E9660A
GY Zou
Baron-Kenny
framework
Limitation of
Baron-Kenny
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
Baron-Kenny
framework
Limitation of
Baron-Kenny
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
Baron-Kenny
framework
Limitation of
Baron-Kenny
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
Baron-Kenny
framework
Limitation of
Baron-Kenny
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
Baron-Kenny
framework
Limitation of
Baron-Kenny
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
Baron-Kenny
framework
Limitation of
Baron-Kenny
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
Baron-Kenny
framework
Limitation of
Baron-Kenny
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
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- Epidemiology, Trigraph, Das Model, The Mediator, msm, GY Zou