1. Scale, Causal Pies and Interaction 1h
Hein Stigum
Presentation, data and programs at:
Litt over en time, kutte og rydde noe
Jan-19
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2. Agenda Concepts Methods Scale Causal Pies
Interaction and Effect Modification
Methods
Regression and Scale
Regression and Interaction
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3. Scale
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4. The importance of scale
Additive scale
Absolute increase
Females: 30-20=10
Males: =10
Conclusion:
Same increase for males and females
y, RD
Multiplicative scale
Relative increase
Females: 30/20=1.5
Males: /10=2.0
Conclusion:
More increase for males
RR (OR, HRR)
Jan-19
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5. Obesity and death
RD: The effect of obesity on death increases with age!
RR: The effect of obesity on death decreases with age!
RR=2.0
RR=1.5
Obese
Start with additive description
At what age does depression affect death most?
Thin as a nail
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6. Lessons learned Scale is important
Use both additive and multiplicative
When reporting RR or RD or similar, always report reference risk
Jan-19
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7. Causal pies
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8. Causal pies Sufficient cause: Three causes for a disease
1 to 3 (AIDS)
Component cause:
A to F (A=HIV, B=sex, E=injection)
Necessary cause:
A (HIV)
Interaction
A and B (smoke+radoncancer)
Induction time:
time to accumulate A to C (accumulate mutations cancer)
Attributable fraction (AF)
Sum>100% (remove E:33%, remove B:66%, Remove A:100%)
Three causes for a disease
Component: A, B, …
Sufficient: 1, 2 and 3
Necessary: A, HIV necessary for AIDS
Interaction: A and B, plus A and F but only if E is present. Alcohol, tobacco and larynx cancer
Induction time= accumulation of component causes
Sum AF is unbounded, remove E:33%, remove B:66%, Remove A:100%
Jan-19
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9. Pies and Risk of lung cancer
Cases
Risk 10 1% 70 7% 20 2%
Observable?
Risk Difference (RD) 30 3%
Jan-19
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10. Interaction, Effect modification
Jan-19
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11. Definitions of interaction
Risk factors A and B
No additive interaction: =0
RDAB=RDA+RDB
RDA is independent of B (and vice versa)
The 3 definitions are identical
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12. Comparing definitions of no additive interaction
risks U S R
What happens if radon-smoke interaction in not 0?
So far so good!
Jan-19
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13. Interaction and scale Lesson learned:1% 7% 2% 0%
Lesson learned:
No additive interaction  multiplicative interaction
Interaction is scale dependent
Jan-19
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14. Interaction versus Effect Modification
Risk factors (Actions)
Smoking
Asbestos
Two risk factors acting together
smoking and asbestos may act together to produce lung cancer
Variables (No actions)
Sex
Age
The effect of a risk factor modified by a variable
The effect of smoking on heart disease is different for men and women
The two definitions are mathematically equivalent,
only the type of variable differs
Both concepts are scale dependent!
Jan-19
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15. Regression AND Interaction and scale
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16. Regression and scale
Linear models (linear-regression, -risk, -survival): additive
No interaction if:
RDAB=RDA+RDB or RDA is independent of B
“Other” models (logistic, Poisson, log-risk, Cox): multiplicative
RRAB=RRA*RRB or RRA is independent of B
Jan-19
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17. Estimating interaction in regression
Linear model
U A
U B
U A B
Observable?
Effects
is independent of B if b3=0
Test
Interaction if b30
ConfidenceInterval (easy or technical)
Jan-19
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18. Regression example Linear risk model (all variables=0/1)1% 7% 2% 3%
Linear risk model (all variables=0/1)
𝐿𝑢𝑛𝑔𝐶𝑎𝑛𝑐𝑒𝑟= 𝑏 0 + 𝑏 1 𝑠𝑚𝑜𝑘𝑒+ 𝑏 2 𝑟𝑎𝑑𝑜𝑛+ 𝑏 3 𝑠𝑚𝑜𝑘𝑒∙𝑟𝑎𝑑𝑜𝑛
𝐿𝑢𝑛𝑔𝐶𝑎𝑛𝑐𝑒𝑟= 𝑠𝑚𝑜𝑘𝑒+0.02𝑟𝑎𝑑𝑜𝑛+0.03𝑠𝑚𝑜𝑘𝑒∙𝑟𝑎𝑑𝑜𝑛
0.07 if radon=0
0.10 if radon=1
Stata: margins, dydx(smoke) at(radon=(0 1))
Jan-19
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19. Stratify or use interaction term
Alt 1 : Two models (stratify on radon)
Easy
No test for interaction
Inefficient (12 estimates)
Alt 2: Model with interaction
Technical (ci)
Test for interaction
Efficient (7 estimates)
p=number of covariates
Estimates=2(p+1) versus p+2
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20. Summing up 1 Scale (additive or multiplicative) is important
Causal Pies (SCC)
Multifactorial, Additive
Jan-19
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21. Summing up 2 Interaction/ effect modification Regression
Same concept (action*action / action*immutable)
Scale dependent
Regression
Linear models are additive
“All” other models are multiplicative
In both: estimate interaction as product term
Jan-19
H.S.