Date post: | 22-Dec-2015 |
Category: |
Documents |
View: | 219 times |
Download: | 0 times |
Intermediate methods in observational epidemiology
2008
Confounding - I
800 200 500 500
80 100 50 250
180 300Mortality
18% 30%
Deaths
Intervention No intervention
240 240
24% 24%
65 175 65 175
Intervention No intervention
Experimental(n=2000)
1300 700
650 350 650 350
1300 700
Observational(n= 2000)
OBSERVATION VS. EXPERIMENT
Absent, mortality = 10%
Present, mortality = 50%
Confounding variable:
Confounding variable
Less common in the group that undergoes the intervention
Increased mortality (“outcome”)
(DUAL) ASSOCIATION OF CONFOUNDING VARIABLE WITH BOTH OUTCOME AND INDEPENDENT
VARIABLE
Mortality according to the intervention, stratified by the confounder
Confounding variable:
Intervention: N No. of deaths
Mortality
Present Yes 200 100 50.0%
No 500 250 50.0%
Absent Yes 800 80 10.0%
No 500 50 10.0%
800 200 500 500
80 100 50 250
180 300
18% 30%
Intervention No intervention
No. Deaths:
Mortality:
Absent, mortality = 10%
Present, mortality = 50%
Confounding variable:
One of the solutions to eliminate confounding: stratify
Israeli Study, see Kahn & Sempos, pp. 105
MI Case Control
140 29 711 SBP (mmHg)
< 140 27 1244
OR= 1.88
• Is the association causal? •Is it due to a third (confounding) variable (e.g., age)?
BP MI?
Age
A variable is onlya confounder if dualassociation is present
Age Vs SBP 140 <140
60 124 79 Age
< 60 616 1192
OR= 3.0
Age Vs MI MI Controls
60 15 188 Age
< 60 41 1767
OR= 3.4
Does age meet the criteria to be a confounder? Yes
Age
Increased odds of systolic hypertension (“exposure”)
Increased odds of myocardial infarction (“outcome”)
(DUAL) ASSOCIATION OF AGE WITH BOTH SYSTOLIC HYPERTENSION AND MYOCARDIAL INFARCTION
Confounder
Exposure
Outcome
CONFOUNDING EFFECT
… and not in the causality pathway between exposure and outcome:
Confounder
Exposure
Outcome
Blood Pressure MI Risk
Age SBP MI CONT
60 140 9 115
<140 6 73 OR=
<60 140 20 596
<140 21 1171 OR=
0.9
1.9
• Is it appropriate to calculate an adjusted OR? NO
Odds Ratios not homogeneous
Assumption when doing adjustment: Homogeneity of odds ratios (no multiplicative interaction).
Ways to assess if confounding is present:
Strategy 1:Does the variable meet the criteria to be a confounder (relation with exposure and outcome)?
Strategy 2: If the effect of that variable (on exposure and outcome) is controlled for (e.g., by stratification or adjustment) does the association change?
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
• Stratified methods – Direct method– Mantel-Haenszel adjustment of Odds Ratios
• Regression methods
Matching in Case-Control Studies
Matching in a Case-Control Study
• Objective: To achieve comparability between cases and controls with regard to confounding variables
• Technique: For each case, choose a control without the case disease, of the same or similar age, at same service, same sex, etc.
