Linear models in Epidemiology

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Presentation transcript:

Linear models in Epidemiology Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/ Confounding and interaction, Kleinbaum and Kupper, Jægtvolden Feb-19 H.S.

Agenda Concepts Methods Examples Additive and multiplicative scale Regression models Ordinary linear regression Logistic Linear binomial model Examples Feb-19 H.S.

Scale Feb-19 H.S.

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 Feb-19 H.S.

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 H.S.

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 H.S.

Biologic interaction Biologic interaction two component causes acting together in a sufficient cause preferably additive Feb-19 H.S.

Regression models Feb-19 H.S.

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 H.S.

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.

Distribution and link examples OBS: not for traditional case control data Link: Identity  linear model  additive scale Feb-19 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) 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.

Smoke and snuff use Feb-19 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 + Benefit for listener/reader - Possible problem for analyst Feb-19 H.S.

Work around problems Binreg tricks Restrict range Use robust linear regression Feb-19 H.S.

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 H.S.

Restrict range Linear binomial on age 20-60 years Feb-19 H.S.

Linear robust regression Feb-19 H.S.

Linear robust vs linear binomial Linear robust will always give an answer Feb-19 H.S.

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.