Linear models in Epidemiology

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Linear models in Epidemiology - PowerPoint PPT Presentation

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 modelsinEpidemiology

Hein Stigum

Presentation, data and programs at:

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

H.S.

Agenda
• Concepts
• Methods
• Regression models
• Ordinary linear regression
• Logistic
• Linear binomial model
• Examples

H.S.

Scale

H.S.

The importance of 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
• Smoking and CHD
• More CHD among men
• RR smoking same for males and females

H.S.

Depression and death

RR from depression decreases with age

RR=2.0

RR=1.5

H.S.

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

H.S.

Regression models

H.S.

Generalized Linear Models, GLM

Linear regression

Logistic regression

Linear binomial

H.S.

• Distribution family
• Given by data
• Influence p-values and confidence intervals
• May chose
• Determines association measure (OR, RR, RD)

H.S.

OBS: not for traditional case control data

H.S.

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
• 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

- Possible problem for analyst

H.S.

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

H.S.

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

H.S.

Summing up
• Linear models

+ Easy to interpret