epidemiology kept simple chapter 8 measures of association & potential impact
TRANSCRIPT
Epidemiology Kept Simple
Chapter 8
Measures of Association & Potential Impact
Gerstman Chapter 8 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
Gerstman Chapter 8 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
Gerstman Chapter 8 4
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…
Gerstman Chapter 8 5
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
Gerstman Chapter 8 6
• 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
Gerstman Chapter 8 7
• In relative terms I have
2% ÷ 1% = 2, or twice the risk
• This is the relative risk associated with the exposure
Applied to Risks
Gerstman Chapter 8 8
Terminology
For simplicity sake, the terms “risk” and “rate” will be applied to all incidence and prevalence measures.
Gerstman Chapter 8 9
Risk DifferenceRisk Difference (RD) Risk Difference (RD) absolute absolute effect associated with exposureeffect associated with exposure
01 RRRD
where where
RR11 ≡ risk in the exposed group ≡ risk in the exposed group RR00 ≡≡ risk in the non-exposed grouprisk in the non-exposed group
Interpretation: Interpretation: ExcessExcess risk in absolute risk in absolute termsterms
Gerstman Chapter 8 10
Relative RiskRelative Risk (RR) Relative Risk (RR) relative effect relative effect associated with exposure or the “risk associated with exposure or the “risk ratioratio””
0
1
R
RRR
where where
RR11 ≡ risk in the exposed group ≡ risk in the exposed group RR00 ≡≡ risk in the non-exposed grouprisk in the non-exposed group
Interpretation: excess risk in relative Interpretation: excess risk in relative termsterms..
Gerstman Chapter 8 11
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
Gerstman Chapter 8 12
Example
Risk 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 100,000
0.122
yrs-p 100,000
7.67
yrs-p 100,000
4.54
Gerstman Chapter 8 13
Example
Relative Risk
0
1
R
RRR
What is the effect of improved fitness on mortality in relative terms?
55.0yrs-p 100,000per 0.122
yrs-p 100,000per 7.67
The effect of the exposure is to cut the risk almost in half.
Gerstman Chapter 8 14
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”)
Gerstman Chapter 8 15
2-by-2 Table FormatDisease + Disease − Total
Exposure + 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
Gerstman Chapter 8 16
Fitness Data, table formatFitness Improved?
Died Person-years
Yes 25 -- 4054
No 32 -- 2937
67.61000,104054
25
1
11
N
AR
95.108000,102937
32
0
00
N
AR
Rates per 10,000 person-years
Gerstman Chapter 8 17
Food borne Outbreak Example
Disease + Disease − Total
Exposure + 63 25 88
Exposure –
1 6 7
Total 64 31 95
7159.088
63
1
11 N
AR 1429.0
7
1
0
00 N
AR
Exposure ≡ eating a particular dishDisease ≡ gastroenteritis
Gerstman Chapter 8 18
Food borne Outbreak Data
71
8863
0
1 R
RRR
1429.0
7159.0 01.5
Exposed group had 5 times the risk
Disease + Disease − Total
Exposure + 63 25 88
Exposure – 1 6 7
Total 64 31 95
Gerstman Chapter 8 20
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 5.2
Mod. smoker (2) 106 10.6
Heavy sm. (3) 224 22.4
2.501
25
0
11
R
RRR 6.10
01
106
0
22 R
RRR
Gerstman Chapter 8 21
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− Total
E+ A1 B1 N1
E− A0 B0 N0
Total M1 M0 N
01
01
00
11
AB
BA
BA
BAOR
“Cross-product ratio”
Similar to a RR, but based on odds rather than risks
Gerstman Chapter 8 22
Odds Ratio, ExampleMilunsky et al, 1989, Table 4
NTD = Neural Tube DefectNTD+ NTD−
Folic Acid+ 10 10,703
Folic Acid− 39 11,905
01
01
AB
BAOR
Exposed group had 0.29 times (about a quarter) the risk of the nonexposed group
39703,10
905,1110
29.0
Gerstman Chapter 8 23
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
Gerstman Chapter 8 24
Attributable Fraction Exposed Cases (AFe)
RR
RRAFe
1 :formula Equivalent
1
01 :formula alDefinitionR
RRAFe
Proportion of exposed cases averted with elimination of the exposure
Gerstman Chapter 8 25
Example: AFe
RR of lung CA associated with moderate smoking is approx. 10.4. Therefore:
RR
RRAFe
1
Interpretation: 90.4% of lung cancer in moderate smokers would be averted if they had not smoked.
904.4.10
14.10
Gerstman Chapter 8 26
Attributable Fraction, Population (AFp)
population nonexposedin rate
rate overall
where
:formula alDefinition
0
0
R
R
R
RRAFp
Proportion of all cases averted with elimination of exposure from the population
Gerstman Chapter 8 27
AFp equivalent formulas
populationin exposure of prevalence where
)1(1
)1(
e
e
ep
p
RRp
RRpAF
exposed are that cases of proportion where
c
cep
p
pAFAF
Gerstman Chapter 8 28
AFp for Cancer Mortality, Selected Exposures
Exposure Doll & Peto, 1981 Miller, 1992
Tobacco 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% -