Joint vs Marginal Confounder - The INCLEN Trust

Joint Versus Marginal
Confounding

Data-Based Confounding
(Single C)
Crude estimate
c ^
meaningful
Adjusted estimate
a ^
Note:
denotes any effect measure of interest

Data-Based Joint Confounding
(2 or more C's)
Crude estimate
c ^
meaningful
Adjusted estimate
a ^
(C 1 , C 2 , ... , C p )
Note:
denotes any effect measure of interest

Click on the question to see its answer.
Continue
Data-Based
Joint
c ^
a ^
Confounding
(C 1 , C 2 , ... , C p )
Study Questions
Suppose a follow-up study was conducted to evaluate an
E - D relationship. Age and smoking status were
detemined as possible control variables.
Suppose further that aRR(age, smoking) = 2.4,
aRR(age) = 1.7, aRR(smoking) = 1.9, and cRR = 1.5.
(Assume all quantities above are estimates)
1. Is this evidence of joint confounding Why or why not

Study Questions
Suppose a follow-up study was conducted to evaluate an
E - D relationship. Age and smoking status were
detemined as possible control variables.
Suppose further that aRR(age, smoking) = 2.4,
aRR(age) = 1.7, aRR(smoking) = 1.9, and cRR = 1.5.
(Assume all quantities above are estimates)
1. Is this evidence of joint confounding Why or why not
Click on the question to see its answer.
Continue

Data-Based
Joint
c ^
a ^
Confounding
(C 1 , C 2 , ... , C p )
Study Questions
Suppose for a different follow-up study of the same E - D
relationship that once again age and smoking status were
possible control variables.
Suppose further that aRR(age, smoking) = 1.4, aRR(age) =
2.4, aRR(smoking) = 2.4, and cRR = 1.5.
(Assume all quantities above are estimates)
2. Is this evidence of joint confounding Why or why not

Study Questions
Suppose for a different follow-up study of the same E - D
relationship that once again age and smoking status were
possible control variables.
Suppose further that aRR(age, smoking) = 1.4, aRR(age) =
2.4, aRR(smoking) = 2.4, and cRR = 1.5.
(Assume all quantities above are estimates)
2. Is this evidence of joint confounding Why or why not
Click on the question to see its answer.
Continue

Data-Based
Joint
Confounding
c ^
a ^
(C 1 , C 2 , ... , C p )
Data-Based Marginal Confounding
c^
meaningful
a^ (C j )
where C j
is one of p potential confounders.

Data-Based Marginal Confounding
c^
a^ (C j
)
where C j
is one of p potential confounders.
Study Questions
Suppose a follow-up study was conducted to evaluate an E - D
relationship. Age and smoking status were determined as possible
control variables. Suppose that aRR(age, smoking) = 2.4 and cRR =
1.5.
(Assume all quantities above are estimates)
3. Is this evidence of marginal confounding Why or why not
4. If the aRR(age) = 1.4, does this provide evidence of marginal
confounding
5. Does this mean that we should not control for age as a confounder
Click on the question to see its answer.

c a^
(C j )
where C j
is one of p potential confounders.
Study Questions
Suppose a follow-up study was conducted to evaluate an E - D
relationship. Age and smoking status were determined as possible
control variables. Suppose that aRR(age, smoking) = 2.4 and cRR =
1.5.
(Assume all quantities above are estimates)
3. Is this evidence of marginal confounding Why or why not
4. If the aRR(age) = 1.4, does this provide evidence of marginal
confounding
5. Does this mean that we should not control for age as a confounder
Click on the question to see its answer.

where
c C j
is one of a^ p potential (C j ) confounders.
where C j
is one of p potential confounders.
Study Questions
Suppose a follow-up study Study was Questions conducted to evaluate an E - D
relationship. Age and smoking status were determined as possible
Suppose a follow-up study was conducted to evaluate an E - D
relationship.
control variables.
Age and
Suppose
smoking
that
status
aRR(age,
were
smoking)
determined
= 2.4
as
and
possible
cRR =
control 1.5. variables. (Assume Suppose all that quantities aRR(age, above smoking) are estimates) = 2.4 and cRR =
3. 1.5. Is this evidence of
(Assume
marginal
all
confounding
quantities above
Why
are
or why
estimates)
not
3. 4. Is If the this aRR(age) evidence = of 1.4, marginal does this confounding provide evidence Why or of why marginal not
4. confounding
If the aRR(age) = 1.4, does this provide evidence of marginal
5. confounding
Does this mean that we should not control for age as a confounder
5. Does this mean that we should not control for age as a confounder
Click on the question to see its answer.
Click on the question to see its answer.

where C j
is one of p potential confounders.
c a^ (C j )
Study Questions
where C j
is one of p potential confounders.
Suppose a follow-up study was conducted to evaluate an E - D
relationship. Age and smoking status were determined as possible
control variables. Suppose Study that aRR(age, Questions smoking) = 2.4 and cRR =
Suppose 1.5. a follow-up (Assume study all was quantities conducted above to evaluate are estimates) an E - D
3. relationship. Is this evidence Age of and marginal smoking confounding status were Why determined or why as not possible
4. control If the aRR(age) variables. = 1.4, Suppose does this that provide aRR(age, evidence smoking) of = marginal 2.4 and cRR =
1.5. confounding (Assume all quantities above are estimates)
3. 5. Is Does this this evidence mean that of marginal we should confounding not control Why for age or why as a confounder not
4. If the aRR(age) = 1.4, does this provide evidence of marginal
confounding
5. Does Click this on the mean question that we to should see its not answer. control for age as a confounder
Click on the question to see its answer.

