Download Risk ratio - Epidemiology Matters

Are exposures associated with
disease?
Epidemiology matters: a new introduction to methodological foundations
Chapter 6
Seven steps
1.
Define the population of interest
2.
Conceptualize and create measures of exposures and health
indicators
3.
Take a sample of the population
4.
Estimate measures of association between exposures and health
indicators of interest
5.
Rigorously evaluate whether the association observed suggests a
causal association
6.
Assess the evidence for causes working together
7.
Assess the extent to which the result matters, is externally valid,
to other populations
Epidemiology Matters – Chapter 1
2
1. Associations
2. Ratio measures
3. Difference measures
4. Population attributable risk proportion
5. Summary
Epidemiology Matters – Chapter 6
3
1. Associations
2. Ratio measures
3. Difference measures
4. Population attributable risk proportion
5. Summary
Epidemiology Matters – Chapter 6
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Associations
 First we start with measures of disease
occurrence and frequency
 Association now involves the comparison of
two measures
Epidemiology Matters – Chapter 6
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Example: Farrlandia associations
Farrlandia population
 10,000 people without heart disease
 Follow population for 5 years
 3,000 people smoke
 410 of smokers develop heart disease
 No loss to follow-up or change in smoking status
over time
Epidemiology Matters – Chapter 6
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Example: Farrlandia associations
Risk of heart disease among 3,000 smokers and 7,000 nonsmokers, over 5 years
Epidemiology Matters – Chapter 6
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Example: Farrlandia risk
Incidence (risk)
 Risk of disease among exposed
(smokers)
diseased smokers
population at baseline
Epidemiology Matters – Chapter 6
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Example: Farrlandia risk
Incidence (risk)
 Risk of disease among unexposed
(non-smokers)
diseased non-smokers
population at baseline
Epidemiology Matters – Chapter 6
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Example: Farrlandia risk
Incidence of heart disease among smokers = 13.7%
Incidence of heart disease among non-smokers = 5%
How much larger is 13.7% than 5%?
Is the difference between 13.7% and 5% meaningful?
Epidemiology Matters – Chapter 6
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1. Associations
2. Ratio measures
3. Difference measures
4. Population attributable risk proportion
5. Summary
Epidemiology Matters – Chapter 6
11
Ratios
A way to quantify the magnitude of difference
between two measures of disease
Epidemiology Matters – Chapter 6
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Ratios

Risk ratios

95% confidence interval for a risk ratio

Example of 95% confidence intervals for a risk ratio

Central Limit Theory assumptions and confidence
intervals

Rate ratios

Odds ratios

95% confidence interval for the odds ratio
Epidemiology Matters – Chapter 6
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Risk ratio
Numerator
 Conditional risk of disease among exposed
Denominator
 Conditional risk of disease among unexposed
Epidemiology Matters – Chapter 6
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a
b
a+b
c
d
c+d
a+c
b+d
Epidemiology Matters – Chapter 6
a+b+c+d
15
Risk ratio
Numerator
Risk of disease in exposed
Denominator
Risk of disease in unexposed
Epidemiology Matters – Chapter 6
=
a
a+b
c
c+d
16
Disease incidence over time
Non-diseased Diseased
Exposed
Epidemiology Matters – Chapter 6
Unexposed
17
Disease incidence over time
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Disease incidence over time
Epidemiology Matters – Chapter 6
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Disease incidence over time
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2 x 2 table
Epidemiology Matters – Chapter 6
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Risk ratio
Numerator
Risk of disease in exposed
Denominator
Risk of disease in unexposed
Epidemiology Matters – Chapter 6
=
a
a+b
c
c+d
22
2 x 2 table
Risk ratio =
Epidemiology Matters – Chapter 6
8
--10
-------- = 1.6
5
--10
23
2 x 2 table
Risk ratio =
8
--10
-------5
--10
Risk ratio =
a
--a+b
-------c
--c+d
Epidemiology Matters – Chapter 6
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Risk ratio interpretation

