E9660A
GY Zou
BaronKenny
framework
Limitation of
BaronKenny
Causal mediation
analysis
Estimation by
prediction
(Standardization)
Estimation by inverse
prob weighting
(MSM)
Estimation by model
fitting (SAS macro)
E9660A: Advanced Statistical Methods for
Epidemiology
Causal Mediation Analysis
GY Zou
October 18, 2013
E9660A
GY Zou
BaronKenny
framework
Limitation of
BaronKenny
Causal mediation
analysis
Estimation by
prediction
(Standardization)
Estimation by inverse
prob weighting
(MSM)
Estimation by model
fitting (SAS macro)
Let effect of
X
on
Y
be
β
1
β
1
includes two parts
•
direct effect of
X
on
Y
;
•
indirect effect of
X
on
Y
through
M
;
•
DAG
Y
M
γ
X
β
2
β
3
•
3 tests
Y
=
α
1
+
β
1
X
M
=
α
2
+
β
2
X
Y
=
α
3
+
β
3
X
+
γ
M
•
decomposition of
β
1
β
1
=
β
3
+
β
2
γ
•
or
β
1

β
3
=
β
2
γ
•
First model redundant
E9660A
GY Zou
BaronKenny
framework
Limitation of
BaronKenny
Causal mediation
analysis
Estimation by
prediction
(Standardization)
Estimation by inverse
prob weighting
(MSM)
Estimation by model
fitting (SAS macro)
Y
=
α
1
+
β
1
X
redundant
•
Substituting
M
=
α
2
+
β
2
X
into
Y
=
α
3
+
β
3
X
+
γ
M
•
yields
Y
=
α
3
+
β
3
X
+
γ
(
M
=
α
2
+
β
2
X
)
= (
α
3
+
α
2
γ
) + (
β
3
+
β
2
γ
)
X
E9660A
GY Zou
BaronKenny
framework
Limitation of
BaronKenny
Causal mediation
analysis
Estimation by
prediction
(Standardization)
Estimation by inverse
prob weighting
(MSM)
Estimation by model
fitting (SAS macro)
Confounding
DAG
C
Y
M
X
•
Models
(
M
=
α
2
+
β
2
X
+
θ
C
Y
=
α
3
+
β
3
X
+
γ
M
+
φ
C
•
Substituting
M
into
Y
yields
Y
= (
α
3
+
γα
2
)+(
β
3
+
γβ
2
)
X
+(
γθ
+
φ
)
C
E9660A
GY Zou
BaronKenny
framework
Limitation of
BaronKenny
Causal mediation
analysis
Estimation by
prediction
(Standardization)
Estimation by inverse
prob weighting
(MSM)
Estimation by model
fitting (SAS macro)
Estimation of mediation
•
Fit two models to get
b
β
3
,
b
β
2
and
b
γ
and their associated
variance estimates (need delta methods for variance of
b
γ
b
β
2
;
•
Estimate the difference of coefficients for
X
without
and with
M
in the model (need sandwich estimator to
get the correct variance);
E9660A
GY Zou
BaronKenny
framework
Limitation of
BaronKenny
Causal mediation
analysis
Estimation by
prediction
(Standardization)
Estimation by inverse
prob weighting
(MSM)
Estimation by model
fitting (SAS macro)
GEE approach for
β
1

β
3
•
Schluchter (2008) Flexible approaches to computing
mediated effects in generalized linear models:
Generalized estimating equations and bootstrapping.
Multivariate Behavioral Research
43: 268–288.
•
Data layout from
y
i
,
x
i
,
c
1
,
· · ·
,
c
p
,
m
i
:
Y
X
C
1
· · ·
C
p
G
M
*
Record 1
y
i
x
i
c
1
· · ·
c
p
0
0
Record 2
y
i
x
i
c
1
· · ·
c
p
1
m
i
•
Fit model of
Y
=
β
0
+
β
1
X
+
θ
(
X
×
G
) +
γ
M
*
i.e.,
θ
is mediation effect.
E9660A
GY Zou
BaronKenny
framework
Limitation of
BaronKenny
Causal mediation
analysis
Estimation by
prediction
(Standardization)
Estimation by inverse
prob weighting
(MSM)
Estimation by model
fitting (SAS macro)
SAS code for using GEE
approach for
β
1

β
3
•
data setup;
data total;
set yourdata(in=in0) yourdata(in=in1);
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 Fall '13
 MM
 Epidemiology, Trigraph, Das Model, The Mediator, msm, GY Zou