Measures of Association & Potential Impact

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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

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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

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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