Scale, Causal Pies and Interaction 1h

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Presentation transcript:

Scale, Causal Pies and Interaction 1h Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/ Litt over en time, kutte og rydde noe Jan-19 H.S.

Agenda Concepts Methods Scale Causal Pies Interaction and Effect Modification Methods Regression and Scale Regression and Interaction Jan-19 H.S.

Scale Jan-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 y, RD Multiplicative scale Relative increase Females: 30/20=1.5 Males: 20/10=2.0 Conclusion: More increase for males RR (OR, HRR) Jan-19 H.S.

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 Start with additive description At what age does depression affect death most? Thin as a nail Jan-19 H.S.

Lessons learned Scale is important Use both additive and multiplicative When reporting RR or RD or similar, always report reference risk Jan-19 H.S.

Causal pies Jan-19 H.S.

Causal pies Sufficient cause: Three causes for a disease 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 Component: A, B, … Sufficient: 1, 2 and 3 Necessary: A, HIV necessary for AIDS Interaction: A and B, plus A and F but only if E is present. Alcohol, tobacco and larynx cancer Induction time= accumulation of component causes Sum AF is unbounded, remove E:33%, remove B:66%, Remove A:100% Jan-19 H.S.

Pies and Risk of lung cancer Cases Risk 10 1% 70 7% 20 2% Observable? Risk Difference (RD) 30 3% Jan-19 H.S.

Interaction, Effect modification Jan-19 H.S.

Definitions of interaction Risk factors A and B No additive interaction: =0 RDAB=RDA+RDB RDA is independent of B (and vice versa) The 3 definitions are identical Jan-19 H.S.

Comparing definitions of no additive interaction risks U S R What happens if radon-smoke interaction in not 0? So far so good! Jan-19 H.S.

Interaction and scale Lesson learned: 1% 7% 2% 0% Lesson learned: No additive interaction  multiplicative interaction Interaction is scale dependent Jan-19 H.S.

Interaction versus Effect Modification Risk factors (Actions) Smoking Asbestos Two risk factors acting together smoking and asbestos may act together to produce lung cancer 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 The two definitions are mathematically equivalent, only the type of variable differs Both concepts are scale dependent! Jan-19 H.S.

Regression AND Interaction and scale Jan-19 H.S.

Regression and scale Linear models (linear-regression, -risk, -survival): additive No interaction if: RDAB=RDA+RDB or RDA is independent of B “Other” models (logistic, Poisson, log-risk, Cox): multiplicative RRAB=RRA*RRB or RRA is independent of B Jan-19 H.S.

Estimating interaction in regression Linear model U A U B U A B Observable? Effects is independent of B if b3=0 Test Interaction if b30 ConfidenceInterval (easy or technical) Jan-19 H.S.

Regression example Linear risk model (all variables=0/1) 1% 7% 2% 3% Linear risk model (all variables=0/1) 𝐿𝑢𝑛𝑔𝐶𝑎𝑛𝑐𝑒𝑟= 𝑏 0 + 𝑏 1 𝑠𝑚𝑜𝑘𝑒+ 𝑏 2 𝑟𝑎𝑑𝑜𝑛+ 𝑏 3 𝑠𝑚𝑜𝑘𝑒∙𝑟𝑎𝑑𝑜𝑛 𝐿𝑢𝑛𝑔𝐶𝑎𝑛𝑐𝑒𝑟=0.01+0.07𝑠𝑚𝑜𝑘𝑒+0.02𝑟𝑎𝑑𝑜𝑛+0.03𝑠𝑚𝑜𝑘𝑒∙𝑟𝑎𝑑𝑜𝑛 0.07 if radon=0 0.10 if radon=1 Stata: margins, dydx(smoke) at(radon=(0 1)) Jan-19 H.S.

Stratify or use interaction term Alt 1 : Two models (stratify on radon) Easy No test for interaction Inefficient (12 estimates) Alt 2: Model with interaction Technical (ci) Test for interaction Efficient (7 estimates) p=number of covariates Estimates=2(p+1) versus p+2 Jan-19 H.S. 19 19

Summing up 1 Scale (additive or multiplicative) is important Causal Pies (SCC) Multifactorial, Additive Jan-19 H.S.

Summing up 2 Interaction/ effect modification Regression 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 Jan-19 H.S.