Data-Based
c ^
Joint
a
^
Primary criterion
Confounding
Data-Based Marginal Confounding
c^
a^ (C j )
(C 1 , C 2 , ... , C p )
where C j
is one of p potential confounders.

(C 1 , C 2 , …, C p )

Data-Based
c ^
Joint
Confounding
a
^
(C (C 1
, 1 , C 22 ,, ... …,, C p ) p
)
Data-Based Marginal Confounding
c^
a^ (C j
)
Can determine whether SOME potential
confounders NEED NOT be controlled
Study Questions
6. In the follow-up study described in the previous study question, the
aRR(age, smoking) = 2.4, the cRR = 1.5, the aRR(age) = 1.5, and the
aRR(smoking) = 2.4. Does this mean that we do not have to control
for age
(Assume all quantities above are estimates)
Click on the question to see its answer
Continue

Data-Based
c ^
Joint
Confounding
a
^
(C 1
(C , C 1 , 2
C, 2 ... , …, , C p )
Data-Based Marginal Confounding
c^
a^ (C j
)
Can determine whether SOME potential
confounders NEED NOT be controlled
Study Questions
6. In the follow-up study described in the previous study question, the
aRR(age, smoking) = 2.4, the cRR = 1.5, the aRR(age) = 1.5, and the
aRR(smoking) = 2.4. Does this mean that we do not have to control
for age
(Assume all quantities above are estimates)
Click on the question to see its answer
Continue

Data-Based
c ^
Joint
Confounding
a
^
(C 1 , C 2 , ... , C p )
Data-Based Marginal Confounding
c^
a^ (C j
)
Study Questions
7. What problem might there be in practice that could prevent
estimating the effect that controls for all risk factors
(e.g., C1, C2, . . ., Cp)
8. What should we do if there are too many potential confounders in
our list and we are unable to determine the appropriate adjusted
estimate
9. What if the choice of such a subset becomes difficult
Click on the question to see its answer
Continue

c ^
a ^
(C 1 , C 2 , ... , C p )
Data-Based Marginal Confounding
c^
a^ (C j
)
Study Questions
7. What problem might there be in practice that could prevent
estimating the effect that controls for all risk factors
(e.g., C1, C2, . . ., Cp)
8. What should we do if there are too many potential confounders in
our list and we are unable to determine the appropriate adjusted
estimate
9. What if the choice of such a subset becomes difficult
Click on the question to see its answer
Continue

Data-Based Marginal Confounding
c^
c^
a^ (C j )
a^ (C j
)
Study Questions
7. What problem might there be in practice that could prevent
estimating the effect that controls for all risk factors
(e.g., C1, C2, . . ., Cp)
Study Questions
7. 8. What problem should we might do if there be are in too practice many that potential could confounders prevent in
estimating our list and the we effect are unable that controls to determine for all the risk appropriate factors adjusted
estimate
(e.g., C1, C2, . . ., Cp)
9. What if the choice of such a subset becomes difficult
8. What should we do if there are too many potential confounders in
our list and we are unable to determine the appropriate adjusted
Click on the question to see its answer
estimate
9. What if the choice of such a subset becomes difficult
Continue
Click on the question to see its answer
Continue

c a^
(C a ^
j
)
(C 1
, C 2
, ... , C p
)
Data-Based Marginal Study Questions Confounding
c ^
7. What problem might
c^ there be in practice that could prevent
estimating the effect that controls for all risk factors
(e.g., C1, C2, . . ., Cp) a^ (C j
)
8. What should we do if there are too many potential confounders in
our list and we are unable Study to determine Questions the appropriate adjusted
estimate
9. 7. What if problem the choice might of there such a be subset in practice becomes that difficult could prevent
estimating the effect that controls for all risk factors
(e.g., Click C1, on the C2, question . . ., Cp) to see its answer
8. What should we do if there are too many potential confounders in
our list and we are unable to determine the appropriate adjusted
estimate
9. What if the choice of such a subset becomes difficult
Continue
Click on the question to see its answer
Continue

Summary
• Data-based joint confounding occurs when there is a
meaningful difference between the estimated crude effect
and the estimated adjusted effect which simultaneously
controls for all the potential confounders.
• Data-based marginal confounding occurs when there is a
meaningful difference between the estimated crude effect
and the estimated adjusted effect which controls for only
one of several potential confounders.
• Our conclusions regarding confounding should be based
on joint confounding whenever possible.