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Scale, Causal Pies and Interaction 1 h

Scale, Causal Pies and Interaction 1 h. Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/. Agenda. Concepts Scale Causal Pies Interaction and Effect Modification Methods Regression and Scale Regression and Interaction. Scale. The importance of scale.

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Scale, Causal Pies and Interaction 1 h

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  1. Scale, Causal Piesand Interaction1h Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/ H.S.

  2. Agenda • Concepts • Scale • Causal Pies • Interaction and Effect Modification • Methods • Regression and Scale • Regression and Interaction H.S.

  3. Scale H.S.

  4. The importance of scale Additive scale Absoluteincrease Females: 30-20=10 Males: 20-10=10 Conclusion: Same increase for males and females y, RD Multiplicativescale Relative increase Females: 30/20=1.5 Males: 20/10=2.0 Conclusion: More increase for males RR (OR, HRR) H.S.

  5. Obesity and death RD: The effect of obesity on death increases with age! RR: The effect of obesity on death decreases with age! RR=2.0 RR=1.5 Obese Thin as a nail H.S.

  6. Lessons learned • Scale is important • Use both additive and multiplicative • When reporting RR or RD or similar, always report reference risk H.S.

  7. Causalpies H.S.

  8. Causal pies • Sufficient cause: • 1 to 3 (AIDS) • Component cause: • A to F (A=HIV, B=sex, E=injection) • Necessary cause: • A(HIV) • Interaction • A and B (smoke+radoncancer) • Induction time: • time to accumulate A to C (accumulate mutations cancer) • Attributable fraction (AF) • Sum>100% (remove E:33%, remove B:66%, Remove A:100%) Three causes for a disease H.S.

  9. Pies and Riskof lung cancer N=1000 Cases Risk 10 1% 70 7% 20 2% Observable? Risk Difference (RD) 30 3% H.S.

  10. Interaction,Effect modification H.S.

  11. Definitions of interaction • No additive interaction: • =0 • RDAB=RDA+RDB • RDA is independent of B (and vice versa) • The 3 definitions are identical • Risk factors A and B H.S.

  12. Comparing definitions of no additive interaction risks U S R What happens if radon-smoke interaction in not 0? So far so good! H.S.

  13. Interaction and scale 1% 7% 2% 0% Lesson learned: No additive interaction multiplicative interaction Interaction is scale dependent H.S.

  14. Interaction versus Effect Modification Interaction Effect Modification Variables (No actions) Sex Age The effect of a risk factor modified by a variable The effect of smoking on heart disease is different for men and women • Risk factors (Actions) • Smoking • Asbestos • Two risk factors acting together smoking and asbestos may act together to produce lung cancer The two definitions are mathematically equivalent, only the type of variable differs Both concepts are scale dependent! H.S.

  15. Regression AND Interaction and scale H.S.

  16. Regression and scale • Linear models (linear-regression, -risk, -survival): additive • No interaction if: RDAB=RDA+RDBor RDA is independent of B • “Other” models (logistic, Poisson, log-risk, Cox): multiplicative • No interaction if: RRAB=RRA*RRBor RRA is independent of B H.S.

  17. Estimating interaction in regression Linear model Observable? U A B U A U B Effects is independent of B if b3=0 Test Interaction if b30 ConfidenceInterval (easy or technical) H.S.

  18. Regression example 1% 7% 2% 3% Linear risk model (all variables=0/1) 0.07 if radon=0 0.10 if radon=1 • Stata: margins, dydx(smoke)at(radon=(0 1)) H.S.

  19. Stratify or use interaction term Alt 2: Model with interaction Technical (ci) Test for interaction Efficient (7 estimates) • Alt 1 : Two models (stratify on radon) • Easy • No test for interaction • Inefficient (12 estimates) Mar-14 H.S. 19

  20. Summing up 1 • Scale (additive or multiplicative) is important • Causal Pies (SCC) • Multifactorial, Additive H.S.

  21. Summing up 2 • Interaction/ effect modification • Same concept (action*action / action*immutable) • Scale dependent • Regression • Linear models are additive • “All” other models are multiplicative • In both: estimate interaction as product term H.S.

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