Example of Matched Case-Control Study
• Cases: aplastic anemia seen in Baltimore from 1978-80
• Controls: patients with non-hematologic/nonmalignant disorders, matched to cases on age (± 5 years), sex, ethnic background and hospital of admission
• Hypothesis: subclinical HBV is associated with Aplastic Anemia
Matched case-control study
• 42 yr old black woman• 40 yr old white male• 57 yr old white woman• 55 yr old white woman• 48 yr old black men
• 44 yr old AA woman- diab.• 37 yr old white male- MI• 60 yr old white woman- AP• 55 yr old white woman- lupus• 49 yr old AA men- meningioma
Cases of Aplastic Anemia Controls (Patients)*
(*Admitted to the same hospital as index case with other diseases)
PAIRS
Cases
smoker nonsmoker
Controls
smoker
nonsmoker
Pair No. Case Control
1 smoker nonsmoker
2 smoker nonsmoker
3 nonsmoker smoker
4 smoker nonsmoker
5 nonsmoker nonsmoker
6 nonsmoker nonsmoker
7 nonsmoker smoker
8 smoker nonsmoker
9 nonsmoker nonsmoker
10 smoker smoker
Pairs of Cases and Controls Individually Matched by Age and Sex
PAIRS
Cases
smoker nonsmoker
Controls
smoker
nonsmoker
Pair No. Case Control
1 smoker nonsmoker
2 smoker nonsmoker
3 nonsmoker smoker
4 smoker nonsmoker
5 nonsmoker nonsmoker
6 nonsmoker nonsmoker
7 nonsmoker smoker
8 smoker nonsmoker
9 nonsmoker nonsmoker
10 smoker smoker
Pairs of Cases and Controls Individually Matched by Age and Sex
PAIRS
Cases
smoker nonsmoker
Controls
smoker
nonsmoker XXXX
Pair No. Case Control
1 smoker nonsmoker
2 smoker nonsmoker
3 nonsmoker smoker
4 smoker nonsmoker
5 nonsmoker nonsmoker
6 nonsmoker nonsmoker
7 nonsmoker smoker
8 smoker nonsmoker
9 nonsmoker nonsmoker
10 smoker smoker
Pairs of Cases and Controls Individually Matched by Age and Sex
PAIRS
Cases
smoker nonsmoker
Controls
smoker X X
nonsmoker XXXX
Pair No. Case Control
1 smoker nonsmoker
2 smoker nonsmoker
3 nonsmoker smoker
4 smoker nonsmoker
5 nonsmoker nonsmoker
6 nonsmoker nonsmoker
7 nonsmoker smoker
8 smoker nonsmoker
9 nonsmoker nonsmoker
10 smoker smoker
Pairs of Cases and Controls Individually Matched by Age and Sex
PAIRS
Cases
smoker nonsmoker
Controls
smoker X X
nonsmoker XXXX X X X
Pair No. Case Control
1 smoker nonsmoker
2 smoker nonsmoker
3 nonsmoker smoker
4 smoker nonsmoker
5 nonsmoker nonsmoker
6 nonsmoker nonsmoker
7 nonsmoker smoker
8 smoker nonsmoker
9 nonsmoker nonsmoker
10 smoker smoker
Pairs of Cases and Controls Individually Matched by Age and Sex
PAIRS
Cases
smoker nonsmoker
Controls
smoker X X X
nonsmoker XXXX X X X
Pair No. Case Control
1 smoker nonsmoker
2 smoker nonsmoker
3 nonsmoker smoker
4 smoker nonsmoker
5 nonsmoker nonsmoker
6 nonsmoker nonsmoker
7 nonsmoker smoker
8 smoker nonsmoker
9 nonsmoker nonsmoker
10 smoker smoker
Pairs of Cases and Controls Individually Matched by Age and Sex
= 4/2= 2.0
Odds Ratio for Matched Case-Control Studies
ORNo Pairs C a Co
No Pairs C a Co
. /
. /
Favors hypothesis
Against hypothesis
PAIRS
Cases
smoker nonsmoker
Controls
smoker 1 2
nonsmoker 4 3
Risk Factors for Brain Tumors in Subjects Aged <20 years: A Case-Control Study
(Gold et al, Am J Epidemiol 1979;109:309-19)
• Exploratory study of risk factors for brain tumors
• Subjects < 20 yrs old
• Cases: primary malignant brain tumors in Baltimore in 1965-75
• Normal controls: chosen from birth certificates on file, and matched on cases by sex, date of birth (±1 year) and race
• Interviews with parents of children
Risk Factors for Brain Tumors: Birthweight
3818<3629 g
783629+ gControls’ birthweight
<3629 g3629+ g
Cases’ birth weightExposed: 3629+ g
Unexposed: <3629 g
Odds Ratio= 18/7= 2.6
(Gold et al, Am J Epidemiol 1979;109:309-19)
A few notes on “Matching”• Most frequently used in case-control studies• Frequency vs. individual matching• Advantages:
– Intuitive, easy to explain– Guarantees certain degree of comparability in small studies– Efficient (if matching on a strong confounder)– Particularly useful when outpatients are studied, and sample size is
relatively small (e.g., <100 cases and <100 controls)• Example: Case-control study of risk factors for emphysema:
– For each newly diagnosed case of emphysema seen in an Outpatient Unit, select the next (control) patient without diabetes, with an age ± 2 years, of the same sex, and educational status
• Disadvantages:– Costly, usually logistically complicated– Inefficient if matching on a weak confounder– Questionable representativiness of control group (limits its use for other
case-control comparisons)– Cannot study the matching variable (and additive interaction)– Possibility of residual confounding
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• Statistical significance and confounding
Types of confounding
• Positive confoundingWhen 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 confoundingWhen 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).