Ratios > 1.0 indicate rate is higher among
exposed than unexposed

Ratios = 1.0 indicate no association

Ratios < 1.0 indicate rate is lower among
exposed than unexposed
Epidemiology Matters – Chapter 6
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Risk ratio
95% confidence interval
 Sample, by chance, will often not represent exact
disease and exposure experience of population
 Confidence intervals help to understand variability in
study estimates due to chance in sampling process
Epidemiology Matters – Chapter 6
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Steps: risk ratio
95% confidence interval
1. Take natural log of risk ratio
ln (Risk ratio)
2. Estimate standard error (SE)
Epidemiology Matters – Chapter 6
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Steps: risk ratio
95% confidence interval
3. Estimate upper and lower bounds on log
scale
 95% confidence interval upper bound
ln(Risk ratio) + 1.96(SE[ln(Risk ratio)])
 95% confidence interval lower bound
ln(Risk ratio) - 1.96(SE[ln(Risk ratio)])
Epidemiology Matters – Chapter 6
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Steps: risk ratio
95% confidence interval
4. Exponentiate upper and lower bounds
5. Report and interpret estimate and confidence
interval
Sample: In these data, the exposed
individuals had [risk ratio estimate] times the
risk of the outcome compared with the
unexposed, with a 95% confidence interval
for
the observed risk ratio ranging from
[lower
bound] to [upper bound].
Epidemiology Matters – Chapter 6
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Example: risk ratio
95% confidence interval
 Measure association between family history of
Alzheimer’s disease (AD) and incidence of AD among
those aged >70
 Random sample of 1,000 individuals aged >70, no
symptoms of AD
 Followed for 20 years
 Measure symptoms of AD every year
 No losses to follow-up
Epidemiology Matters – Chapter 6
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Example: risk ratio
95% confidence interval
Risk ratio =
Epidemiology Matters – Chapter 6
a
--a+b
-------c
--c+d
31
Example: risk ratio
95% confidence interval
1. Take natural log of risk ratio
ln (Risk ratio) = ln(1.548) = 0.437
2. Estimate standard error (SE)
Epidemiology Matters – Chapter 6
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Example: risk ratio
95% confidence interval
3. Estimate upper and lower bounds on log
scale
 95% confidence interval upper bound
ln(Risk ratio) + 1.96(SE[ln(Risk ratio)])
0.437 + 1.96(0.1796)
 95% confidence interval lower bound
ln(Risk ratio) - 1.96(SE[ln(Risk ratio)])
0.437 - 1.96(0.1796)
Epidemiology Matters – Chapter 6
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Steps: risk ratio
95% confidence interval
4. Exponentiate upper and lower bounds
5. Report and interpret estimate and confidence interval
Individuals >70 in Farrlandia with a family history
of AD had 1.55 times the risk of developing AD
over 20 years, with a 95% confidence interval for
the risk ratio of 1.09 to 2.20.
Epidemiology Matters – Chapter 6
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Central Limit Theory
 Validity of confidence interval relies on Central
Limit Theory (CLT)
 Remember, assumptions of CLT
 Large sample size
 Each cell in 2 x 2 ≥ 5
Epidemiology Matters – Chapter 6
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Rate ratio
 Risk ratios ideal with little or no loss to follow-up
 Most studies have substantial loss to follow-up
 Rate ratio more accurate representation of
incidence when loss to follow-up an issue
Epidemiology Matters – Chapter 6
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Rate ratio
Epidemiology Matters – Chapter 6
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Rate ratio
Numerator
Rate of disease in exposed
Denominator
Rate of disease in unexposed
=
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Rate ratio interpretation
Similar to risk ratio
 Ratios > 1.0 indicate rate is higher among
exposed than unexposed
 Ratios = 1.0 indicate no association
 Ratios < 1.0 indicate rate is lower among
exposed than unexposed
Epidemiology Matters – Chapter 6
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Steps: rate ratio
95% confidence interval
1. Take natural log of rate ratio
ln (Rate ratio)
2. Estimate standard error (SE)
Epidemiology Matters – Chapter 6
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Steps: rate ratio
95% confidence interval
3. Estimate upper and lower bounds on log
scale
 95% confidence interval upper bound
ln(Rate ratio) + 1.96(SE[ln(Rate ratio)])
 95% confidence interval lower bound
ln(Rate ratio) - 1.96(SE[ln(Rate ratio)])
Epidemiology Matters – Chapter 6
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Steps: rate ratio
95% confidence interval
4. Exponentiate upper and lower bounds
