Transcript No Slide Title

Confounding
A plot of the population of Oldenburg at the end of each year against
the number of storks observed in that year, 1930-1936.
Ornitholigische Monatsberichte 1936;44(2)
Mortality rate in six countries in the Americas, 1986
Country
Mortality rate
(per 1000)
3.8
4.4
4.9
6.7
7.3
8.7
Costa Rica
Venezuela
Mexico
Cuba
Canada
US
Question:
Are people living in Costa Rica or Venezuela at
lower risk of mortality than people in Canada or
the US?
(assuming vital statistics are correct)
 Yes
No
Mortality rate in six countries in the Americas, 1986
Country
Mortality rate
(per 1000)
3.8
4.4
4.9
6.7
7.3
8.7
Costa Rica
Venezuela
Mexico
Cuba
Canada
US
Next question:
Is the observed association causal in nature, i.e.,
is there something about living in Costa Rica or
Venezuela that makes the population have lower
risk of death than the population of Canada or the
US?
Yes
 No
Country
Age
distribution
?
Mortality
N=14,054 middle age adults from 4 US communities
Comparing risk profile according to known CVD risk factors:
 Low Risk individuals (n=623):
- Never smokers
- Total cholesterol <200 mg/dL
- HDL cholesterol >65mg/dL
- LDL cholesterol <100 mg/dL
- Triglycerides <170 mg/dL
- Glycemia <140 mg/dL
- BP<140/90 mm Hg, no Rx
- No Hx of CVD, htn, diabetes, high cholesterol
 Rest (n=13,431): at least one of the above.
Low risk
Rest
Number
Age (years)
Male (%)
Education <12 years (%)
Family history CHD (%)
623
51.6
19.7
12.9
39.4
13431
54.3
46.1
23.6
44.6
BMI (kg/m2)
Subscapular skinfold
Triceps skinfold
Fibrinogen (mg/dL)
Apolipoprotein B (mg/dL)
Apolipoprotein AI (mg/dL)
26.1
22.0
26.6
280.0
147.2
61.2
27.8
24.9
25.0
303.5
132.3
95.0
Low risk
Rest
Number
Age (years)
Male (%)
Education <12 years (%)
Family history CHD (%)
623
51.6
19.7
12.9
39.4
13431
54.3
46.1
23.6
44.6
BMI (kg/m2)
Subscapular skinfold
Triceps skinfold
Fibrinogen (mg/dL)
Apolipoprotein B (mg/dL)
Apolipoprotein AI (mg/dL)
26.1
22.0
26.6
280.0
147.2
61.2
27.8
24.9
25.0
303.5
132.3
95.0
!?
Low risk
Rest
Number
Age (years)
Male (%)
Education <12 years (%)
Family history CHD (%)
623
51.6
19.7
12.9
39.4
13431
54.3
46.1
23.6
44.6
BMI (kg/m2)
Subscapular skinfold
Triceps skinfold
Fibrinogen (mg/dL)
Apolipoprotein B (mg/dL)
Apolipoprotein AI (mg/dL)
26.1
22.0
26.6
280.0
147.2
61.2
27.8
24.9
25.0
303.5
132.3
95.0
LR
Rest
F
29.0
30.1
M
16.8
19.1
Low risk
Rest
Number
Age (years)
Male (%)
Education <12 years (%)
Family history CHD (%)
623
51.6
19.7
12.9
39.4
13431
54.3
46.1
23.6
44.6
BMI (kg/m2)
Subscapular skinfold
Triceps skinfold
Fibrinogen (mg/dL)
Apolipoprotein B (mg/dL)
Apolipoprotein AI (mg/dL)
26.1
22.0
26.6
280.0
147.2
61.2
27.8
24.9
25.0
303.5
132.3
95.0
LR
Rest
F
29.0
30.1
M
16.8
19.1
Common feature of previous examples
Exposure
Confounder
?
Disease
Outcome
A variable can be a confounder if all
the following conditions are met:
• It is associated with the exposure of
interest (causally or not).
• It is causally related to the outcome.
• AND ... It is not part of the
exposure  outcome causal pathway
Ways to assess if confounding is
present:
1) Does the variable meet the criteria to
be a confounder (relation with exposure
and outcome)?
2) If the effect of that variable (on
exposure and outcome) is controlled for
(e.g., by stratification or adjustment)
does the association change?
Strategy #1: Does the variable meet
the criteria to be a confounder?
Hypothetical case-control study of risk factors for
malaria. 150 cases, 150 controls; gender distribution.
Cases Controls
Males
Females
88
62
150
68
82
150
OR= [88 x 82] ÷ [68 x 62]
= 1.71
Question:
Is male gender causally related to the risk of malaria?
Yes
No
 Further study is needed
Confounder for a male gender-malaria
association?
Male
gender
?
?
Malaria
Confounder for a male gender-malaria
association?
Male
gender
Outdoor
occupation
?
Malaria
First criterion: Is the putative confounder
