measures of association 2013
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Measures of Association
SPH 231
February 7, 2013
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Measures of Association
• Comparing the frequency of disease between exposed and unexposed
• Measures of association (effect)• There are two types of measures of
association– Absolute measures– Relative measures
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Measures of Association
• Show the strength of the relationship between an exposure and outcome
• Indicate how more or less likely a group is to develop disease as compared to another group
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Absolute Measures of Association
• Based on DIFFERENCE between two measures of disease frequency
• May range from -1 to 1– If value of difference measure=0 then no
difference between exposed and unexposed• Difference measures are useful for
assessing the public health impact of an exposure
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Absolute Measures of Association
• Incidence – Risk difference = Cumulative Incidence in
Exposure – Cumulative Incidence in Unexposed
– Rate Difference = Incidence Rate in Exposed – Incidence Rate in Unexposed
• Prevalence– Prevalence Difference = Prevalence in
Exposed – Prevalence in Unexposed
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Absolute Measures of Association
• Incidence Differences– Both differences measure the excess number
of NEW cases among the exposed compared to the unexposed
• Prevalence Differences– Measures excess number of EXISTING cases
among exposed compared to unexposed at a particular point in time
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Relative Measures of Association
• The RATIO of two disease frequencies– Risk Ratio (aka Cumulative Incidence Ratio,
aka Relative Risk)– Rate Ratio – Prevalence Ratio
• Relative measures may be interpreted as the excess Risk, Rate, or Prevalence in exposed relative to the unexposed
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Relative Measures of Association
• Relative measures may range from 0 to infinity
• Relative measures assess the strength of association between exposure and disease and are useful in identifying risk factors
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Data Layouts• Typically, epidemiologists organize study
data as a 2x2 table– Column = Disease or Outcome status (Yes or
No)– Row = Exposure Status (Yes or No)
• Study participants assigned to one of the four cells according to their individual exposure and disease state
• Results used to calculate and compare frequency of disease according to exposure
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2 x 2 TablesUsed to summarize counts of disease and exposure to calculate measures of association
Outcome
Exposure Yes No Total
Yes a b a + b
No c d c + d
Total a + c b + d a + b + c + d
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2 x 2 Tables
a = number exposed with outcomeb = number exposed without outcomec = number not exposed with outcomed = number not exposed without outcome
******************************a + b = total number exposedc + d = total number not exposeda + c = total number with outcomeb + d = total number without outcomea + b + c + d = total study population (N)
a b
c d
OutcomeYes No
ExposureYes
No
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Example
100 900
100 1900
Exposed
Unexposed
1,000
2,000
200 2,800 3,000
Diseased Non-diseased
* Assume incidence data over 1 year
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Cumulative incidence
• Cumulative incidence in the exposed =
• Cumulative incidence in the unexposed =
a
a b
c
c d
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Example
100 900
100 1900
Exposed
Unexposed
1,000
2,000
200 2,800 3,000
Diseased Non-diseased
* Assume incidence data over 1 year
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Example
• Cumulative incidence in the exposed =
• Cumulative incidence in the unexposed =
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Interpretation
• Cumulative incidence in the exposed:
-10% of the exposed group developed the disease in the study period
• Cumulative incidence in the unexposed:
-5% of the unexposed group developed the disease in the study period
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Risk difference and ratio
• Risk Difference =
• Risk Ratio (Relative Risk, RR) =
a c
a b c d
aa b
cc d
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Example
100 900
100 1900
Exposed
Unexposed
1,000
2,000
200 2,800 3,000
Diseased Non-diseased
* Assume incidence data over 1 year
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Example
• Risk Difference =
• Risk Ratio =
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Interpretation
• Risk Difference:In a population of 100 exposed people, there would be 5 additional cases of disease than what you would observe if exposure was absent in the study period
• Risk Ratio:The risk of developing the disease in the exposed group is two times the risk of developing the disease in the unexposed group in the study period
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Relative Risk Example
Escherichia coli?
Pink hamburger Yes No
Total
Yes 23 10 33
No 7 60 67
Total 30 70 100
a / (a + b) 23 / 33RR = = = 6.67
c / (c + d) 7 / 67
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Odds Ratio• Used with case-control studies
• Population at risk is not known (selected participants by disease status)
• Calculate odds instead of risks a x d
OR = b x c
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2x2 tables
a b
c d
Diseased Non-diseased
Exposed
Unexposed
a+b
c+d
a+c a+d a+b+c+d = N
* Assume incidence data over 1 year
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Odds
• Odds of disease in the exposed =
• Odds of disease in the unexposed =
a
b
c
d
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Odds Ratio
• Odds Ratio =
= a/b x d/c
= a x d / b x c
a/b
c/d
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Example
100 900
100 1900
Exposed
Unexposed
1,000
2,000
200 2,800 3,000
Diseased Non-diseased
* Assume incidence data over 1 year
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Example
• Odds of disease in the exposed =
• Odds of disease in the unexposed =
1000.11
900
1000.05
1900
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Example
• Odds Ratio =
100100 *1900900 2.11
100 100 * 9001900
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Interpretation
• Odds Ratio:
(OR as an estimate of RR)
The risk of developing the disease in the exposed group is 2.11 times the risk of developing the disease in the unexposed group during the study period
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Odds Ratio Example
Increased Blood Pressure
Caffeine intake “high”? Yes No
Total
Yes 130 115 245
No 120 135 255
Total 250 250 500
a x d 130 x 135OR = = = 1.27
b x c 115 x 120
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Interpreting Risk and Odds Ratios
RR or OR < 1
• Exposure associated with decreased risk of outcome
RR or OR = 1
• No association between exposure and outcome
RR or OR> 1
• Exposure associated with increased risk of outcome
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Interpretation• RR = 5
– People who were exposed are 5 times more likely to have the outcome when compared with persons who were not exposed
• RR = 0.5– People who were exposed are half as likely to have
the outcome when compared with persons who were not exposed
• RR = 1– People who were exposed are no more or less likely
to have the outcome when compared to persons who were not exposed
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Measures of Association (Effect)
• Prevalence difference• Prevalence ratio• Risk difference• Risk ratio• Incidence rate difference• Incidence rate ratio• Odds ratio
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