Numerical Examples Manish Chaudhary MPH BPKISH manish 264gmail

Numerical Examples Manish Chaudhary MPH (BPKISH) manish 264@gmail. com

Question 1 • Example: In January, 3 new cases of trachoma were detected in a village. There were already 10 people in the village who had the disease, but two successfully completed a course of therapy during the month and were considered cured. The population of the village was 2600. In this case: • the incidence rate is • the period prevalence rate is • the point prevalence rate as of 31 January is

Answer 1 • • • the incidence rate is (3/2600) x 1000 or 1. 2 per 1000 or 0. 1% the period prevalence rate is (3+10)/2600) x 1000 or 5 per 1000 or 0. 5% the point prevalence rate as of 31 January is ((3+10 -2)/2600) x 1000 or 4. 2 per 1000 or 0. 4%.

Q. 2 In 1994, 49 140 malaria cases occurred among males and the remaining 23 250 occurred among females a) What is the ratio of male : female cases? b) What percentage of the total cases occurred in males? In females?

EXAMPLES: Calculating Ratios for Different Variables • Example A: A city of 4, 000 persons has 500 clinics. Calculate the ratio of clinics person. • 500 / 4, 000 x 10 n = 0. 000125 clinics person • To get a more easily understood result, you could set 10 n = 104 = 10, 000. Then the ratio becomes: • 0. 000125 x 10, 000 = 1. 25 clinics per 10, 000 persons • You could also divide each value by 1. 25, and express this ratio as 1 clinic for every 8, 000 persons. • Example B: Delaware’s infant mortality rate in 2001 was 10. 7 per 1, 000 live births. 2 New Hampshire’s infant • mortality rate in 2001 was 3. 8 per 1, 000 live births. Calculate the ratio of the infant mortality rate in Delaware to that in New Hampshire. • 10. 7 / 3. 8 x 1 = 2. 8: 1 Thus, Delaware’s infant mortality rate was 2. 8 times as high as New Hampshire’s infant mortality rate in 2001.

• EXAMPLES: Calculating Cumulative Incidence (Risk) • Example A: In the study of diabetics, 100 of the 189 diabetic men died during the 13 -year follow-up period. • Calculate the risk of death for these men. • Numerator = 100 deaths among the diabetic men • Denominator = 189 diabetic men • 10 n = 102 = 100 • Risk = (100 / 189) x 100 = 52. 9% • Example B: In an outbreak of gastroenteritis among attendees of a corporate picnic, 99 persons ate potato salad, 30 of whom developed gastroenteritis. Calculate the risk of illness among persons who ate potato salad. • Numerator = 30 persons who ate potato salad and developed gastroenteritis • Denominator = 99 persons who ate potato salad • 10 n = 102 = 100 • Risk = “Food-specific attack rate” = (30 / 99) x 100 = 0. 303 x 100 = 30. 3%

• EXAMPLE: Calculating Secondary Attack Rates Consider an outbreak of shigellosis in which 18 persons in 18 different households all became ill. If the population of the community was 1, 000, then the overall attack rate was 18 / 1, 000 x 100% = 1. 8%. One incubation period later, 17 persons in the same households as these “primary” cases developed shigellosis. If the 18 households included 86 persons, calculate the secondary attack rate. • Secondary attack rate = (17 / (86 - 18)) x 100% = (17 / 68) x 100% = 25. 0%

EXAMPLES: Calculating Incidence Rates • • Q : Investigators enrolled 2, 100 women in a study and followed them annually for four years to determine the incidence rate of heart disease. After one year, none had a new diagnosis of heart disease, but 100 had been lost to follow-up. After two years, one had a new diagnosis of heart disease, and another 99 had been lost to follow-up. After three years, another seven had new diagnoses of heart disease, and 793 had been lost to follow-up. After four years, another 8 had new diagnoses with heart disease, and 392 more had been lost to follow-up. The study results could also be described as follows: No heart disease was diagnosed at the first year. Heart disease was diagnosed in one woman at the second year, in seven women at the third year, and in eight women at the fourth year of follow-up. One hundred women were lost to follow-up by the first year, another 99 were lost to followup after two years, another 793 were lost to followup after three years, and another 392 women were lost to follow up after 4 years, leaving 700 women who were followed for four years and remained disease free. Calculate the incidence rate of heart disease among this cohort. Assume that persons with new diagnoses of heart disease and those lost to follow-up were disease-free for half the year, and thus contribute ½ year to the denominator