associated with exposure?
?
Outdoor
occupation
Male
gender
?
Malaria
First criterion: Is the putative confounder
associated with exposure?
.
Outdoor
Indoor
Males
N
(%)
68 (43.5)
88
156 (100)
Females
N
(%)
13
(9.0)
131
144 (100)
OR=7.8
Question:
Is outdoor occupation associated with male gender?
 Yes
No
Second criterion: Is the putative
confounder associated with the outcome
(case-control status)?
Male
gender
Outdoor
occupation
?
?
Malaria
Second criterion: Is the putative
confounder associated with case-control
status?
.
Outdoor
Indoor
Malaria
Cases
N
(%)
63
(42.0)
87
150 (100)
Controls
N
(%)
18
(12.0)
132
150 (100)
OR=5.3
Question:
Is outdoor occupation (or something for which this
variable is a marker of --e.g., exposure to mosquitoes)
causally related to malaria?
 Yes
No
Third criterion: Is the putative confounder
in the causal pathway exposure  outcome?
.
?
Outdoor
occupation
Male
gender
?
Yes, it could be
 Probably not
Malaria
Note: Judgment and knowledge about the
socio-cultural context are critical to answer
this question
Question:
Provided that:
• Crude association between male gender and malaria: OR=1.71
and
• ... Outdoor occupation is more frequent among males, and
• ... Outdoor occupation is associated with greater risk of malaria …
What would be the expected magnitude of the association between
male gender and malaria after controlling for occupation (i.e.,
assuming the same degree of outdoor occupation in males and
females)?
 The (adjusted) association estimate will be smaller than 1.71
The (adjusted) association estimate will =1.71
The (adjusted) association estimate will greater than 1.71
Strategy #2: Does controlling for the
putative confounder change the magnitude
of the exposure-outcome association?
Malaria
Cases Controls
88
68
62
82
150
150
Males
Females
Indoor
occupation
Outdoor
occupation
Males
Females
Cases
53
10
63
Controls
15
3
18
OR=1.06
OR=1.71
Males
Females
Cases
35
52
87
Controls
53
79
132
OR=1.00
Ways to control for confounding
• During the design phase of the study:
– Randomized trial
– Matching
– Restriction
• During the analysis phase of the study:
– Stratification
– Adjustment
Examples of stratification
Triceps skinfold
Low risk
Rest
26.6
25.0
Males
Females
Malaria
Cases Controls
88
68
62
82
150
150
Outdoor
occupation
Cases Controls
Males
53
15
Females
10
3
63
18
OR=1.06
LR
Rest
F
29.0
30.1
M
16.8
19.1
OR=1.71
Indoor
occupation
Cases Controls
Males
35
53
Females
52
79
87
132
OR=1.00
Note that confounding is present when:
• RR/ORpooled different from RR/ORstratified
and
• RR/OR1 = RR/OR2 = …= RR/ORz
Examples of adjustment
Males
Females
Outdoor
occupation
Malaria
Cases Controls
88
68
62
82
150
150
OR=1.06
OR=1.71
Indoor
occupation
OR=1.00
Adjusted OR*=1.01
*Using the Mantel-Haenszel method, to be discussed.
Country
Costa Rica
Venezuela
Mexico
Cuba
Canada
US
Crude Mortality rate
(per 1000)
3.8
4.4
4.9
6.7
7.3
8.7
Age-adjusted* Mortality rate
(per 1000)
3.7
4.6
5.0
4.0
3.2
3.6
*Adjusted by direct method using the 1960 population of Latin America as the standard population.
Further issues for discussion
• Types of confounding
• Confounding is not an “all or none”
phenomenon
• Residual confounding
• Confounder might be a “constellation” of
variables or characteristics
• Considering an intermediary variable as a
“confounder” for examining pathways
• Confounding: a type of bias?
• Statistical significance and confounding
Types of confounding
• Positive confounding
When the confounding effect results in an
overestimation of the effect (i.e., the crude
estimate is further away from 1.0 than it would be
if confounding were not present).
• Negative confounding
When the confounding effect results in an
underestimation of the effect (i.e., the crude
estimate is closer to 1.0 than it would be if
confounding were not present).
Type of confounding:
Positive Negative
UNCONFOUNDED
3.0
OBSERVED, CRUDE
5.0

