Frequency and measures of association
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Frequency and
measures of association
Center for Clinical Epidemiology and Evidence-Based Medicine (CEEBM)Faculty of Medicine, University of Indonesia – Cipto Mangunkusumo Hospital
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Frequency measures
• Two types:– Someone has the disease already:
prevalence = measure population disease status
– Someone gets the disease in the future: incidence
=measure frequency of disease onset
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Measure of disease occurrence (example)
• Incidence: the rain arriving• Prevalence: the water in the puddle, new and old• Period prevalence: the water in the puddle, during a
period• Point prevalence: at one point of time
The water draining away into the soil or into drains reduce the puddle (i.e. the prevalence) just as recovery or death reduce the number of patients with a problem
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Prevalence
• Proportion of population affected by the disease at a given point in time
• Expressed as a percentage:(number of diseased)/(population) * 100
Number of cases of disease at a specific time
Population exposed at that time
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Frequency measures: prevalence
• Cross-sectional studies– Determinant and disease measured at the same
time – Used in diagnostic research
• Prevalence – Number of persons with the disease at a certain
moment
• Prevalence (%)– Number of persons with the disease / total
population
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Frequency measures: prevalence
• Examples– 50% of the persons with a suspicion of
lung cancer had a lesion on the thorax X-ray
– In a general practice population of 2500 persons, 50 had asthma
– 30% of the Indonesian people smoke
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Frequency measures: prevalence
• Interpretation / relevance– Quantification amount of disease: a priori
probability– public health planning
• Issues– non-response
• prevalence of MI• prevalence of dementia
– selective mortality
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New events…
• Incidence• Incidence rate• Incidence density• Attack rate• Cumulative incidence• Risk• ……
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Frequency measures: Incidence
• Incidence– number of new cases– in the population at risk
• Two types of incidence– Cumulative incidence– Incidence density (incidence rate)
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Frequency measures: Incidence
• Used in prognostic research• Incidence density
– The number of new disease cases in the population divided by the observation time
• Cumulative incidence– new cases in a certain time period in the population at
risk (free of the disease at the start)– proportion / probability– varies between 0 and 1– within certain time period
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Frequency measures: Incidence
• Cumulative incidence: examples– 5-year risk of a second MI– 10-year survival for women with breast
cancer– 1-year risk of a fracture for osteoporotic
women
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Exercise 1
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Exercise 1
Ad question 1: tonsillitisA. Dutch population
B. 1 year
C. incidence
D. 19/1000 or 1.9%
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Exercise 1
Ad question 2: asthmaA. Children in the general practice
B. Certain moment (look into practice data at a certain moment)
C. (point) prevalence
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Exercise 1
Ad question 3: breast cancerA. Women
B. Life
C. Incidence
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Exercise 1
Ad question 4: vertebral collapseA. 9%
B. 55-59 year-old men and women
C. Certain moment
D. (point) prevalence
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Exercise 1
Ad question 5: fracturesA. Post-menopausal women
B. Follow-up duration of the study
C. Incidence
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Frequency measures: Incidence
• How do we calculate an incidence?
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Frequency measures: Incidence
• Cohort approach– Group of persons with the same
characteristics– All participants have the same starting
point (start cohort) • However, baseline can differ in time
– All participants are followed during a certain time period
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Cumulative incidence
• Cumulative incidence excludes prevalence at baseline
• Example:Population 350.000
New cases 1.250
Cumulative incidence 3.6/1000 per year
Number of NEW cases of disease during a period
Population exposed during the period
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Frequency measuresIncidence density
• # new patients / person-years of the population at risk– 10 per 1000 person-years– between 0 and infinity
Number of new/incident cases
Amount of at-risk experience time
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Frequency measures:Incidence: cohort
• 5 persons followed during a year• (N at risk = 5)
– A------------------------------– B------------------------------– C-------------breast cancer– D------------------------------– E------------------------------
• 1-year risk of breast cancer = CI = 1/5=20% per year• ID = 1/4.5 person-years = 222/ 1000 person-years
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Frequency measures: example cohort
• 13 persons followed for 5 years for mortality– A-----------------------------x--Moves away t=2.5
– B-----------------------------x-------------Death t=3.0
– C-------breast cancer/death t=1.0
– D-----------------------------x------------------------------------------- alive t=5.0
– E-----------------------------x--------lost to follow-up t=3.0
– F-----------------------------x--------------------------------------------alive t=5.0
– G-----------------------------x---------------------------breast cancer/death t=4.0
– H-----------------------------x-Myocardial infarction/death t=2.5
– I--------death t=1.0
– J------------------------------x-------------------------------------------alive t=5.0
– K-------------lost to follow-up t=1.5
– L-----------------------------x----------------moves from the area t=3.5
– M--------1---------------2--x----------3---------------4-------------------alive t=5.0
• Total amount time at-risk = 42 years
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Frequency measures: example cohort
• CI = 5/13 = 38%
• ID = 5/42 x 1000 = 199/1000 person-years
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Item Prevalence Cumulative incidence
Incidence density
Numerator All cases counted in a single occasion
New cases occurring during a specified follow-up period
New cases occurring during a specified follow-up period
Denominator All individual examined – cases and non cases
All susceptible individuals present at the start of the study
Sum of time periods during which all individuals could have developed disease
Time Single point or period
Defined period Measure for each individual from beginning of study until disease event or study end
Interpretation Probability of having disease at a point in time
Probability of developing disease over a specific period
How quickly new cases develop over a specified period
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Measures of association
• Epidemiology – Disease = f (determinants)– Is the determinant associated with the
disease? – Is the probability of disease different for
exposed and non-exposed?
