Interaction

1
Interaction

• Hein Stigum
• Presentation, data and programs at
• http//folk.uio.no/heins/

2
Endringer

• Ta ut scale dersom det er dekket i del 1
• Røyk-snus som interaksjonseksempel? Eller et mere
  biologisk preget

3
Agenda

• Concepts
• Additive and multiplicative scale
• Additive and multiplicative regression models
• Biologic interaction
• Statistical interaction
• Methods
• 2 by 2 table
• Interaction in regression
• Binary outcome, additive interaction

4
True or false?

• No interaction in an additive model
• implies
• no interaction in a multiplicative model

5
The importance of scale
Additive scale Absolute increase Females
30-2010 Males 20-1010 Conclusion Same
increase for males and females RD
Multiplicative scale Relative increase Females
30/201.5 Males 20/102.0 Conclusion More
increase for males RR
6
Linear vs log-link models

• Linear

• Log-link models

Linearadditive
Log-linkmultiplicative
7
Biologic Interaction
Counterfactual One cohort under 4
exposure situations

• Cases caused by U
• Cases caused by A (and U)
• Cases caused by B (and U)
• Extra cases caused by A,B interaction.

8
Biologic Interaction 2a
Cases Risk

• CU
• CA
• CB
• CAB

RU CU /N RA (
CA CU )/N RB (
CB CU )/N RAB (CAB CA CB CU )/N
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Biologic Interaction 2b
Cases Risk

• 10
• 20
• 30
• 40

Ru 10 /1000 RA (
2010 )/1000 RB ( 30 10
)/1000 RAB (40302010 )/1000
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Biologic Interaction 3

• Interaction risk
• RAB-RA-RBRU
• If interaction risk0
• ? RAB RA RB-RU
• ? RAB -RU RA-RU RB-RU
• ? RDAB RDA RDB

Interaction if RDAB?RDARDB
11
Biologic vs statistical interaction

• Biologic interaction
• two component causes acting together in a
  sufficient cause
• additive scale
• Statistical interaction
• deviation from a model
• additive RD11 ? RD10 RD01
• multiplicative RR11 ? RR10 ? RR01

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Examples
RD - RR deviation
RD deviation RR -
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Example for discussion

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

14
Depression and death

• RR from depression decreases with age

RR2.0
RR1.5
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Examples for discussion

• Recurrence risk of birth defects
• Recurrence risk (RR2.0) independent of
  consanguinity
• Consanguinity a risk factor
• Obesity and death
• RR from obesity decreases with age

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Equvivalent statements of no additive interaction
1)
Effect ABeffect Aeffect B
2)
Excess risk ABe.r. Ae.r. B
3)
Effect of A is independent of B
4)
Effect of B is independent of A
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Multiplicative interaction in regression
18
Binary outcome, additive interaction

• 1) Use linear model
• 2) Use log-link model, compute RR-1

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Summing up

• Biological interaction should be measured on an
  additive scale
• In regression models
• Use linear models, Easy and fun!
• Use RR or OR models, compare RR-1 in 4
  groups Complicated and boring!