1
Confounding and Effect
Modification
JHU Intro to Clinical Research 1
Karen Bandeen-Roche, Ph.D.
July 23, 2013
JHU Intro to Clinical Research 2
Outline
1. Causal inference: comparing “otherwise similar”
populations
2. “Confounding” is “confusing”
3. Graphical representation of causation
4. Addressing confounding
5. Effect modification
2
JHU Intro to Clinical Research 3
Counterfactual Data Table
Person Drug Y(0) Y(1) Y(1)-Y(0)
1 0 22 16 -6
2 0 18 17 -1
3 0 20 15 -5
4 1 20 18 -2
5 1 18 16 -2
6 1 22 14 -8
Average 20 16 -4
JHU Intro to Clinical Research 4
Actual Data Table
Person Drug Y(0) Y(1) Y(1)-Y(0)
1022? ?
2018? ?
3020? ?
41?18?
51?16?
61?14?
Average 20 16 -4
3
JHU Intro to Clinical Research 5
Goal of Statistical “Causal” Inference
• “Fill-in” missing information in the counterfactual
data table
• Use data for persons receiving the other treatment
to fill-in a persons missing outcome
• Inherent assumption that the other persons are
similar except for the treatment: “otherwise
similar”
• Compare like-to-like
JHU Intro to Clinical Research 6
Confounding
Confound means to “confuse”
When the comparison is between groups that
are otherwise not similar in ways that affect the
outcome
Simpson’s paradox; lurking variables,….
4
Confounding Example:
Drowning and Ice Cream Consumption
JHU Intro to Clinical Research
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Ice Cream consumption
Drowning
rate per
day
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
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Confounding
Epidemiology definition: A characteristic “C” is a
confounder if it is associated (related) with both the
outcome (Y: drowning) and the risk factor (X: ice
cream) and is not causally in between
Ice Cream
Consumption
Drowning
rate
??
5
JHU Intro to Clinical Research 9
Confounding
Epidemiology definition: A characteristic “C” is a
confounder if it is associated (related) with both the
outcome (Y: drowning) and the risk factor (X: ice
cream) and is not causally in between
Ice Cream
Consumption
Drowning
rate
Outdoor
Temperature
JHU Intro to Clinical Research 10
Confounding
Statistical definition: A characteristic “C” is a
confounder if the strength of relationship between the
outcome (Y: drowning) and the risk factor (X: ice
cream) differs overall, versus within values for C
Ice Cream
Consumption
Drowning
rate
Outdoor
Temperature
6
Confounding Example:
Drowning and Ice Cream Consumption
JHU Intro to Clinical Research
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Ice Cream consumption
Drowning
rate
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
Cool temperature
Warm temperature
JHU Intro to Clinical Research 12
Mediation
A characteristic “M” is a mediator if it is causally in
the pathway by which the risk factor (X: ice cream)
leads the outcome (Y: drowning)
Ice Cream
Consumption
Drowning
rate
Cramping
7
JHU Intro to Clinical Research 13
Confounding
Statistical definition: A characteristic “C” is a
confounder if the strength of relationship between the
outcome and the risk factor differs with, versus
without, comparing like to like on C
Thought example:
Outcome = frailty
Exposure = vitamin D intake
Confounders= SES, “health
mindedness,” etc.
Example:
Graduate School Admissions
UC Berkeley
JHU Intro to Clinical Research 14
Number
Applied
Percent
Accepted
Male 1901 55
Female 1119 36
8
JHU Intro to Clinical Research 15
Number
Males
Applied
Number
Males
Accepted
Male
%
Accepted
Female %
Accepted
Number
Females
Accepted
Number
Females
Applied
A 825 512 62 82 89 108
B 560 353 63 68 17 25
C 325 120 37 34 202 593
D 191 53 28 24 94 393
Total 1901 1038 55 36 402 1119
July 2010 JHU Intro to Clinical Research 16
Percent
Admitted
Percent
Male
Applicants
Percent
Female
Applicants
A 654310
B63302
C 351753
D 251035
Total 48 100 100
9
JHU Intro to Clinical Research 17
JHU Intro to Clinical Research 18
What is the lurking variable causing
admissions rates to be lower in departments
to which more women apply?
