Measures of association 2013

Measures of Association

SPH 231

February 7, 2013


• 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


• 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

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


• 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


• 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

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

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

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

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

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

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

Cumulative incidence

• Cumulative incidence in the exposed =

• Cumulative incidence in the unexposed =

a

a b

c

c d

Example

100 900

100 1900

Exposed

Unexposed

1,000

2,000

200 2,800 3,000



Example

• Cumulative incidence in the exposed =

• Cumulative incidence in the unexposed =

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

Risk difference and ratio

• Risk Difference =

• Risk Ratio (Relative Risk, RR) =

a c

a b c d

aa b

cc d

Example

100 900

100 1900

Exposed

Unexposed

1,000

2,000

200 2,800 3,000



Example

• Risk Difference =

• Risk Ratio =

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

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

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

2x2 tables

a b

c d


Exposed

Unexposed

a+b

c+d

a+c a+d a+b+c+d = N


Odds

• Odds of disease in the exposed =

• Odds of disease in the unexposed =

a

b

c

d

Odds Ratio

• Odds Ratio =

= a/b x d/c

= a x d / b x c

a/b

c/d

Example

100 900

100 1900

Exposed

Unexposed

1,000

2,000

200 2,800 3,000



Example

• Odds of disease in the exposed =

• Odds of disease in the unexposed =

1000.11

900

1000.05

1900

Example

• Odds Ratio =

100100 *1900900 2.11

100 100 * 9001900

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

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

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

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

Measures of Association (Effect)

• Prevalence difference• Prevalence ratio• Risk difference• Risk ratio• Incidence rate difference• Incidence rate ratio• Odds ratio

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Measures of association 2013

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