3.0
2.0

0.4
0.3

0.4

0.7
3.0
0.7
0.1
1
Relative risk
10
?
“Qualitative
confounding”
Example of positive confounding
Malaria
Cases Controls
88
68
62
82
150
150
Males
Females
Indoor
occupation
Outdoor
occupation
Males
Females
Cases
53
10
63
OR=1.71
Controls
15
3
18
Males
Females
Cases
35
52
87
Controls
53
79
132
OR=1.00
OR=1.06
Adjusted OR=1.01
Example of negative confounding
An occupational study in which workers
exposed to a certain carcinogen are younger
than those not exposed.
If the risk of cancer increases with age, the
crude association between exposure and
cancer will underestimate the unconfounded
(adjusted) association.
Age: negative confounder.
Examples of qualitative confounding
Triceps skinfold
Country
Costa Rica
Venezuela
Mexico
Cuba
Canada
US
Low risk
Rest
26.6
25.0
Crude Mortality rate
(per 1000)
3.8
4.4
4.9
6.7
7.3
8.7
LR
Rest
F
29.0
30.1
M
16.8
19.1
Age-adjusted* Mortality rate
(per 1000)
3.7
4.6
5.0
4.0
3.2
3.6
*Adjusted by direct method using the 1960 population of Latin America as the standard population.
Rate ratioUS/Mex=
1.78
0.72
• Confounding is not an “all or none” phenomenon
A confounding variable may explain the whole or just part of the observed
association between a given exposure and a given outcome.
• Crude OR=3.0 … Adjusted OR=1.0
• Crude OR=3.0 … Adjusted OR=2.0
• Residual confounding
Controlling for one of several confounding variables does not guarantee
that confounding is completely removed. Residual confounding may be
present when:
- the variable that is controlled for is an imperfect surrogate of the true
confounder,
- other confounders are ignored,
- the units of the variable used for adjustment/stratification are too broad
• The confounding variable may reflect a
“constellation” of variables/characteristics
– E.g., Occupation (SES, physical activity, exposure to environmental risk
factors)
– Healthy life style (diet, physical activity)
ERT
(adjusted)*
Other
factors?
*Adjusted for family history, type of menopause,
smoking, hypertension, diabetes, OC use, high
cholesterol, age, obesity.
?
Low CHD
(Matthews KA et al. Prior to use of estrogen replacement therapy, are users healthier than nonusers? Am J
Epidemiol 1996;143:971-978)
Estrogen-Progestin
Placebo
Kaplan-Meier estimates of the cumulative incidence of
primary coronary heart disease events.
JAMA 1998;280:605-13.
Circulation 1996;94:922-7.
• Treating an intermediary variable as a
confounder (i.e., ignoring “the 3rd rule”)
Under certain circumstances, it might be of interest to
treat an hypothesized intermediary variable acting as a
mechanism for the [risk factor  outcome] association
as if it were a confounder (for example, adjusting for it)
in order to explore the possible existence of additional
mechanisms/pathways. This is done by comparing the
adjusted with the unadjusted values.
EXAMPLE:
It has been argued that obesity is not a risk factor of
mortality. The observed association between obesity
and mortality in many studies might just be the product
of the confounding effect of hypertension.
Obesity
Hypertension
?
Mortality
HOWEVER,
Hypertension is probably not a real confounder but
rather a mechanism whereby obesity causes
hypertension.*
Obesity
Hypertension
Mortality
*Manson JE et al: JAMA 1987;257:353-8.
EVEN IF HYPERTENSION IS A MECHANISM LINKING
OBESITY TO MORTALITY,
it may be of interest to conduct analyses that control for
hypertension, to assess whether alternative
mechanisms may causally link obesity and mortality.
Obesity
Block by
Hypertension
adjustment
Mortality
EXAMPLE:
Is maternal smoking a risk factor of perinatal death?
Is the association confounded by low birth weight?
Maternal
smoking
Low birth
weight
?
Perinatal
mortality
OR RATHER:
Is low birth weight the reason why maternal smoking is
associated to higher risk of perinatal death?
Maternal
smoking
Low birth
weight
Perinatal
mortality
BUT THERE COULD BE AN ADDITIONAL QUESTION:
Does maternal smoking cause perinatal death by
mechanisms other than low birth weight?
Maternal
smoking
Low
birth
Block by
weight
adjustment
Direct
toxic
effect?
Perinatal
mortality
• Statistical significance should not be
used to assess confounding effects
Odds Ratio [age 56/age 55] = 60/40 ÷ 50/50 = 1.5
60
58
56
54
52
50
48
46
44
Age (years)
55
56
• Statistical significance should not be
used to assess confounding effects
Odds Ratio [cases/controls] = 60/40 ÷ 50/50 = 1.5
% post-menopausal
60
58
56
54
52
50
48
46
44
Age (years)
Controls
Cases
55
56
• Statistical significance should not be
used to assess confounding effects
The main strategy must be to evaluate
whether the difference in the confounder is
large enough to explain the association.
Control of Confounding Variables
• Randomization
• Matching
• Adjustment
– Direct
– Indirect
– Mantel-Haenszel
Stratified methods
• Multiple Regression
– Linear
– Logistic
– Poisson
– Cox
Control of Confounding Variables
• Randomization
• Matching
• Adjustment
– Direct
– Indirect
– Mantel-Haenszel
Stratified methods
• Multiple Regression
– Linear
– Logistic
– Poisson
– Cox
Mantel-Haenszel Technique for Adjustment of
the Odds Ratios and Rate Ratios
• Nathan Mantel and William Haenszel were two very
productive statisticians:
2
(ad  bc) ( N 1)
2
 MH 
n1 n2 m1 m2
– Test for homogeneity of stratified OR’s (see Schlesselman,
pp. 193-6, or Kahn & Sempos, pp. 115-6): for the
assessment of multiplicative interaction
– Mantel-Haenszel test for trend
Mantel-Haenszel Technique for Adjustment of Odds Ratios-Example (Israeli Study, see Kahn & Sempos, pp. 105)
MI Case Control
SBP
(mmHg)
140
29
711
< 140
27
1244
OR= 1.88
• Is the association causal?
•Is it due to a third (confounding) variable (e.g., age)?
BP
?
Age
MI
A variable is only
a confounder if dual
association is present
Does age meet the criteria to be a confounder? Yes
140