5. Report and interpret estimate and confidence
interval
Sample: In these data, the exposed
individuals had [rate ratio estimate] times
the rate of the outcome compared with the
unexposed, with a 95% confidence interval
for the observed rate ratio ranging from
[lower bound] to [upper bound].
Epidemiology Matters – Chapter 6
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Odds ratio
 Appropriate measure of association for
prospective study is risk or rate ratio
 If sample individuals with and without disease
and retrospectively assess exposure status,
appropriate measure of association is odds
ratio
Epidemiology Matters – Chapter 6
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Example A
Research question: Is smoking cigarettes during pregnancy a
potential cause of offspring attention-deficit hyperactivity
disorder (ADHD)?
Sample:
 Recruit 5,000 women during pregnancy who are smokers,
and 5,000 women during pregnancy who are not smokers
in Farrlandia
 Prospective study
 Assume no loss to follow-up
Measures: Follow offspring at age 10 and determine which
children developed ADHD and which did not
Epidemiology Matters – Chapter 6
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Example A: risk ratio
Risk ratio =
Epidemiology Matters – Chapter 6
a
--a+b
-------c
--c+d
45
Example A: risk ratio
interpretation
From the prospective study, offspring of women who
smoked in pregnancy have 1.5 times the risk of
developing ADHD over 10 years compared to offspring
of women who did not smoke in pregnancy.
Epidemiology Matters – Chapter 6
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Odds ratio
Numerator
 Odds of disease in exposed
Denominator
 Odds of disease in unexposed
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Example A: odds ratio
Epidemiology Matters – Chapter 6
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Example A: odds ratio
 Odds of ADHD among exposed
 Odds of ADHD among unexposed
 Odds ratio
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Example A: odds ratio
interpretation
The odds of developing ADHD in the first 10
years of life among those exposed are 1.53
times the odds of disease in the unexposed.
Epidemiology Matters – Chapter 6
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Example A: odds and risk ratio
 Odds ratio = 1.53
 Risk ratio = 1.5
 Ratios similar when outcome is relatively rare
in the population
Epidemiology Matters – Chapter 6
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Example B: odds ratio
Research question: Is smoking cigarettes during pregnancy a potential
cause of offspring attention-deficit hyperactivity disorder (ADHD)?
Sample:
 500 10-year-old children in Farrlandia who are seeking care
hyperactivity
 For each child we find with ADHD, we select two children of the same
age from the same physician offices who present for routine well visits
(do not have ADHD) – a purposive sample
 Case control study
Measures: Mothers respond to questions, including whether they smoked
cigarettes while they were pregnant
Epidemiology Matters – Chapter 6
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Example B: odds ratio
Epidemiology Matters – Chapter 6
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Example B: odds ratio
 Odds of exposure among those with ADHD:
 Odds of exposure among those without ADHD:
 Odds ratio in the case control study:
Epidemiology Matters – Chapter 6
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Example B: odds ratio
interpretation
 The odds of exposure (mother smoking in pregnancy)
among those with ADHD are 1.53 times higher
among cases than among controls.
Epidemiology Matters – Chapter 6
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Example A and B: odds ratios
 Odds ratio in prospective cohort study = 1.53
 Odds ratio in case control study = 1.48
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Odds ratio: why we use it (1)
 Exposure odds ratio and disease odds ratio are mathematically equal!
 In the prospective study, we estimated the odds of disease among
exposed and odds of disease among unexposed
 In the case control study, we estimated the odds of exposure among the
diseased and the odds of exposure among the nondiseased.
 When we select our cases and controls correctly, we get an unbiased
estimate of the exposure odds even though we estimate the disease odds.
 This odds ratio is approximately equivalent to the risk ratio when the
disease is rare.
Epidemiology Matters – Chapter 6
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Odds ratio: why we use it (2)
 “When we select our cases and controls
correctly”…
– In our example, cases and controls were selected from
the same underlying population base as the sample
from the prospective study.
– When cases and controls are selected from the same
population base, we can get the same estimate of the
