cases during a span of time. Denominator: includes only people “at risk”. The focus is on measuring the probability of developing disease during a span of time. Frequency of new cases during a span of time in people “at risk”. Incidence X X XX X XX X X X XX

26. “At Risk” Incidence should be assessed in people who are “at risk” of developing the outcome. Ideally, the denominator should NOT include: Those who already have the disease. Those who can’t get it, such as those who are immune or don’t have the organ [e.g. incidence of uterine cancer should be estimated in women who have not already had a hysterectomy].

27. 200320042005 Prevalence in 2003 = 0.00145% Prevalence versus Incidence 20062007200820092010 Prevalence is the probability of having disease at a point in time. X X XX X XX X X X XX Incidence: Frequency of new cases during a span of time in people at risk. Incidence is the probability of developing disease during a span of time.

28. Incidence Both focus on # new cases of disease (numerator) during a period of observation. The difference is the way they handle time. Cumulative incidence (a proportion) Incidence rate (a true rate)

29. Cumulative Incidence A proportion A fixed block of observation time Assumes complete follow-up for all subjects. You don’t know the precise “time at risk” for each person. The time period is described in words (e.g. “… during fall semester” or “during calendar year 2008”). x xxx x xx x xx xx x x x xx x x x x x x Sept. 2011 (120 students) Dec. 2011 (115 students) CI = 60/120 = 50% during fall semester Example: 60 colds in a class of 120 during fall semester.

30. Yes No Got Giardiasis 14 341 355 16 108 124 Yes No 30 449 479 subjects Exposed to Kiddy Pool Cumulative Incidence 12.9% 3.9% This outbreak study involved a fixed population that was observed over the block of time when the outbreak took place. Here, it makes sense to calculate cumulative incidence.

31. If I wanted to estimate the incidence of TB in Boston during calendar year 2005, how would I do it?

32. In reality, people are moving in and out of Boston, and some will die (& no longer be members of the population). But there is no way to know the details of this. The best we can do is assume that the number of people in the population stays the same and they are always at risk. TB Incidence in Boston During 2005?

33. We need to assume the population is fixed, i.e. all people were followed for the entire block of time. CI = # new cases 2005 est. pop. size Cumulative incidence (a proportion) TB Incidence in Boston During 2005?

34. Cumulative Incidence of AIDS in MA During 2004 CI = 523 new AIDS cases = 9.2/100,000 Population at risk: about 5.7 million from 1/1/04 to 1/31/04

35. Cumulative incidence, the proportion of a population that develops a disease during a span of time, can also be assessed repeatedly (during serial ‘spans of time’) to get a feel for how ‘risk’ is changing over time.

36. Stomach CancerCervical Cancer Lung Cancer Breast CancerProstate Cancer Incidence

37. Which group has greater rate of relief? Which group has greater proportion of relief? New drug Old drug X X X X X X X X X X X X 1 2 3 4 5 6 7 8 9 10 o o o o o o o o Here, the outcome of interest is relief of pain (X). Hours Cumulative Incidence Has Limitations

38. Diabetics Non-diabetics X X X X X X X X X X X X 1 2 3 4 5 6 7 8 9 10 o o o o o o o o In a prospective cohort study, like Framingham Heart Study, you have detailed individual follow up, so you know whether they develop heart disease, and you also know when they develop it. Years of Follow Up

39. Subject A- B- C- D- E- F- G- H- I- J- K- L- x x x 1980 1982 1984 1986 1988 1990 1992 1994 1996 IR = 3 = 28 107.7 p-ys 1000 p-yrs Total =107.7 person-yrs Time at Risk 8.3 11.0 14.0 10.2 3.0 7.0 10.0 3.0 9.0 6.2 12.0 X = when they got disease CI = 3 12 over 16 yrs Incidence Rate

40. BeginEnd x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x oooooooooo o oooo # Subjects at Risk Time Incidence Rate (Incidence Density)

41. Total # new cases Total amount of disease-free observation time for a group Incidence Rate =

42. Incidence Rate of HIV Seropositivity in Prostitutes ******************* Follow-up ******************** Subject 198919901991199219931994Disease-free Observation Yrs 1---------+---------------- --------1 2---------?1 3 +---------------- --------2 4---------?1 5 ?3 6 ?5 7 ----------------- --------6 8--------- ?5 9 +---------------- --------1 10---------+---------------- ?1 IR = 4 new AIDS cases = 0.15 = 15/100 P-Yrs 26 person-yrs Sum = 26 yrs

43. CI versus IR? Which has greater incidence rate of heart attack? Which has greater cumulative incidence of heart attack? Diabetics Non- Diabetics X X X X X X X X X X X X 1 2 3 4 5 6 7 8 9 10 o o o o o o o o CI = 6/10 = 60% over 10 years IR = 6/49 p-yrs = 12.2/100 P-yrs CI = 6/10 = 60% over 10 years IR = 6/85 p-yrs = 7/100 P-yrs

44. Postmenopausal Hormones Used Yes No 60 - 51,477.5 30 - 54,308.7 Yes No Person-Years of Follow Up Incidence Rate in treated group = 30 / 54,308.7 = 55.2 / 100,000 P-Yrs in untreated group = 60 / 51,477.5 = 116.6 / 100,000 P-Yrs Got Coronary Artery Disease The denominators are the total disease-free observation time in each group. This takes into account the number of people and how long they were known to be disease-free.