10.1 10
Relative risk
3.0
5.0
3.02.0
0.40.3
0.4
0.7
0.7
3.0
Type of confounding:Positive Negative
TRUE, UNCONFOUNDED
OBSERVED, CRUDEx
x
x
x
X ?
• Confounding is not an “all or none” phenomenonA 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 confoundingControlling for one of several confounding variables does not guarantee that
confounding be 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 is misclassified
• 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)
Residual Confounding: Relationship Between Natural Menopause and Prevalent CHD (prevalent cases v. normal controls), ARIC
Study, Ages 45-64 Years, 1987-89
Model Odds Ratio (95% CI)
1 Crude 4.54 (2.67, 7.85)
2 Adjusted for age: 45-54 Vs. 55+ (Mantel-Haenszel)
3.35 (1.60, 6.01)
3 Adjusted for age:
45-49, 50-54, 55-59, 60-64 (Mantel-Haenszel)
3.04 (1.37, 6.11)
4 Adjusted for age: continuous (logistic regression)
2.47 (1.31, 4.63)
• Confounding is not an “all or none” phenomenonA 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 confoundingControlling for one of several confounding variables does not guarantee that
confounding be 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 is misclassified
• 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)
• 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.
Scenario 1: The relationship of obesity to mortality is confounded by hypertension, i.e., the relationship is
statistical but not causal
Confounding factor or part of the chain of causality?
Obesity
Mortality
Hypertension
confounder
exposure
outcome
Example: relationship of obesity to mortality
Scenario 2: The relationship of obesity to mortality is causal and mediated by hypertension
mediator
Obesity
Mortality
Hypertension
exposure
outcome
Confounding factor or part of the chain of causality?
Example: relationship of obesity to mortality
Scenario 3: In addition to being mediated by hypertension, the causal relationship of obesity to
mortality is direct
Obesity
Mortality
Hypertension
mediator
exposure
outcome
Confounding factor or part of the chain of causality?
Example: relationship of obesity to mortality
Scenario 4: In addition to being mediated by hypertension, the causal relationship of obesity to
mortality is mediated by other mechanisms
Hypertension
mediator
Obesity
MortalityMortality
exposure
outcome
Obesity
Other mechanisms, e.g., diabetes
Confounding factor or part of the chain of causality?
Example: relationship of obesity to mortality
The different scenarios are not mutually exclusive!
Hypertension
mediator
Obesity
MortalityMortality
exposure
outcome
Obesity
Other mechanisms, e.g., diabetes
Confounding factor or part of the chain of causality?
Example: relationship of obesity to mortality
Obesity and Mortality
Relative Risk
Unadjusted 2.5
Adjusted for age, gender and ethnic background 2.0
Adjusted for age, gender, ethnic background and systolic blood pressure (SBP)
1.3
Obesity and Mortality
Relative Risk
Unadjusted 2.5
Adjusted for age, gender and ethnic background 2.0
Adjusted for age, gender, ethnic background and systolic blood pressure (SBP)
1.3
For positive associations (exposures associated with a RR> 1.0):
%.
. .
. .Excess R isk E xp la ined
RR RR
RRUNAD J AD J
UNAD J
1 0
1 0 02 0 1 3
2 0 1 01 0 0 7 0 %
Statistical significance as criteria to assess the presence of confounding
E.g., a confounder might be ruled out in a case-control study solely because there is no statistically significant difference in the levels of the confounder comparing cases and controls.
Exposure
Case-cont
?Confounder
BAD IDEA!
If the confounder is strongly associated with the exposure, even a small difference between cases and controls (not statistically significant because of limited sample size) may still induce confounding… and vice versa
E.g., Study of menopause as predictor of myocardial infarction. Even a small difference in age between cases and controls (e.g., 1 year, NS) may result in confounding due to the strong association between age and “exposure” (menopause).
44
46
48
50
52
54
56
58
60
% p
os
t-m
en
op
au
sal
Age (years) 55 56
Odds Ratio= 60/40 ÷ 50/50 = 1.5
Example: Menopause as a risk factor
44
46
48
50
52
54
56
58
60
% p
os
t-m
en
op
au
sal
Age (years) 55 56
casescontrols
Odds Ratio= 60/40 ÷ 50/50 = 1.5