association between exposure and disease from the
case control study that we would have gotten from a
prospective study from the same population base.
Epidemiology Matters – Chapter 6
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Steps: odds ratio
95% confidence interval
1. Take natural log of odds ratio
ln (Odds ratio)
2. Estimate standard error (SE)
Epidemiology Matters – Chapter 6
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Steps: odds ratio
95% confidence interval
3. Estimate upper and lower bounds on log
scale
 95% confidence interval upper bound
ln(Odds ratio) + 1.96(SE[ln(Odds ratio)])
 95% confidence interval lower bound
ln(Odds ratio) - 1.96(SE[ln(Odds ratio)])
Epidemiology Matters – Chapter 6
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Steps: odds ratio
95% confidence interval
4. Exponentiate upper and lower bounds
5. Report and interpret estimate and confidence
interval
Sample: In these data, the exposed
individuals had [odds ratio estimate] times
the odds of the outcome compared with the
exposed, with a 95% confidence interval for
the observed odds ratio ranging from [lower
bound] to [upper bound].
Epidemiology Matters – Chapter 6
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Summary: odds ratio
 Cannot estimate the risk of disease directly when we
sample people based on whether they have the disease
or not (case control study)
 Can estimate proportion exposed among diseased and
non-diseased
 Estimate odds ratio for exposure
 Odds ratio for exposure = odds ratio for disease
 If disease is rare in population, the odds ratio
approximates the risk ratio from a prospective study
Epidemiology Matters – Chapter 6
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1. Associations
2. Ratio measures
3. Difference measures
4. Population attributable risk proportion
5. Summary
Epidemiology Matters – Chapter 6
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Risk difference
Difference between two risks =
Interpretation: Excess risk due to the exposure
Example: If the risk of disease is 10 per 100,000 in the
unexposed and 15 per 100,000 in the exposed, then 5 per
100,000 cases is associated with the exposure of interest.
Epidemiology Matters – Chapter 6
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Example: Nutrition and obesity
Research question: Are nutrition classes in middle school associated
with the development of obesity in adolescence?
Sample:
 Middle school A, 400 students, receives health education
(intervention)
 Middle school B, 300 students, in neighboring district, does not
receive health nutrition class
 Purposive
Measures: Schools collect students’ height and weight yearly for 5
years
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Example: risk difference
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Example: risk difference
 Incidence proportion (or risk) of obesity among those who had
nutrition class = 0.175 or 17.5%
 Incidence proportion (or risk) of obesity among those who did not
have nutrition class = 0.33 or 33%
 Risk difference
 Incidence proportion of exposed – incidence proportion of
unexposed
 0.175 – 0.33= - 0.155
 Interpretation: There are approximately 15.5 fewer cases of obesity
during adolescence for every 100 adolescents associated with
nutrition class in middle school
Epidemiology Matters – Chapter 6
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Steps: risk difference
95% confidence interval
1. Estimate standard error (SE)
Epidemiology Matters – Chapter 6
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Steps: risk difference
95% confidence interval
2. Estimate upper and lower bounds
 95% confidence interval upper bound
Risk difference + 1.96(SE[Risk difference])
 95% confidence interval lower bound
Risk difference - 1.96(SE[Risk difference])
Epidemiology Matters – Chapter 6
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Steps: risk difference
95% confidence interval
3. Report and interpret estimate and confidence interval
 Sample Positive: In these data, exposure was associated with an
excess of [risk difference estimate] cases compared with the
unexposed, with a 95% confidence interval for the observed excess
cases ranging from [lower bound] to [upper bound].
 Sample Negative: In these data, exposure was associated with an
[risk difference estimate] fewer cases compared with the
unexposed, with a 95% confidence interval for the observed
decrease in cases ranging from [lower bound] to [upper bound].
Epidemiology Matters – Chapter 6
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Example: risk difference
95% confidence interval
1. Estimate standard error (SE)
Epidemiology Matters – Chapter 6
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Example: risk difference
95% confidence interval