<140
60

124
79
< 60
616
1192
Age Vs SBP
Age
OR= 3.0
Age Vs MI
Age
MI
Controls
60
15
188
< 60
41
1767
OR= 3.4
Increased odds of systolic
hypertension (“exposure”)
Age
Increased odds of
myocardial infarction
(“outcome”)
Blood Pressure
Age

60
<60
SBP
MI Risk
MI CONT

140
9
115
<140
6
73
OR= 0.9
Odds Ratios not
homogeneous

140
20
596
<140
21
1171 OR= 1.9
• Is it appropriate to calculate an adjusted ORMH? NO
These findings fail to meet Mantel-Haenszel adjustment
approach’s main assumption: that odds ratios are
homogeneous (no multiplicative interaction).
Mantel-Haenszel Formula for Calculation of
Adjusted Odds Ratios
Exposure Cases Controls
Yes
ai
bi
No
ci
di
Ni
ai di

Ni
i
OR MH 
bi ci =

Ni
i
bi ci ai di
bi ci ai di




 wi ORi
Ni
i Ni bi ci  i
i bi ci
=
bi ci
bi ci
wi



i
N
N
i
i
i
i
Thus, the ORMHis a weighted average of stratum-specific ORs
(ORi), with weights equal to each stratum’s:
bi ci
wi 
Ni
CHD
No CHD
Postmenopausal
118
3606
Pre-menopausal
17
2361
Stratum 1
Age 45-49
ORPOOLED= 4.5
Post
3
171
Pre
10
1428
OR1= 2.5
1612
Stratum 2
Age 50-54
Stratum 3
Age 54-59
Post
14
684
Pre
6
757
Post
Pre
37
1
1408
153
OR2= 2.6
1461
OR3= 4.0
1599
Stratum 4
Age 60-64
Post
Pre
(*adding 1.0 to each cell)
64
0
1343
23
OR4=1.2*
1430
Ages 45-64
31428 14 757 37153 64 23



