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Measures of Association & Potential Impact
2
Important Jargon
• Exposure (E) an explanatory factor; any potential health determinant; the independent variable
• Disease (D) the response; any health-related outcome; the dependent variable
• Measure of association (syn. measure of effect) a statistic that quantifies the relationship between an exposure and a disease
• Measure of potential impact a statistic that quantifies the potential impact of removing a hazardous exposure
3
Arithmetic (αριθμός) Comparisons
• Measures of association are mathematical comparisons
• Mathematic comparisons can be done in absolute terms or relative terms
• Let us start with this ridiculously simple example:
• I have $2 • You have $1
"For the things of this world cannot be made known without a knowledge of mathematics."- Roger Bacon
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Absolute Comparison
• In absolute terms, I have $2 – $1 = $1 more than you
• Note: the absolute comparison was made with subtraction
It is as simple as that…
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Relative Comparison
• Recall that I have $2 and you have $1.
• In relative terms, I have $2 ÷ $1 = 2, or
“twice as much as you”• Note: relative comparison
was made by division
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• Suppose, I am exposed to a risk factor and have a 2% risk of disease.
• You are not exposed and you have a 1% risk of the disease.
Applied to Risks
• Of course we are assuming we are the same in every way except for this risk factor.
• In absolute terms, I have 2% – 1% = 1% greater risk of the disease
• This is the risk difference
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• In relative terms I have 2% ÷ 1% = 2, or twice the risk
• This is the relative risk associated with the exposure
Applied to Risks
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Terminology
For simplicity sake, the terms “risk” and “rate” will be applied to all incidence and prevalence measures.
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Risk Difference
Risk Difference (RD) absolute effect associated with exposure
01 RRRD
where R1 ≡ risk in the exposed group R0 ≡ risk in the non-exposed group
Interpretation: Interpretation: ExcessExcess risk in absolute risk in absolute termsterms
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Relative Risk
Relative Risk (RR) relative effect associated with exposure or the “risk ratio”
0
1
RRRR
where R1 ≡ risk in the exposed group R0 ≡ risk in the non-exposed groupInterpretation: excess risk in relative Interpretation: excess risk in relative
termsterms..
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Example Fitness & Mortality (Blair et al., 1995)
• Is improved fitness associated with decreased mortality?
• Exposure ≡ improved fitness (1 = yes, 0 = no)
• Disease ≡ death(1 = yes, 0 = no)
• Mortality rate, group 1:R1 = 67.7 per 100,000 p-yrs
• Mortality rate, group 0:R0 = 122.0 per 100,000 p-yrs
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ExampleRisk Difference
01 RRRD
The effect of the exposure (improved fitness) is to decrease mortality by 54.4 per 100,000 person-years
What is the effect of improved fitness on mortality in absolute terms?
yrs-p 100,0000.122
yrs-p 100,0007.67
yrs-p 100,0004.54
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ExampleRelative Risk
0
1
RRRR
What is the effect of improved fitness on mortality in relative terms?
55.0yrs-p 100,000per 0.122yrs-p 100,000per 7.67
The effect of the exposure is to cut the risk almost in half.
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Designation of Exposure
• Switching the designmation of “exposure” does not materially affect interpretations
• For example, if we had let “exposure” ≡ failure to improve fitness
• RR = R1 / R0 = 122.0 / 67.7 = 1.80 (1.8 times the risk in the
exposed group (“almost double”)
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2-by-2 Table Format
Disease + Disease − TotalExposure + A1 B1 N1
Exposure – A0 B0 N0
Total M1 M0 N
For person-time data: let N1 ≡ person-time in group 1 and N0 ≡ person-time in group 0, and ignore cells B1 and B0
1
11 N
AR 0
00 N
AR
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Fitness Data, table format
Fitness Improved? Died Person-years
Yes 25 -- 4054No 32 -- 2937
67.61000,104054
25
1
11
NA
R
95.108000,10293732
0
00
NA
R
Rates per 10,000 person-years
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Food borne Outbreak Example
Disease + Disease − TotalExposure + 63 25 88Exposure –
1 6 7
Total 64 31 95
7159.08863
1
11 NAR 1429.0
71
0
00 NAR
Exposure ≡ eating a particular dishDisease ≡ gastroenteritis
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Food borne Outbreak Data
718863
0
1 RRRR 1429.0
7159.0 01.5
Exposed group had 5 times the risk
Disease + Disease − TotalExposure + 63 25 88Exposure – 1 6 7Total 64 31 95
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What do you do when you have multiple levels of exposure?
Compare rates to least exposed “reference” group
LungCA Rate (per 100,000 person-years)
RR
Non-smoker (0) 10 1.0 (ref.)Light smoker (1) 52 5.2Mod. smoker (2) 106 10.6Heavy sm. (3) 224 22.4
2.50125
0
11
RR
RR 6.1001
106
0
22 RRRR
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The Odds Ratio
• When the disease is rare, interpret the same way you interpret a RR
• e.g. an OR of 1 means the risks are the same in the exposed and nonexposed groups
D+ D− TotalE+ A1 B1 N1
E− A0 B0 N0
Total M1 M0 N
01
01
00
11
ABBA
BABA
OR
“Cross-product ratio”
Similar to a RR, but based on odds rather than risks
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Odds Ratio, ExampleMilunsky et al, 1989, Table 4NTD = Neural Tube Defect
NTD+ NTD−Folic Acid+ 10 10,703Folic Acid− 39 11,905
01
01
ABBAOR
Exposed group had 0.29 times (about a quarter) the risk of the nonexposed group
39703,10905,1110
29.0
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Measures of Potential Impact
• These measures predicted impact of removing a hazardous exposure from the population
• Two types– Attributable fraction in
exposed cases– Attributable fraction in
the population as a whole
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Attributable Fraction Exposed Cases (AFe)
RRRRAFe
1 :formula Equivalent
1
01 :formula alDefinitionRRRAFe
Proportion of exposed cases averted with elimination of the exposure
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Example: AFe
RR of lung CA associated with moderate smoking is approx. 10.4. Therefore:
RRRRAFe
1
Interpretation: 90.4% of lung cancer in moderate smokers would be averted if they had not smoked.
904.4.10
14.10
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Attributable Fraction, Population (AFp)
population nonexposedin rate rate overall
where
:formula alDefinition
0
0
RR
RRRAFp
Proportion of all cases averted with elimination of exposure from the population
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AFp equivalent formulas
populationin exposure of prevalence where
)1(1
)1(
e
e
ep
pRRpRRp
AF
exposed are that cases of proportion where
c
cep
p
pAFAF
28
AFp for Cancer Mortality, Selected Exposures
Exposure Doll & Peto, 1981 Miller, 1992Tobacco 30% 29%Dietary 35% 20%Occupational 4% 9%Repro/Sexual 7% 7%Sun/Radiation 3% 1%Alcohol 3% 6%Pollution 2% -Medication 1% 2%Infection 10% -
29Thank you