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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." 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 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