Gender
Admission
??
10
JHU Intro to Clinical Research 19
What is the lurking variable causing
admissions rates to be lower in departments
to which more women apply?
Gender
Admission
Department to
which applied
Department to
which applied
JHU Intro to Clinical Research 20
Number
Males
Applied
Number
Males
Accepted
Male
%
Accepted
Female –
Male %
Accepted
Female %
Accepted
Number
Females
Accepted
Number
Females
Applied
A 825 512 62 +20 82 89 108
B 560 353 63 +5 68 17 25
C 325 120 37 -3 34 202 593
D 191 53 28 -4 24 94 393
Total 1901 1038 55 -19 36 402 1119
11
July 2010 JHU Intro to Clinical Research 21
in admission rates between
women and men:
in admission rates between
women and men:
JHU Intro to Clinical Research 22
…Now for something entirely different
Particulate air pollution and mortality
12
Chicago
Los Angeles
July 2010
13
Correlation: Daily mortality and
PM
10
• New York -0.031
• Chicago -0.036
• Los Angeles -0.019
> Season could be confounding the correlation
between PM
10
and mortality.
> What would happen if we “removed” season from
the analysis?
Season-specific correlations
All Year Winter Spring Summer Fall
NY -0.031 0.059 0.059 0.086 0.100
Chicago -0.036 -0.017 0.054 0.140 -0.030
LA -0.019 0.157 0.063 0.042 -0.118
14
Overall association for New York
15
16
Season-specific associations are positive, overall
association is
negative
17
Overall correlations
All Year Average over
Seasons
New York -0.031 0.076
Chicago -0.036 0.037
LA -0.019 0.036
Overall correlations
All Year
“Unadjusted”
Average 4
within-season
values
“Adjusted”
Average 12
within month
values
“Adjusted”
New York
-0.031 0.076 0.079
Chicago
-0.036 0.037 0.063
LA
-0.019 0.036 0.050
18
JHU Intro to Clinical Research 35
Effect modification
A characteristic “E” is an effect modifier if the
strength of relationship between the outcome (Y:
drowning) and the risk factor (X: ice cream) differs
within levels of E
Ice Cream
Consumption
Drowning
rate
Outdoor
temperature
Outdoor
temperature
Effect Modification Example:
Drowning and Ice Cream Consumption
JHU Intro to Clinical Research
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Ice Cream consumption
Drowning
rate
*
*
*
*
*
*
*
*
*
*
*
*
*
Cool temperature
Warm temperature
19
37
Question: Does aspirin use modify the association
between treatment and adverse outcomes?
July 2008 JHU Intro to Clinical Research 38
20
JHU Intro to Clinical Research 39
JHU Intro to Clinical Research 40
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Aspirin use modifies the effect of treatment
on the risk of stroke?
Losartan –vs-
Atenolol
Stroke
Aspirin Use
Confounding vs. Effect Modification
Confounding
• Bias (overall) because
treatment groups differ by a
relevant characteristic
• Persons taking vitamin D
appear less frail because
they have more resources to
protect their health
• Addressed by computing
effects in comparable people
(vit D effect in persons with
equal resources)
Effect modification
• Subgroup effects; contextual
effects; different
mechanisms
• Vitamin D more effectively
prevents frailty in younger-
old because they better
metabolize Vitamin D
• Addressed by comparing
effects across groups (Vit D
effect in older-old minus Vit
D effect in younger-old)
JHU Intro to Clinical Research
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22
JHU Intro to Clinical Research 43
Summary
1. Causal inference: comparing “otherwise similar”
populations
2. Confounding means confusing: comparing
otherwise
groups
3. Stratify by confounders and make comparisons
within strata, then pool results across strata to
avoid the effects of confounding
4. Effect modification when the treatment effect
varies by stratum of another variable
