Lecture 3,4 Dr. Maha Saud Khalid Measurement of disease frequency Ratio Proportions Rates Ratio Proportions Rates BMS 244

Introduction.. Ratios! How to Use Ratios? How to Simplify? Proportions! Properties of proportions? How to use proportions? Rate homework Outline:

Introduction Every disease or condition needs to be measured- in a population. Group of people with a common characteristic like age, race, sex. Calculation of measures of disease frequency depends on correct estimates of number of people who are potentially susceptible. e.g. Breast cancer People who are susceptible are called population at risk- e.g. Diabetics.

The simplest method to express frequency is to count the number of persons in the group studies who have a particular disease or a particular characteristic. BUT the number of cases of a disease may vary from place to place according to the number of people in each place. Thus, we have to relate number of cases of a disease to the population from which these cases come.

Measures of disease frequency should take into account :  Number of individuals affected with the disease.  Size of source population.  Length of time the population was followed.

Numerator - number of EVENTS observed for a given time Denominator - population in which the events occur (population at risk)

Ratio is the relationship between two numbers (one is divided by the other). It does not relate to a particular time. Those included in the numerator are not included in the denominator. So, the numerator represents the number of events that meet a specific criterion WHILE the denominator represents the number of events that meet a different criterion. RATIO

A fraction in which the numerator is not part of the denominator. e.g. Fetal death ratio: Fetal deaths/live births. Fetal deaths are not included among live births, by definition.

Examples: Sex Ratio = Number of males Number of females Risk Ratio = Risk of disease in one group (exposed) Risk of disease in another group (unexposed)

`Ratio? A ratio is a comparison of two numbers. Ratios can be written in three different ways: a to b a:b Because a ratio is a fraction, b can not be zero Ratios are expressed in simplest form

The ratio of boys and girls in the class is 12 to 11. 4cm 1cm This means, for every 12 boys you can find 11 girls to match. There could be just 12 boys, 11 girls. There could be 24 boys, 22 girls. There could be 120 boys, 110 girls…a huge class What is the ratio if the rectangle is 8cm long and 2cm wide? Still 4 to 1, because for every 4cm, you can find 1cm to match The ratio of length and width of this rectangle is 4 to 1.. The ratio of cats and dogs at my home is 2 to 1 How many dogs and cats do I have? We don’t know, all we know is if they’d start a fight, each dog has to fight 2 cats. How to Use Ratios?

How to simplify ratios? The ratios we saw on last slide were all simplified. How was it done? Ratios can be expressed in fraction form… This allows us to do math on them. The ratio of boys and girls in the class is The ratio of the rectangle is The ratio of cats and dogs in my house is

Now I tell you I have 12 cats and 6 dogs. Can you simplify the ratio of cats and dogs to 2 to 1? == Divide both numerator and denominator by their Greatest Common Factor 6. How to simplify ratios?

A person’s arm is 80cm, he is 2m tall. Find the ratio of the length of his arm to his total height To compare them, we need to convert both numbers into the same unit …either cm or m. Let’s try cm first! Once we have the same units, we can simplify them. How to simplify ratios?

Let’s try m now! Once we have the same units, they simplify to 1. To make both numbers integers, we multiplied both numerator and denominator by 10 How to simplify ratios?

If the numerator and denominator do not have the same units it may be easier to convert to the smaller unit so we don’t have to work with decimals… 3cm/12m = 3cm/1200cm = 1/400 2kg/15g = 2000g/15g = 400/3 5ft/70in = (5*12)in / 70 in = 60in/70in = 6/7 2g/8g = 1/4 Of course, if they are already in the same units, we don’t have to worry about converting. Good deal How to simplify ratios?

= = = = = More examples…

Proportion A fraction in which the numerator is part of the denominator. e.g. Fetal death rate: Fetal deaths/all births All births includes both live births and fetal deaths. o Synonyms for proportions are: a risk and, (if expressed per 100) a percentage. o Most fractions in epidemiology are proportions.

2 --- = 0.5 = 50% 4 Proportion The division of 2 numbers Numerator INCLUDED in the denominator In general, quantities are of same nature In general, ranges between 0 and 1 Percentage = proportion x 100

Proportion of rotten apples = 2/4 = 50%

Oranges to apples- a proportion?

What is a proportion? A proportion is an equation that equates two ratios The ratio of dogs and cats was 3/2 The ratio of dogs and cats now is 6/4=3/2 So we have a proportion : Proportions!

2x6=12 3x4 = 12 3x4 = 2x6 Cross Product Property Properties of a proportion?

Cross Product Property ad = bc means extremes Properties of a proportion?

Let’s make sense of the Cross Product Property… For any numbers a, b, c, d:

If Then Reciprocal Property Can you see it? If yes, can you think of why it works? Properties of a proportion?

Solve for x: 7(6) = 2x 42 = 2x 21 = x Cross Product Property How about an example?

Solve for x: 7x = 2(12) 7x = 24 x = Cross Product Property Can you solve it using Reciprocal Property? If yes, would it be easier? How about another example?

Solve for x: 7x = (x-1)3 7x = 3x – 3 4x = -3 x = Cross Product Property Again, Reciprocal Property? Can you solve this one?

3-Rate Ideally, a proportion in which change over time is considered, but in practice, often used interchangeably with proportion, without reference to time, (as I did previously for fetal death rate).

Rates 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 However rate is frequently used instead of ratio or proportion !! Time is included in the denominator !!Rate

Rate = Number of events (disease or death) in a specified period Number of population at risk of these events in the same period K is a constant used to get a whole number to avoid fraction. The rate is multiplied by 1,000, 10,000 or 100,000 for ease of interpretation. x K

Rate = 0.02 / year 100 Observed in 2013

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

Home works 1 AIDS cases: 4000 male cases 2000 female cases Q:What is the proportion of male cases among all cases? Female cases among all cases?

Homeworks2 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?