Transcript แนวคิดพื้นฐานทางระบาดวิท

Confounding, Effect Modification and Odd-Ratio
ดร. อรพิน กฤษณเกรียงไกร
คณะสาธารณสุขศาสตร์
มหาวิทยาลัยนเรศวร
Confounding bias
Criterion:
A variable, C, is a confounder of a variable, X, if
 C is associated with X
 C is associated with the outcome variable, Y
 C is not a link in the causal chain between X and the outcome
variable, Y
Note: If Y is dichotomous (0/1) C must be associated with X
separately for people with Y=0 and for people with Y = 1
Notation:
X
Y
C
Confounding bias
Example:
Assume it is found that people who consume alcohol have a higher
risk of developing oral cancer (OR >1).
Alcohol use
Oral cancer
Smoking
If the percentage of smokers is higher among people who drink
alcohol then among people who don’t (among those with and
those without oral cancer), part or all of apparent association
between alcohol use and oral cancer is due to smoking. After
adjusting for smoking the OR of alcohol consumption decreases
and moves closer to 1.
Confounding bias
Example:
Assume it is found that being Mormon protects against oral cancer
(OR >1).
Being Mormon
Oral cancer
Smoking
If the percentage of smokers is lower among Mormons than among
other people (among those with and those without oral cancer),
the apparent protective effect of being Mormon is due to the
lower percentage of smokers among Mormons. After adjusting
for smoking the OR of “being Mormon” increases and moves
closer to 1.
Confounding bias
Example:
Assume it is found that people with high stress levels are at an only slightly
greater risk of developing coronary heart disease (CHD) than people with
low stress levels (OR >1).
High stress level
CHD
Aspirin intake
If the percentage of people who take Aspirin is higher among those with high
stress level (among those with and among those without CHD), the
association between high stress levels and CHD is underestimated. The
underestimation is due to the higher percentage of people with high stress
levels. After adjusting for Aspirin intake the OR of high stress level
increases and moves further away from 1.
Confounding bias
Example:
In a study of the association between drinking water and oral
cancer is “smoking” a confounder?
It depends on whether the percentage of smokers varies among
people with different drinking water supplies.
Note:
We can adjust for confounding (i.e. try to eliminate confounding) in
the statistical analysis through.
– Stratification of the effects of 2 factors are mixed.
– Multivariate statistical modeling
Example of adjusting for confounding by stratification
Crude 2x2 table
D
D
Total
RF
1000
838
1838
RF
100
262
362
Total
1100
1100
2200
OR = 3.13
Risk factor (RF), confounder (C), and disease (D)
There is an association between risk factor (RF) and disease (D).
Question: Is the OR distorted due to confounding?
Crude 2x2 table
OR = 3.13
D
D
Total
RF
1000
838
1838
RF
100
262
362
Total
1100
1100
2200
1. Determine, separately for D and D, whether the confounder (C) and
the risk factor (RF) are associated.
2x2 table of RF and C for people
w/ the disease
D
D
Total
RF
900
100
1000
RF
10
90
Total
910
190
2x2 table of RF and C for people
w/o the disease
D
D
Total
RF
819
19
838
100
RF
91
171
262
1100
Total
910
190
1100
OR = 81 (very strong association) OR = 81 (very strong association)
Crude 2x2 table
OR = 3.13
D
D
Total
RF
1000
838
1838
RF
100
262
362
Total
1100
1100
2200
2. Determine, separately for RF and RF, whether the confounder (C)
and the outcome (D) are associated.
2x2 table of C and D for people
w/ the disease
D
D
Total
RF
900
819
1719
RF
100
19
Total
1000
838
2x2 table of C and D for people
w/o the disease
D
D
Total
RF
10
91
101
119
RF
90
171
261
1838
Total
100
262
362
OR = 0.2 (strong association)
OR = 0.2 (strong association)
Example of adjusting for confounding by stratification
1. Determine, separately for D and D, whether the confounder (C) and the risk
factor (RF) are associated.
The risk factor and the confounder are associated among those with
and among those without the disease (OR is similar or the same for
both stratum). Condition 1 is satisfied.
2. Determine, separately for RF and RF, whether the confounder (C)
and the outcome (D) are associated.
The confounder and the outcome are associated among those with
and among those without the disease (OR is similar or the same for
both stratum). Condition 2 is satisfied.
3. We must determine whether it is safe to assume C is not a link in
the causal chain between RF and D. If this assumption can be made
we can conclude that C is a confounder of D.