45. CI = 1 - e (-IR x T), where 'e' = 2.71828 CI = IR x T Incidence rate can be used to estimate cumulative incidence. The approximation (CI = IR x T) doesn’t take into account the fact that the size of the population at risk declines over time.

46. Year Pop. Deaths 1 100050 2 95048 3 90545 4 86043 5 81741 Suppose IR = 50/1000 person-years (0.050 per year), and population size is initially 1,000. CI = IR x T predicts 50 deaths per year x 5 = 250 deaths. However, the population is finite and is dwindling so # people at risk diminishes.

47. 4.7 x 15 = 70.5 In addition to a diminishing population, the IR may not be constant. As people age, their risk of dying in an MVA changes.

48. Obesity Risk of Non-fatal Myocardial Infarction Association? <21 21-23 23-25 25-29 >29 BMI: wgt kg hgt m 2 # MIs (non-fatal) 41 57 56 67 85 person-years of observation 177,356 194,243 155,717 148,541 99,573 rate of MI per 100,000 P-Yrs (incidence) 23.1 29.3 36.0 45.1 85.4 Multiple Exposure Groups

49. Yes No Got Giardiasis 14 341 355 16 108 124 Yes No 30 449 479 subjects Exposed to Kiddy Pool Cumulative Incidence 12.9% 3.9% Cumulative Incidence Make Sense Here This was a fixed population studied for a brief period, so it makes sense to calculate cumulative incidence.

50. 200320042005 20062007200820092010 X X XX X XX X X X XX Incidence: Frequency of new cases during a span of time in people at risk. Incidence is the probability of developing disease during a span of time. Incidence provides a way of measuring the risk of becoming diseased.

51. Prevalence provides a measure of the probability of currently having a condition. Incidence provides a way of measuring the probability (risk) of developing a condition.

52. Summary Prevalence (a proportion) = People# People with disease at a point in time Total People# People in the study population Cumulative Incidence (a proportion) = People# new cases in a specified period Total People# People (at risk) in the study population Incidence Rate (a rate) = People # new cases of disease People-Time Total observation time in a group at risk

53. Diabetes requires additional attention to diet, monitoring of blood sugar levels, attention to medications, skin care, risk of infections, etc. How would I determine how much of a burden diabetes is in nursing homes in Norfolk County, MA? How might I determine the risk of developing diabetes among nursing homes residents in Norfolk County, MA? How might I determine whether an exercise program for nursing home residents reduces the risk getting diabetes? Diabetes in a Nursing Home

54. HIV prevalence peaked in 2000 then began to decline due to increased education and awareness and high death rates. http://www.avert.org/hiv-aids-kenya.htm Prevalence is influence by the rate at which new cases are being added to the population and by the average duration of disease.

55. If the prevalence is <10%, and incidence rate, and average duration of disease have been relatively constant for a while, their relationship can be expressed by the equation above. This can also predict the effects of changing incidence rate or average duration. Prevalence Depends on Incidence & Duration of Disease Prevalence = Incidence x Average Duration of Disease P = IR x D

57. Calculating the Mean Duration of Disease Example: Lung cancer: If incidence = 46 new cancers per 100,000 P-Yrs (i.e., in a population of 100,000 you expect 46 cases per year), and prevalence = 23 per 100,000 population. What is the average duration of lung cancer? If P = I x D, then D = P / I Since D = P/IR then D = 23/100,000 persons= 0.5 years 46/100,000 person-years Conclusion: Individuals with lung cancer survived an average of 6 months from the time of diagnosis to death.

58. In one year there were 1,807 deaths from TB in the US (population=231,534,000) so the mortality rate for TB was 7.8 per million. [ 1,807/231,534,000 = 7.8/million per year] The incidence of fatal cases of a disease in a population during a specified time period. In the same year there were 1,973,000 deaths from all causes in the US, so the all-cause mortality rate was 852/100,000 population. [1,973,000 /231,534,000 = 852/100,000/year] Mortality ‘Rate’ (Cumulative incidence)

59. The incidence of non-fatal cases of a disease in a population during a specified time period. Morbidity ‘Rate’ Example: in 1982 there were 25,250 non-fatal cases of TB in US population. Midyear population was 231,534,000, Morbidity rate of TB =25,520 / 231,534,000 = 11.0 / 100,000 in 1982 (Cumulative Incidence)

60. The proportion of exposed people who develop disease. (Not really a rate; it’s a special type of cumulative incidence.) SARS exposure Attack ‘Rate’ (Cumulative Incidence)