1461
1599 1430  3.04
OR MH  1612
17110 684 6 14081 1343 0



1612 1461 1599
1430
?
Stratum-specific odds ratios: 2.5, 2.6, 4.0, 1.2
Average= 3.04
CHD
No CHD
Postmenopausal
118
3606
Pre-menopausal
17
2361
Stratum 1
Age 45-49
ORPOOLED= 4.5
Post
3
171
Pre
10
1428
OR1= 2.5
1612
Stratum 2
Age 50-54
Stratum 3
Age 54-59
Post
14
684
Pre
6
757
Post
Pre
37
1
1408
153
OR2= 2.6
1461
OR3= 4.0
1599
Stratum 4
Age 60-64
Post
Pre
(*adding 1.0 to each cell)
64
0
1343
23
OR4=1.2*
1430
Ages 45-59
31428 14 757 37153


1612
1461
1599
OR MH 
 2.83
17110 684 6 14081


1612 1461 1599
Stratum-specific odds ratios: 2.5, 2.6, 4.0
Average= ORMH 2.83
There is an analogous procedure to obtain an
adjusted Rate Ratio from stratified data in a
prospective study (see Kahn & Sempos, pp. 219-221)
Person
Events
Time
Stratum i
Exposed
ai
Li
Unexposed
bi
Li
ni
ti
RateRatio MH
ai Li

ti
i

bi Li

i ti
Mortality of Individuals with High and Low Vitamin C/Beta-Carotene Intake
Index, by Smoking Status, Western Electric Company Study (Pandey et al, Am J
Epidemiol 1995;142:1269-78)
Vitamin C/Beta
Carotene
Index
No.
deaths
No. of
Personyears
High
53
5143
Low
57
4260
Non-smokers
Total
Smokers
Rate Ratio MH
RR= 0.77
9403
High
111
6233
Low
138
6447
Total
Stratified
Rate Ratio
RR= 0.83
12680
ai Li 53 4260 111 6447


t
12680  0.81
 i i  9403
bi Li 57  5143 138  6233


9403
12680
i ti
Formulas for calculating confidence intervals
for the ORMH are available (Schlesselman, p.
184, Szklo & Nieto, Appendix A.8)
All
participants
RF+
RF-
Strata of potential
confounder Z
ORPooled
Z= 1
RF+
ORZ=1
RF-
Z= 2
RF+
ORZ=2
RF-
Z=3
RF+
ORZ=3
RF-
Z=…
If ORPooled ~ (ORZ=1~ ORZ=2 ~ ORZ=3, …) Z is not a confounder:
~
~
~
report crude OR (ORPooled)
If ORPooled
(ORZ=1~ ORZ=2 ~ ORZ=3, …) Z is a confounder:
~
~
report ORPooled and adjusted OR
Z is an effect modifier. Do not
ORZ=3, …
If ORZ=1 ORZ=2
adjust: report Z-specific ORs
Correspondence between the “matched” odds
ratios and the Mantel-Haenszel method
CONTROLS
BREAST CANCER CASES
Yes
No
8
23
45
362
Yes
No
OR??
OR= 45/23= 1.96
(Adapted from Heinone et al, Lancet 2:675, 1974)
No. pairs
8
Reserpine
+
-
Case
1
0
Control
1
0
(a x d)/N
(b x c)/N
0
0
1/2
0
0
1/2
0
0
2
45
+
-
1
0
0
1
2
23
+
-
0
1
1
0
2
362
+
-
0
1
0
1
2
Reserpine Use and Breast Cancer
CONTROLS
Yes
No
BREAST CANCER CASES
Yes
No
8
23
45
362
OR= 45/23= 1.96
(1 0)
(11)
(0  0)
(0 1)
8 
 45 
 23 
 362
2
2
2
OR MH  2

(1 0)
(0  0)
(11)
(0 1)
8 
 45 
 23 
 362
2
2
2
2
(11)
 45
45
2

 196
.
(11)
 23 23
2
Stratification Methods
• Advantages
– Easy to understand and compute
– Allow simultaneous assessment of
interaction
• Disadvantages
– Cannot handle a large number of variables
(zero cells are problematic in direct
adjustment)
– Each calculation requires a rearrangement
of tables