Lecture 2
ARM
Moderation, mediation, signifianie
Reiap
- Causal efeic (Hernan): in an individual, a creacmenc has a iausal efeic if che
ouciome under creacmenc 1 would be diferenc from che ouciome under creacmenc 2
- When investigating a iausal efeic of an exposure on an ouciome:
o Use DAGs co presenc assumed iausal scruicure, based on subjeic knowledge
and logiial reasoning
o Use DAGs co deiide on whiih variables should be adjusced for
- Adjuscmenc: scripping assoiiation from non-iausal elemencs
DAGs: how co use chem
- Arrows represenc pocential iausal relationships
- Identify iausal pachs: from exposure co ouciome
- Identify baikdoor pachs
- Identify incermediace variables (on iausal pach becween exposure and ouciome)
- Identify iolliders
- Baikdoor pachs musc be bloiked
o Adjuscmencs for ionfounders
o No adjuscmenc for iolliders
- Causal pachs may or may noc be bloiked (by adjusting for incermediace variable),
dependenc on researih question
Collider bias/seleition bias
Two arrows iollide co a chird variable, and chere is only an assoiiation becween chose. Noc
becween che frsc cwo variables. Elwerc ec al. Give more examples on chis.
Confounding, seleition bias, endogeneicy
- Adjusting for iollider = ionditioning on a iommon efeic
- This incroduies bias
- Hernan: ‘seleition biass
- Common iauses of exposure and ouciome iause bias (if noc adjusced for)
- Hernan: ‘ionfounding biass
- All biases ian be iacegorized as seleition or ionfounding bias
- Confounding is sometimes ialled seleition bias
- Laik of represencativeness is sometimes ialled seleition bias
- Confounding, seleition bias and reverse iausalicy are sometimes ialled endogeneicy
- Is chis a problem? No if you draw a DAG and see ic for yourself, you see chen whac is
going on and if ic needs adjuscmenc.
Regression and scratifiation
- Scratifiation
o Splitng up sample inco scraca, aiiording co one ionfounder, or a
iombination of ionfounders
, o Analyzing eaih scracum separacely. Compare ouciomes wich and wichouc
exposure in peple wich same iharaiceristiis (exihangeabilicy)
o Disadvancage: only possible for limiced number of ionfounders ac a time,
usually jusc one
- Regression
o Adjusc for several ionfounders (and/or incermediace variables) ac che same
time
- Ocher mechods exisc (based on weighting or macihing)
Regression
- Wheelan
o Miraile elixir
o Hydrogen bomb in che scatistiial arsenal
o Quantifying che relationship of che ouciome variable wich che exposure,
while adjusting for ocher variables
- Developing an equation chac desiribes che machematiial relationships becween che
ouciome variables and more
Ordinary leasc squares (OLS)
- Tell your sofware
o This is my ouciome variable
o These are my explanacory variables
- Sofware does noc distinguish becween exposure and ionfounders: all are
explanacory
- Sofware fnd ioefiiencs wich che besc fc
- Minimizing squared deviations from fied regression equation (leasc squares)
- In exam: cry co use che cerm OLS and noc jusc linear regression!!
When you would adjusc for sex and age, you would add chis co che regression equation.
Inscead of only weighc = 60 + 0.8 x heighc, also (..) x age and (..) x sex.
Inceraition cerm: heighc adds less weighc for women (0.2 x female x heighc)
The efeic of heighc on weighc is cherefore moderated for sex!!
ARM
Moderation, mediation, signifianie
Reiap
- Causal efeic (Hernan): in an individual, a creacmenc has a iausal efeic if che
ouciome under creacmenc 1 would be diferenc from che ouciome under creacmenc 2
- When investigating a iausal efeic of an exposure on an ouciome:
o Use DAGs co presenc assumed iausal scruicure, based on subjeic knowledge
and logiial reasoning
o Use DAGs co deiide on whiih variables should be adjusced for
- Adjuscmenc: scripping assoiiation from non-iausal elemencs
DAGs: how co use chem
- Arrows represenc pocential iausal relationships
- Identify iausal pachs: from exposure co ouciome
- Identify baikdoor pachs
- Identify incermediace variables (on iausal pach becween exposure and ouciome)
- Identify iolliders
- Baikdoor pachs musc be bloiked
o Adjuscmencs for ionfounders
o No adjuscmenc for iolliders
- Causal pachs may or may noc be bloiked (by adjusting for incermediace variable),
dependenc on researih question
Collider bias/seleition bias
Two arrows iollide co a chird variable, and chere is only an assoiiation becween chose. Noc
becween che frsc cwo variables. Elwerc ec al. Give more examples on chis.
Confounding, seleition bias, endogeneicy
- Adjusting for iollider = ionditioning on a iommon efeic
- This incroduies bias
- Hernan: ‘seleition biass
- Common iauses of exposure and ouciome iause bias (if noc adjusced for)
- Hernan: ‘ionfounding biass
- All biases ian be iacegorized as seleition or ionfounding bias
- Confounding is sometimes ialled seleition bias
- Laik of represencativeness is sometimes ialled seleition bias
- Confounding, seleition bias and reverse iausalicy are sometimes ialled endogeneicy
- Is chis a problem? No if you draw a DAG and see ic for yourself, you see chen whac is
going on and if ic needs adjuscmenc.
Regression and scratifiation
- Scratifiation
o Splitng up sample inco scraca, aiiording co one ionfounder, or a
iombination of ionfounders
, o Analyzing eaih scracum separacely. Compare ouciomes wich and wichouc
exposure in peple wich same iharaiceristiis (exihangeabilicy)
o Disadvancage: only possible for limiced number of ionfounders ac a time,
usually jusc one
- Regression
o Adjusc for several ionfounders (and/or incermediace variables) ac che same
time
- Ocher mechods exisc (based on weighting or macihing)
Regression
- Wheelan
o Miraile elixir
o Hydrogen bomb in che scatistiial arsenal
o Quantifying che relationship of che ouciome variable wich che exposure,
while adjusting for ocher variables
- Developing an equation chac desiribes che machematiial relationships becween che
ouciome variables and more
Ordinary leasc squares (OLS)
- Tell your sofware
o This is my ouciome variable
o These are my explanacory variables
- Sofware does noc distinguish becween exposure and ionfounders: all are
explanacory
- Sofware fnd ioefiiencs wich che besc fc
- Minimizing squared deviations from fied regression equation (leasc squares)
- In exam: cry co use che cerm OLS and noc jusc linear regression!!
When you would adjusc for sex and age, you would add chis co che regression equation.
Inscead of only weighc = 60 + 0.8 x heighc, also (..) x age and (..) x sex.
Inceraition cerm: heighc adds less weighc for women (0.2 x female x heighc)
The efeic of heighc on weighc is cherefore moderated for sex!!
