# Rapport - Proportion - Taux

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```Rates and measures
(of disease occurrence)
Chris Williams (adapted from EPIET slides)
Statistics track (STA)
• Rates, ratios, proportions
• Graphs and maps; tables
• Sensitivity and specificity
• Hypothesis testing; confidence intervals
• Sampling techniques and sample size
Descriptive studies - context in epidemiology
Epidemiology studies the occurrence of illness:
the frequency and distribution of diseases in the population
and their determinants
frequency and distribution: who, when, where
determinants: why
1 person in Lazareto was stung by a
jellyfish- How to express this?
Ouch!
1 person in Lazareto was stung by a
jellyfish- How to express this?
Descriptive studies – measuring disease occurrence
counts
number of cases
“we have 5 cases of tetanus”
On its own very little informative!!
Who is in the denominator ????
In what time period did they occur???
Jellyfish sting counts
Week 1
Week 2
Week 3
Measuring disease occurrence
Proportion
Ratio
Rate
What, who is in the denominator ????
In what time period did they occur???
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
males
=
population
400 / 1000 = 40%
Proportion of rotten apples
=2/4
= 50%
Oranges to apples- a proportion?
Ratio
• The division of two numbers
• Numerator NOT INCLUDED in the denominator
• Allows to compare quantities of different nature
males
=
females
5 / 2 = 2.5 /1
beds
=
doctors
850 / 10 = 85 / 1
participants
=
facilitators
3/1
Rate
• The division of 2 numbers
• TIME INCLUDED in the denominator
• Speed of occurrence of an event over time
Births in 2007
Population in 2007
= 2000 / 15 000 000 =
= 0.00013 = 1.3 per 10,000 inhabitants per year
• Rate may be expressed in any power of 10:
100, 1000, 10000, 100 000…
Measuring disease occurrence
Number of cases of disease
Population
– Number of cases of a disease in a given population at
a specific time
– Proportion of the population that had the disease at a
given time
– Probability of having the disease
prevalence
Measuring disease occurrence
Number of NEW cases of disease during a period
Population at the beginning of the period
– Number of new cases of a disease in a in a given
population at a specific time
– Proportion of the population that acquire or develop a
disease in a period of time
– Probability of developing a disease
incidence
(cumulative incidence)
Measuring disease occurrence
Incidence Rate
• Proportion of the population that acquire or develop a
diseases in a period of time
• Speed of developing a disease
Number of NEW cases of disease
Total person- time of observation
Denominator:
- is a measure of time
- the sum of each individual’s time at risk
and free from disease
Time-person
Person 1 l
3
Person 2 l
4
x
Person 3 l
Person 4l
Person 5 l
6
3
1
x
x
Person 5l
5
22 p.y
2003
2004
2005
2006
2007
2008
2009
Cumulative Incidence = 3 cases / 6 persons = 50%
Incidence Rate = 3 cases / 22 person-years = 0.14
= 14 cases / 100 person-years
How many facilitator weeks?
Week 1
Week 2
Week 3
Measuring disease occurrence
Attack Rate
• Cumulative incidence during an outbreak
Expressed for the entire epidemic period, from the
first to the last case
• Not really a rate but a proportion!
Outbreak of cholera in country X in March 1999
Number of cases
490
Population
18,600
Attack rate
2.6%
Measuring disease
occurrence
Descriptive
Prevalence
Probability of
having the disease
Burden
Incidence
Probability of
developing the disease
RISK
Measuring disease occurrence
Let’s talk about ODDS now
Probability that an event will happen
Probability that an event will not happen
Jellyfish odds today
Odds
Probability that an event will happen
Probability that an event will not happen
Stung
Swimming off
lazareto
3
No
Total
sting
5
8
3/8
Odds of sting = ------------- = 3:5 = 0.6
5/8
Odds of a rare event
equals the risk of rare event
,
Summary of disease occurence
• PREVALENCE
• INCIDENCE
– Cumulative incidence
– Incidence rate
– Attack rate
• ODDS
Buffy Summers, “Class Protector”
• Host: ..Sunnydale High isn't really like other
high schools. A lot of weird stuff happens
here.&quot;
Students:”Zombies! Hyena people!”
Host:&quot;But whenever there was a problem..
you seemed to show up and stop it. Most of
the people here have been saved by you.
We're proud to say that the class of '99 has
the lowest mortality rate of any graduating
class in Sunnydale history. And we know
that at least part of that is because of you
For lunch time… what are these?
Number of deaths in 2007 in Spain
Spanish population in 2007
Cases of diabetes in 2008 in Spain
Spanish population in 2008
16 malaria deaths
1000 deaths occured
30 guests with diarrhoea
300 wedding guests
100 hours at the Lazareto bar
150 hours in the lecture room
References
• Epidemiology, an introduction. Rothman KJ.
• Epidemiology in Medicine. Henneckens CH, Buring JE.
• Modern infectious disease epidemiology. Giesecke J.
• Dictionary of epidemiology. Last J.
Risks, Odds and 2x2 tables
Cases Non cases
Exposed (e)
a
b
a+b
Non exposed (ne) c
d
c+d
a+c
b+d
Risk of being a case in exposed = a / a+b
Risk of being a case in non exposed = c / c+d
Odds of being exposed among cases
= (a/a+c)/(c/a+c)= a / c
Odds of being exposed among non cases
= (b/b+d)/(d/b+d)= b/d
Odds of a rare event
equal the risk of rare event
The number of hepatitis cases during an outbreak
Cases Non-cases Total
Hepatitis A
30
49,970
50,000
30 / 50,000
Odds of disease = ------------------------ = 0.006
49,970 / 50,000
Risk (CI) of disease = 30/50,000
= 0.006
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