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Linear models in Epidemiology. Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/. Agenda. Concepts Additive and multiplicative scale Methods Regression models Ordinary linear regression Logistic Linear binomial model Examples. Scale. The importance of scale.

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linear models in epidemiology

Linear modelsinEpidemiology

Hein Stigum

Presentation, data and programs at:

http://folk.uio.no/heins/

H.S.

agenda
Agenda
  • Concepts
    • Additive and multiplicative scale
  • Methods
    • Regression models
      • Ordinary linear regression
      • Logistic
      • Linear binomial model
  • Examples

H.S.

scale

Scale

H.S.

the importance of scale
The importance of scale

Additive scale

Absolute increase

Females: 30-20=10

Males: 20-10=10

Conclusion:

Same increase for males and females

RD

Multiplicative scale

Relative increase

Females: 30/20=1.5

Males: 20/10=2.0

Conclusion:

More increase for males

RR

H.S.

examples for discussion
Examples for discussion
  • Smoking and CHD
    • More CHD among men
    • RR smoking same for males and females

H.S.

depression and death
Depression and death

RR from depression decreases with age

RR=2.0

RR=1.5

H.S.

biologic interaction
Biologic interaction
  • Biologic interaction
    • two component causes acting together in a sufficient cause
    • preferably additive

H.S.

generalized linear models glm
Generalized Linear Models, GLM

Linear regression

Logistic regression

Linear binomial

H.S.

glm distribution and link
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)

H.S.

distribution and link examples
Distribution and link examples

OBS: not for traditional case control data

Link: Identity  linear model  additive scale

H.S.

being bullied 3 models
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)

H.S.

the linear binomial model
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

H.S.

work around problems
Work around problems
  • Binreg tricks
  • Restrict range
  • Use robust linear regression

H.S.

binreg stata tricks
Binreg (Stata) tricks
  • If binreg does not converge, try (one of):
    • binreg y x1 …, rd ml search difficult

H.S.

summing up
Summing up
  • Linear models

+ Easy to interpret

+ Interactions on additive scale

    • Numerical problems on risk outcome
  • Better description of reality?
  • Should de used more!

H.S.