1. Linear models in Epidemiology
Hein Stigum
Presentation, data and programs at:
Confounding and interaction, Kleinbaum and Kupper, Jægtvolden
Feb-19
H.S.

2. Agenda Concepts Methods Examples Additive and multiplicative scale
Regression models
Ordinary linear regression
Logistic
Linear binomial model
Examples
Feb-19
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3. Scale
Feb-19
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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 RD
Multiplicative scale
Relative increase
Females: 30/20=1.5
Males: /10=2.0
Conclusion:
More increase for males RR
Feb-19
H.S.

5. Examples for discussion
Smoking and CHD
More CHD among men
RR smoking same for males and females
Det er like farlig å røke for menn som for kvinner
Feb-19
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6. Depression and death RR from depression decreases with age RR=2.0
Start with additive description
At what age does depression affect death most?
Feb-19
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7. Biologic interaction Biologic interaction
two component causes acting together in a sufficient cause
preferably additive
Feb-19
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8. Regression models
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9. Generalized Linear Models, GLM
Linear regression
Logistic regression
Less different if low prevalence/weak covariate
Must specify distribution and link function
Linear binomial
Feb-19
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10. GLM: Distribution and link
Distribution family
Given by data
Influence p-values and confidence intervals
Link function
May chose
Determines prediction shape (=link-1)
Determines scale (additive/multiplicative)
Determines association measure (OR, RR, RD)
Feb-19
H.S.

11. Distribution and link examples
OBS: not for traditional case control data
Link: Identity  linear model  additive scale
Feb-19
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12. Being bullied, 3 models
glm bullied Island Norway Finland Denmark sex age, family(binomial) link(logit)
glm bullied Island Norway Finland Denmark sex age, family(binomial) link(log)
glm bullied Island Norway Finland Denmark sex age, family(binomial) link(identity)
After OR/RR, what is the prevalence of bullying?
After RD, what is the risk of being bullied if girls from Finland?
Feb-19
H.S.

13. Smoke and snuff use
Feb-19
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14. The linear binomial model
Pro
Easy to interpret
Absolute risk and risk difference
Absolute risk for any covariate combination
Con
May predict risk outside (0 , 1)
May not converge
In sum
+ Benefit for listener/reader
- Possible problem for analyst
Feb-19
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15. Work around problems Binreg tricks Restrict range
Use robust linear regression
Feb-19
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16. Binreg (Stata) tricks If binreg does not converge, try (one of):
binreg y x1 …, rd ml search difficult
IRLS= interative reweighed least squares
Feb-19
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17. Restrict range
Linear binomial on age years
Feb-19
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18. Linear robust regression
Feb-19
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19. Linear robust vs linear binomial
Linear robust will always give an answer
Feb-19
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20. Summing up Linear models Better description of reality?
+ Easy to interpret
+ Interactions on additive scale
Numerical problems on risk outcome
Better description of reality?
Should de used more!
Feb-19
H.S.