Transcript 5.6 - INAYA Medical College

BMS 244
Ratio
Proportions
Rates
Measurement of disease
frequency
Lecture 3,4
Dr. Maha Saud Khalid
Outline:
• Introduction ..
• Ratios!
How to Use Ratios?
How to Simplify?
Proportions!
Properties of proportions?
How to use proportions?
• Rate
• homework
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
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
a
b
Because a ratio is a fraction, b can not be zero
Ratios are expressed in simplest form
How to Use Ratios?
• The ratio of boys and girls in the class is 12 to
11.
This means, for every 12 boys you
can find 11 girls to match.
Howcould
manybedogs
cats do
• There
justand
12 boys,
11I have?
We don’t know, all we know is if
girls.
they’d
startbea 24
fight,
each
has to
• There
could
boys,
22dog
girls.
fightcould
2 cats.
• There
be 120 boys, 110
4cm
girls…a huge class
1cm
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 to simplify ratios?
• The ratios we saw on last
slide were all simplified.
How was it done?
Ratios can be expressed
a
in fraction form…
b
a
b
This allows us to do math on
them.
The ratio of boys and girls in the class is
12
11
The ratio of the rectangle is
4
1
The ratio of cats and dogs in my house
is
2
1
How to simplify ratios?
• Now I tell you I have 12 cats and 6 dogs. Can you simplify the ratio of cats
and dogs to 2 to 1?
12 / 6
6/6
=
12
6
=
2
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!


arm
height
80cm
2m

80cm
200cm
80
200

2
5
Once we have the
same units, we can
simplify them.
How to simplify ratios?
•
Let’s try m now!
arm
height
80cm
we have the
0.8m Once
same units, they


simplify to 1.
2m
2m

8
20

To make both numbers integers, we
multiplied both numerator and
denominator by 10
2
5
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
More examples…
8
24
40
200
27
9
=
1
3
12
50
=
1
5
27
18
=
3
1
=
6
25
=
3
2
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.
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
2
--- = 0.5 = 50%
4
Proportion of rotten apples
=
2/4
= 50%
Oranges to apples- a proportion?
Proportions!
What is a proportion?
a c

b d
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 :
3 6

2 4
Properties of a proportion?
3 6

2 4
2x6=12
Cross Product Property
3x4 = 12
3x4 = 2x6
Properties of a proportion?
•
Cross Product Property
a c

b d
ad = bc
means
extremes
Properties of a proportion?
Let’s make sense of the Cross Product Property…
For any numbers a, b, c, d:
a c

b d
a
d  c
b
a
c
d  d
b
d
a
d b  bc
b
ad  bc
Properties of a proportion?
• Reciprocal Property
3 6

If
2 4
Then
2 4

3 6
Can you see it?
If yes, can you think of
why it works?
How about an example?
7 x

2 6
7(6) = 2x
42 = 2x
21 = x
Solve for x:
Cross Product Property
How about another example?
7 12

2 x
Solve for x:
7x = 2(12)
Cross Product Property
7x = 24
x = 24
7
Can you solve it using
Reciprocal Property? If
yes, would it be easier?
Can you solve this one?
7
3

x 1 x
7x = (x-1)3
Solve for x:
Cross Product Property
7x = 3x – 3
4x = -3
x= 
3
4
Again, Reciprocal
Property?
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
Rate
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 !!
Rate =
Number of events (disease or death)
in a specified period
Number of population at risk
of these events in the same period
xK
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.
Rate
Observed in 2013
2
----- = 0.02 / year
100
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?