2. Estimate upper and lower bounds
 95% confidence interval upper bound
Risk difference + 1.96(SE[Risk difference])
- 0.155 + 1.96(0.02) = -0.1158
 95% confidence interval lower bound
Risk difference - 1.96(SE[Risk difference])
- 0.155 - 1.96(0.02) = -0.1942
Epidemiology Matters – Chapter 6
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Example: risk difference
95% confidence interval
3. Report and interpret estimate and confidence
interval
 Negative: Middle high nutrition education is
associated with 15.5 fewer cases of obesity
per 100 adolescents over five years, with a
95% confidence interval for the observed
decrease in cases from 11.6 to 19.4 fewer
cases.
Epidemiology Matters – Chapter 6
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Rate difference
 Difference between two rates
 Interpretation: Similar to risk difference; excess rate due to the
exposure
 Example: If the rate of disease is 8 per 100,000 person years in the
exposed and 4 per 100,000 person years in the unexposed, then 4
per 100,000 person-years of exposure is associated with the
exposure of interest
Epidemiology Matters – Chapter 6
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Steps: rate difference
95% confidence interval
1. Estimate standard error (SE)
PY1 = total person time contributed among exposed
PY2 = total person time contributed among the
unexposed
Epidemiology Matters – Chapter 6
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Steps: rate difference
95% confidence interval
2. Estimate upper and lower bounds
 95% confidence interval upper bound
Rate difference + 1.96(SE[Rate difference])
 95% confidence interval lower bound
Rate difference - 1.96(SE[Rate difference])
Epidemiology Matters – Chapter 6
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Steps: rate difference
95% confidence interval
3. Report and interpret estimate and confidence interval
 Sample Positive: In these data, exposure was associated with an
increases of [rate difference estimate] in the rate compared with
the unexposed, with a 95% confidence interval for the observed
excess rate ranging from [lower bound] to [upper bound].
 Sample Negative: In these data, exposure was associated with an
decrease of [rate difference estimate] in the rate compared with
the unexposed, with a 95% confidence interval for the observed
decrease in the rate ranging from [lower bound] to [upper bound].
Epidemiology Matters – Chapter 6
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Risk/rate differences
Risk/rate ratios
When is a ratio measure appropriate versus a
difference measure?
Why would we use one over the other?
Epidemiology Matters – Chapter 6
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Risk/rate differences
Risk/rate ratios
Difference measures (risk / rate difference)
provide a measure of the potential direct public
health benefit of intervention.
Ratio measures (risk / rate / odds ratio) provide
an intuitive summary of the magnitude of
differences in two exposures.
Epidemiology Matters – Chapter 6
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1. Associations
2. Ratio measures
3. Difference measures
4. Population attributable risk proportion
5. Summary
Epidemiology Matters – Chapter 6
80
Population attributable
risk proportion (PARP)
 Population attributable fraction
 Measure of the proportion of the total disease
burden associated with exposure
Epidemiology Matters – Chapter 6
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Example: PARP
 Proportion of people who develop heart
disease among smokers and nonsmokers
 Risk of heart disease in smokers = 13.7%
 Risk of heart disease in nonsmokers = 5%
 PARP would be calculated as:
Epidemiology Matters – Chapter 6
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Example PARP
 Interpretation A: 64% of the heart disease in the
population of Farrlandia is potentially
attributable to smoking.
 Interpretation B: If we were to convince all of the
smokers to quit, we would reduce the incidence
of heart disease by 64%.
 PARP is particularly useful measure in public
health practice
Epidemiology Matters – Chapter 6
83
1. Associations
2. Ratio measures
3. Difference measures
4. Population attributable risk proportion
5. Summary
Epidemiology Matters – Chapter 6
84
Seven steps
1.
Define the population of interest
2.
Conceptualize and create measures of exposures and health
indicators
3.
Take a sample of the population
4.
Estimate measures of association between exposures and health
indicators of interest
5.
Rigorously evaluate whether the association observed suggests a
causal association
6.
Assess the evidence for causes working together
7.
Assess the extent to which the result matters, is externally valid,
to other populations
Epidemiology Matters – Chapter 1
85
epidemiologymatters.org
Epidemiology Matters – Chapter 1
86