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!

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 1Week 2Week 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 males population = 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 beds doctors 850 / 10 == 85 / 1 males females = 5 / 2 = 2.5 /1 3 / 1 = participants facilitators

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 / = = = 1.3 per 10,000 inhabitants per year Rate may be expressed in any power of 10: 100, 1000, 10000, …

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 individuals 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 l x x l l x l l l Person p.y Person 2 Person 3 Person 4 Person 5 Time-person

Week 1Week 2Week 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 PrevalenceIncidence Probability of having the disease Probability of developing the disease RISKBurden

Measuring disease occurrence Lets talk about ODDS now Probability that an event will happen Probability that an event will not happen

Jellyfish odds today

Odds StungNo sting Total Swimming off lazareto 358 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

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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 Spain Spanish population in 2007 Cases of diabetes in 2008 in Spain Spanish population in 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.

CasesNon cases Exposed (e)aba+b Non exposed (ne)cdc+d a+cb+d Risks, Odds and 2x2 tables 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 CasesNon-casesTotal Hepatitis A 3049,97050,000 The number of hepatitis cases during an outbreak 30 / 50,000 Odds of disease = = ,970 / 50,000 Risk (CI) of disease = 30/50,000 = 0.006