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?

1 person in Lazareto was stung by a jellyfish- How to express this?

Ouch!

Who is in the denominator ????In what time period did they occur???

number of cases“we have 5 cases of tetanus”

On its own very little informative!!

counts

Descriptive studies – measuring disease occurrence

Week 1 Week 2 Week 3

Jellyfish sting counts

Proportion Ratio Rate

What, who is in the denominator ????In what time period did they occur???

Measuring disease occurrence

• 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

malespopulation

= 400 / 1000 = 40%

Proportion of rotten apples

=2/4 = 50%

Oranges to apples- a proportion?

• The division of two numbers

• Numerator NOT INCLUDED in the denominator

• Allows to compare quantities of different nature

Ratio

bedsdoctors 850 / 10 = = 85 / 1

malesfemales

= 5 / 2 = 2.5 /1

3 / 1 =participantsfacilitators

• The division of 2 numbers• TIME INCLUDED in the denominator• Speed of occurrence of an event over time

Rate

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

Number of NEW cases of disease during a period

Population at the beginning of the period

Measuring disease occurrence

–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)

Incidence Rate

Number of NEW cases of disease

Total person- time of observation

• Proportion of the population that acquire or develop a diseases in a period of time

• Speed of developing a disease

Denominator:- is a measure of time - the sum of each individual’s time at risk and free from disease

Measuring disease occurrence

Cumulative Incidence = 3 cases / 6 persons = 50%

Incidence Rate = 3 cases / 22 person-years = 0.14

= 14 cases / 100 person-years

2003 2004 2005 2006 2007 2008 2009

l

x

xll x

l

l

l

Person 1 3

4

6

3

1

5

22 p.y

Person 2

Person 3

Person 4

Person 5

Person 5

Time-person

Week 1 Week 2 Week 3

How many facilitator weeks?

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!

Measuring disease occurrence

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 Incidence

Probability ofhaving the disease

Probability ofdeveloping the disease

RISKBurden

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

Stung No sting

Total

Swimming off lazareto 3 5 8

3/8

Odds of sting = ------------- = 3:5 = 0.6 5/8

Probability that an event will happen

Probability that an event will not happen

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."Students:”Zombies! Hyena people!”Host:"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 SpainSpanish population in 2007

Cases of diabetes in 2008 in Spain

Spanish population in 2008

16 malaria deaths 1000 deaths occured

30 guests with diarrhoea300 wedding guests

100 hours at the Lazareto bar150 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.

Cases Non cases

Exposed (e) a b a+b

Non exposed (ne) c d c+d

a+c b+d

Risks, Odds and 2x2 tables

Risk of being a case in exposed = a / a+bRisk of being a case in non exposed = c / c+d

Odds of being exposed among cases= (a/a+c)/(c/a+c)= a / cOdds 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

Cases Non-cases Total

Hepatitis A

30 49,970 50,000

The number of hepatitis cases during an outbreak

30 / 50,000

Odds of disease = ------------------------ = 0.006 49,970 / 50,000

Risk (CI) of disease = 30/50,000 = 0.006