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Ratios,Proportions and Rates

Ratios,Proportions and Rates. MAE Course 2005. Measures of frequency. The basic tools to describe quantitatively the causes and patterns of disease, or any other event related to health in human populations. For example: How many people are affected by a certain disease?

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Ratios,Proportions and Rates

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  1. Ratios,Proportions and Rates MAE Course 2005

  2. Measures of frequency • The basic tools to describe quantitatively the causes and patterns of disease, or any other event related to health in human populations. • For example: How many people are affected by a certain disease? What is the rate at which the disease in occurring through time? How does the disease burden vary by geographical region, by sex, by age, or various modes of exposure? Etc., etc.

  3. Objectives Define and use Ratios Proportions Rates Odds

  4. Example To measure an event Count No. of new of AIDS cases City A 58 City B 35

  5. To measure an event Count No. new AIDS cases Cases Year Population City A 58 1990 25,000 City B 35 1989-90 7,000

  6. To measure an event Count No. new AIDS casesYearPopulation City A 58 1990 25,000 City B 35 1989-90 7,000 Divide City A: 58 / 25,000 / 1 year City B: 35 / 7,000 / 2 years

  7. To measure an event Count No. new AIDS casesYearPopulation City A 58 1990 25,000 City B 35 1989-90 7,000 Divide City A: (58/25,000)/ 1 year City B: (35/7,000)/ 2 years Compare City A: 232/100,000 per year City B: 250/100,000 per year

  8. Ratio • Proportion • Rate What, who is in the denominator ? ???

  9. = 5 / 2 = 2.5 / 1 Ratio • The quotient of 2 numbers • Numerator NOT necessarily INCLUDED in the denominator • Allows to compare quantities of different nature

  10. Ratio, Examples • # beds per doctor • 850 beds/10 doctors • R = 85 beds for 1 doctor • # participants per facilitator • # inhabitants per latrine • Sex ratio: Male / Female Female / Male • Odds ratio • Rate ratio • Prevalence ratio

  11. Ratio of AIDS case rates between city A and city B. City A: 232/100,000 persons per year City B: 250/100,000 persons per year Q: What is the ratio of the rates for city A compared to city B? city B compared to city A?

  12. Proportion • The quotient of 2 numbers • Numerator NECESSARILY INCLUDEDin the denominator • Quantities have to be of the same nature • Proportion always ranges between 0 and 1 • Percentage = proportion x 100 2 --- = 0.5 = 50% 4

  13. Proportion, Example AIDS cases: 4000 male cases 2000 female cases Q: What is the proportion of male cases among all cases? Female cases among all cases?

  14. Example The Proportion HIV-positive Among 500 persons tested last week for HIV in city A, 50 were HIV‑positive: 32 men and 18 women. Q: What is the proportion of persons who are HIV‑positive? Q: What proportion of the HIV‑positives are male?

  15. Population 3500women 6500 men Proportion of men = 6500 / (3500 + 6500) = 0.65 or 65 % Male to female ratio = 6500 / 3500 = 1.86 Female to male ratio = 3500/6500 = 0.54 Example

  16. Numerator • number EVENTS observed for a given time Observed in 1998 Rate • The quotient of 2 numbers • Speed of occurrence of an event over time

  17. Numerator • number of EVENTS observed for a given time • Denominator • population in which the events occur • (population at risk) • - includes time Observed in 1998 2 ----- = 0.02 / year 100 Rate • The quotient of 2 numbers • Speed of occurrence of an event over time

  18. Something that may change over time Something that is observed during some time Measures the speed of occurrence of an event Measures the probability to become sick by unit of time Measures the risk of disease Time is included in the denominator !! However rate is frequently used instead of ratio or proportion !! Rates

  19. Rate, Example • Mortality rate of tetanus in X country in 1995 • Tetanus deaths: 17 • Population in 1995: 58 million • Mortality rate = 0.029/100,000/year • Rate may be expressed in any power of 10 • 100, 1,000, 10,00, 100,000

  20. Odds Probability that an event will happen Probability that an event will not happen Won Lost Total ------------------------------------------------------------------------------------------------------------------------------------------------ UZ basketball team 200114 1 15 -------------------------------------------------------------------------------------------------------------------------------------------------- 14 / 15 Odds = ------------- 1 / 15 Odds of winning = 14 : 1 = 14 Odds of not winning = 1 : 14 = 0.07

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