61. The proportion of diseased people who die - in this case 2/6 = 33%. (Again, not a rate, but a special type of cumulative incidence.) It measures severity or risk of dying if you have the disease. Example: 60% of people who got bubonic plague died. Case Fatality ‘Rate’ (Cumulative Incidence)

62. Live birth ‘rate’: the total number of live births in one year per unit of population, e.g. per 1,000 females of childbearing age. Infant mortality ‘rate’: the number of deaths in children under 1 year of age occurring during a one year period per 1,000 live births. Autopsy ‘rate’: the proportion of people with a particular finding on postmortem exam. Birth defect ‘rate’: the prevalence of a birth defect (congenital anomaly) at the point of birth. The denominator can be either “live births” or “total” births (live births + stillbirths) but does not include aborted fetuses. (Cumulative incidence) (Prevalence)

63. The frequency of new cases of tuberculosis in Boston during a given calendar year is… 1.Prevalence 2.Cumulative incidence 3.Incidence rate 4.None of the above

64. The % of deceased males who are found to have prostate cancer at autopsy? 1.Prevalence 2.Cumulative incidence 3.Incidence rate 4.None of the above

65. The % of people who have malaria that is resistant to treatment with chloroquine? 1.Prevalence 2.Cumulative incidence 3.Incidence rate 4.None of the above

66. The number of newly diagnosed brain tumors in a calendar year per 100,000 Massachusetts children? 1.Prevalence 2.Cumulative incidence 3.Incidence rate 4.None of the above

67. The number of previously healthy women who had a stroke during 40,000 person-years of follow up? 1.Prevalence 2.Cumulative incidence 3.Incidence rate 4.None of the above

68.  Express prevalence and cumulative incidence as % or # per 1,000 or 10,000, etc.  Express incidence rate as # per 1,000 person-yrs or 10,000 person-years, etc.  Remember to state the time period of observation for cumulative incidence. In General: However, for the exercises that follow and for post class quiz #2, you will need to answer with the specific numerator and denominator for some questions, to make sure that you are including and excluding the right subjects.

69. Study population of 1,000. Dashed line = disease present (Lung Cancer) Patients 1, 2, 3, & 4) had the disease before the study began. During the year of the study, 6 new cases occur (start of dashed lines). Among the total of 10 cases, there were 6 deaths during the year The 990 other individuals in the study did not become ill or die. 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead Prevalence of disease on:Jan. 1, 1994? July 1, 1994? Dec. 31, 1994? X X X X X X

70. Prevalence on Jan. 1, 1994? A.0/1000 B.4/1000 C.6/1000 D.4/996 E.5/996 F.6/996 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead

71. Prevalence on July 1, 1994? A.4/997 B.4/1000 C.6/1000 D.4/996 E.5/996 F.5/997 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead

72. Prevalence on Dec. 31, 1994? A.4/1000 B.4/996 C.4/994 D.6/1000 E.6/996 F.6/994 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead

73. Study population of 1,000. Dashed line = disease present (Lung Cancer) Patients 1, 2, 3, & 4) had the disease before the study began. During the year of the study, 6 new cases occur (start of dashed lines). Among the total of 10 cases, there were 6 deaths during the year The 990 other individuals in the study did not become ill or die. 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead X X X X X X What was the cumulative incidence during 1994?

74. Cumulative incidence in 1994? 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead A.4/1000 B.6/1000 C.10/1000 D.4/996 E.6/996 F.10/996

75. Study population of 1,000. Dashed line = disease present (Lung Cancer) Patients 1, 2, 3, & 4) had the disease before the study began. During the year of the study, 6 new cases occur (start of dashed lines). Among the total of 10 cases, there were 6 deaths during the year The 990 other individuals in the study did not become ill or die. 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead X X X X X X What was the population mortality rate during 1994? (Use population at beginning of year for calculation)

76. Population mortality rate in 1994? 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead A.4/10 or 40% B.6/10 or 60% C.4/1000 or 0.4% D.6/1000 or 0.6% E.6/996 F.10/1000

77. Study population of 1,000. Dashed line = disease present (Lung Cancer) Patients 1, 2, 3, & 4) had the disease before the study began. During the year of the study, 6 new cases occur (start of dashed lines). Among the total of 10 cases, there were 6 deaths during the year The 990 other individuals in the study did not become ill or die. 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead X X X X X X What was the case-fatality rate during 1994?

78. Case fatality rate? 1994 1995 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan 1<---------------------------------------------------------------------------------------------------------Alive 2<---------------------------------------Dead 3<--------------------------------------------------------------Dead 4<-----Dead 5 -----------------------------------------------------------------------------------------------------Alive 6 ----------------------------Dead 7 -------------------------------------------------------------------------Alive 8 ------------Dead 9 ------------------------------------------------------------Alive 10 ---------------------------------------Dead A.6/10 or 60% B.6/1000 or 6% C.6/996 D.4/996 E.4/10