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Measures of association
• Research question? Is smoking associated with lung cancer?
• Cohort approach– divide the cohort in smokers and non-smokers– estimate the incidence density (or CI) in each
group– prior: ID smokers > ID not smokers
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Measures of association
Disease
Yes No
Yes a - PY1
Determinant
No c - PY0
ID1 a/py1
ID0 c/py0
RR = =
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Measures of association
• Smoking and lung cancer Disease
Yes No Yes 440 - 22.008 py
DeterminantNo 212 - 21.235 py
RR = (440/22.008) / (212/21.235) = 2.0
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Measures of association
• Risk difference between exposed and non-exposed– CI or ID– public health impact
• Risk difference smoking and lung cancer– 20/1000 py - 10/1000 py = 10 / 1000
personyears
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Measures of association
• Research question: Does smoking increase the risk of lung cancer ?
• Case-control study– select cases and controls – Estimate the frequency of smoking among cases
and controls– prior: % smokers among cases > % smokers
among controls
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Measures of association
Disease
Yes No
Yes a b
Determinant
No c d• RR?• Odds ratio = (a/c) / (b/d) = ad / bc
– Odds= the chance of something happening/the chance of it not happening
– Odds Ratio - a ratio of two odds
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Measures of association
• Smoking and lung cancer (controls = 10% random sampling from cohort)
DiseaseYes No
Yes 440 300 740Determinant
No 212 350 562
• Odds ratio (440/212) / (300/350) = 2.42
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Measures of association
• Smoking and lung cancer Disease
Yes No Yes 440 300 740
DeterminantNo 212 350 562
• RR = (440/740) / (212/562) = 1.57 (shouldn’t be calculated)• Odds ratio (440/212) / (300/350) = 2.42
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Measures of association• Smoking and lung cancer
Disease Yes No
Yes 440 3000 3440Determinant
No 212 3500 3712
• Now entire cohort as control• RR = (440/3440) / (212/3712) = 2.23• Odds ratio =(440/212) / (3000/3500) = 2.42• RR (a/(a+b)) / (c/(c+d)) ~ (a/c) / (b/d)
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Frequency measures:Therapeutic research
• Suppose: you see a patient with an increased blood pressure who you want to treat with blood pressure decreasing drugs. He asks about the effect of this treatment on the prognosis
• Research question: Does treatment decrease the probability of CVD?
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Frequency measures:Incidence
• Intervention study (RCT) – Estimate incidence density (or CI) for each group– prior: ID treated < ID not treated
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Exercises 2 and 3
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Exercise 2
A. People of age 55 years and older
B. 5 years
C. Incidence (probably cumulative)
D. Relative risk and risk difference
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Exercise 2
Risksmokers = 41/1736 = 0.024
Risknon-smokers = 107/5949 = 0.018 - RR = 0.024/0.018 = 1.3
Smokers have a 1.3 x higher probability of CVD than non-smokers
- RD = 0.024 - 0.018 = 0.006 Smokers have a 5-year risk of CVD that is 0.6% higher than that of non-smokers
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Exercise 3
1. Case-control study
2. Severe head injury
3. Population
4. Alzheimer’s disease
5. Odds ratio
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Exercise 3
Severe head injury in the past
Alzheimer Yes No
Severe Yes 33 31
Head injury No 165 167
OR = (33x167)/(31x165)=1.1
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SummaryFrequency and measures of
association
• Frequency– Prevalence– Incidence
• cumulative• density
• Association- Relative risk
- Rate ratio- Risk ratio
- Odds ratio- Risk difference
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Outcome measures
• Diagnostics?
• Prognostics?
• Etiology?
• Intervention?
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Outcome measures• Diagnostics
– Prevalence (abs. risk), posterior probability, Se, Sp, PV+, PV-, OR, AUC
• Prognostics– Incidence (abs. risk), OR, AUC
• Etiology– Incidence (abs. risk), RR, OR
• Intervention– Incidence (abs. risk), RR, RD, mean
difference, NNT
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Effect estimate
• Does a single effect estimate, e.g. RR=1.5 or RR=1.0 give sufficient information?
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Effect estimate
• No, because it does not tell anything about precision
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P-values versus confidence intervals
• P-value: The probability that the found association (or more extreme) occurs given the nullhypothesis is true (often with arbitrary cut-off of 5%)
• Confidence interval:Range of possible effect estimates that you would find if you would repeat the research (infinitely) often
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P-values
• Statistical significance (is not the same as clinical relevance)
• Dependent on– Size of the effect
– Size of the study population
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Example
• American study on losing weight in obese people
• Intervention: 1. Half an hour per day sports+ diet advice
2. only half an hour sports
• Numbers: 2 x 10.000 people
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Example
• BMI before– Group 1: 30.0
– Group 2: 30.0
• After p<0.0001
Effect size not in article but turned out to be
in group 1: 27.6
in group 2: 27.8
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Example
• Similar study in England• Now with 2 x 50 people• BMI before
– Group 1: 28.5– Group 2: 28.4
• Weight after– Group 1: 23.5– Group 2: 25.5 p=0.15
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P-values
• Paradoxal results possible:
1. Significant effect, but clinically not relevant
2. Clinically relevant effect, but not significant
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Confidence interval (CI)
• Objective impression of the size of the effect and the precision of the effect estimate
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Relation p-values and CI
• For OR and RR; if the 95%CI does not contain 1 than p < 0.05
• For mean difference; if 0 not in the 95%CI than p < 0.05
• And vice versa
• Don't do this, because information CI is not fully used
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Concluding
• Never consider p-values alone, but also effect estimates
• Present effect estimates always with confidence intervals