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Linear models in Epidemiology

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

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  1. Linear modelsinEpidemiology Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/ H.S.

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

  3. Scale H.S.

  4. 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.

  5. Examples for discussion • Smoking and CHD • More CHD among men • RR smoking same for males and females H.S.

  6. Depression and death RR from depression decreases with age RR=2.0 RR=1.5 H.S.

  7. Biologic interaction • Biologic interaction • two component causes acting together in a sufficient cause • preferably additive H.S.

  8. Regression models H.S.

  9. Generalized Linear Models, GLM Linear regression Logistic regression Linear binomial H.S.

  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) H.S.

  11. Distribution and link examples OBS: not for traditional case control data Link: Identity  linear model  additive scale H.S.

  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) H.S.

  13. Smoke and snuff use H.S.

  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 H.S.

  15. Work around problems • Binreg tricks • Restrict range • Use robust linear regression H.S.

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

  17. Restrict range H.S.

  18. Linear robust regression H.S.

  19. Linear robust vs linear binomial H.S.

  20. 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.

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