Answer • • • Numerator = number of new cases of heart disease = 0 + 1 + 7 + 8 = 16 Denominator = person-years of observation = (2, 000 + ½ x 100) + (1, 900 + ½ x 1 + ½ x 99) + (1, 100 + ½ x 793) + (700 + ½ x 8 + ½ x 392) = 6, 400 person-years of follow-up or Denominator = person-years of observation = (1 x 1. 5) + (7 x 2. 5) + (8 x 3. 5) + (100 x 0. 5) + (99 x 1. 5) + (793 x 2. 5) + (392 x 3. 5) + (700 x 4) = 6, 400 person-years of follow-up Person-time rate = Number of new cases of disease or injury during specified period Time each person was observed, totaled for all persons = 16 / 6, 400 =. 0025 cases person-year = 2. 5 cases per 1, 000 person-years In contrast, the incidence proportion can be calculated as 16 / 2, 100 = 7. 6 cases per 1, 000 population during the four-year period, or an average of 1. 9 cases per 1, 000 per year (7. 6 divided by 4 years). The incidence proportion underestimates the true rate because it ignores persons lost to follow-up, and assumes that they remained disease free for all four years.

• The diabetes follow-up study included 218 diabetic women and 3, 823 non diabetic women. By the end of the study, 72 of the diabetic women and 511 of the nondiabetic women had died. The diabetic women were observed for a total of 1, 862 person-years; the nondiabetic women were observed for a total of 36, 653 person-years. • Calculate the incidence rates of death for the diabetic and non-diabetic women.

• For diabetic women, numerator = 72 and denominator = 1, 862 Person-time rate = 72 / 1, 862 = 0. 0386 deaths person-year = 38. 6 deaths per 1, 000 person-years • For nondiabetic women, numerator = 511 and denominator = 36, 653 Person-time rate = 511 / 36, 653 = 0. 0139 deaths person-year = 13. 9 deaths per 1, 000 person-years

Figure 3. 1 represents 10 new cases of illness over about 15 months in a population of 20 persons. Each horizontal line represents one person. The down arrow indicates the date of onset of illness. The solid line represents the duration of illness. The up arrow and the cross represent the date of recovery and date of death, respectively. Figure 3. 1 New Cases of Illness from October 1, 2004 through September 30, 2005 Example A: Calculate the incidence rate from October 1, 2004, to September 30, 2005, using the midpoint population (population alive on April 1, 2005) as the denominator. Express the rate per 100 population.

answers • Incidence rate numerator = number of new cases between October 1 and September 30 = 4 (the other 6 all had onsets before October 1, and are not included) • Incidence rate denominator = April 1 population = 18 (persons 2 and 8 died before April 1) Incidence rate = (4 / 18) x 100 = 22 new cases per 100 population

Figure 3. 1 represents 10 new cases of illness over about 15 months in a population of 20 persons. Each horizontal line represents one person. The down arrow indicates the date of onset of illness. The solid line represents the duration of illness. The up arrow and the cross represent the date of recovery and date of death, respectively. Figure 3. 1 New Cases of Illness from October 1, 2004 through September 30, 2005 Example B: Calculate the point prevalence on April 1, 2005. Calculate the period prevalence from October 1, 2004, to September 30, 2005.

• Point prévalence = (7 / 18) x 100 = 38. 89% • Period prevalence = (10 / 20) x 100 = 50. 0%

• In hilly district of Nepal with the population of 100000, there were 4000 births and 400 infant deaths in the year 2007. Out of these deaths 160 died within the first 28 days of the birth and 220 were still births. 2000 cases of ARI appeared among children of under one in the same year. Find a) Neonatal mortality rate b) Infant mortality rate c) Incidence rate of ARI.

• 11 cases of typhoid occurred among 110 children attending a Child care Center. Each infected child came from a different family. A total number of persons in the 11 affected families were 31. One incubation period leaser, 5 family members of the 7 infected children also developed Typhoid. Calculate the primary and secondary attack rate with the prevalence of typhoid.

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