4. Determine the OR of the risk factor (RF) separately for C and C
2x2 table of C and D for people
w/ the disease
D
D
Total
RF
10
91
101
119
RF
90
171
261
1838
Total
100
262
362
D
D
Total
RF
900
819
1719
RF
100
19
Total
1000
838
2x2 table of RF and D for people
w/ the disease
RF
D
900
D
819
Total
1719
RF
10
91
Total
910
910
OR = 10
2x2 table of C and D for people
w/o the disease
2x2 table of RF and D for people
w/o the disease
RF
D
100
D
19
Total
119
101
RF
90
171
261
1820
Total
190
190
368
OR = 10
Example of adjusting for confounding by stratification


The crude OR of the RF (3.13) underestimates the true effect;
the adjusted OR is much greater than the crude OR.
An example of this type of confounding is the high stress level/
aspirin/ coronary heart disease example above.
Note:
After stratification (i.e. after separation of the effects) we find that
 The effect of the RF is not what we thought at first based on the
crude OR
 The effect of the RF is the same for those with and for those
without the confounder.
Example of adjusting for confounding by stratification
Calculate the crude OR for the RF and the outcome.
2.
Calculate the stratified OR’s for the RF and the outcome
stratified by the levels of the confounder.
If the crude OR and the stratified OR’s are very similar, no
confounding is present.
If the stratified OR’s are very similar but are different from the crude
OR, confounding is present.
If the stratified OR’s are different from each other and different from
the crude OR, effect modification is present.
1.
Effect Modification (Interaction)
We encounter effect modification when the effect of one variable
depends on another variable.
Example:
Assume a new treatment for a certain disease works very well for
young people but not very well for old people.
The effect of the treatment depends on age. We say that effect
modification is present or that an interaction between treatment
and exists.
Effect Modification (Interaction)
Example:
In a study of the association between a fatty diet and CHD is “high
cholesterol level” a confounder?
 High cholesterol is associated with a fatty diet (whether or not
CHD is present).
 High Cholesterol is associated with CHD.
The first two requirements for a confounder are satisfied.
 High cholesterol is a link in the causal chain between a fatty diet
and CHD and can therefore not be a confounder.
Fatty diet
High cholesterol
CHD
Effect Modification (Interaction)
Note 1:
Effect modification is not a bias but a description of the effect.
Therefore, if effect modification is present our goal is to detect and to
describe it.
Recall:
If confounding is present we try to eliminate it by stratification or multivariate
statistical modeling.
Note 2:
Effect modification can be detected through
 Stratification
 Multivariate statistical modeling
Effect Modification (Interaction)
What is the difference between confounding and effect modification?
Recall: Smoking is a confounder of the association between alcohol
consumption and oral cancer.
Thus, the effect of alcohol consumption on oral cancer is mixed with
the effect of smoking on oral cancer. To determine the true effect
of alcohol consumption on oral cancer we must separate the two
effects through stratification.
Note: The effect of alcohol consumption on oral cancer is the same
for smokers and non-smokers, i.e. it does not depend on a
person’s smoking status.
Effect Modification (Interaction)
Smoking is an effect modifier of the association between asbestos
exposure and lung cancer.
Thus, the effect of asbestos exposure on lung cancer depends on
smoking status.
The crude OR of asbestos exposure shows an average effect for
smokers and non-smokers. This information is not very useful.
However, if we stratify by smoking status and calculate the
stratified OR’s of asbestos exposure, we get information about the
effect of asbestos exposure on lung cancer separately for smokers
and for non-smoker.
The two stratified OR’s are different from each other and from the
crude OR
Example of detecting effect modification by stratification
Crude 2x2 table
D
RF
34
RF
110
Total
144
D
48
91
139
Total
82
201
283
OR = 0.59
Oral contraceptive use
seems to protect against
Ovarian cancer.
Risk factor (RF) is oral contraceptive use; Effect Modifier (EM)
age; and disease (D) ovarian cancer
Question: Since oral contraceptives have changed over the years,
is the protective effect of oral contraceptives true for older and
for younger women?
Crude 2x2 table
OR = 0.59
D
D
Total
RF
34
48
82
RF
110
91
201
Total
144
139
283
We can answer this question if we stratify by age
2x2 table of RF and D for old women
D
D
Total
RF
4
23
27
RF
98
74
Total
102
97
2x2 table of RF and D for young women
D
D
Total
RF
30
25
55
172
RF
12
17
29
199
Total
42
42
84
OR = 0.13 (protective effect)
OR = 1.7 (increase risk)
Effect Modification (Interaction)
Note that the stratified odds ratios are different from each other and
from the crude OR. This indicates that effect modification is present
and that the crude OR is not a complete (or vary useful) description
of the effect.
The stratified analysis indicates that oral contraceptives only protect
against ovarian cancer among older women, but slightly increase
the risk of developing ovarian cancer among younger women.
Note: Stratified OR’s can also be obtained from regression models.
Statistical models are most useful when we are considering multiple
risk factors, confounders, and effect modifiers, and when
continuous variables are present.
Effect Modification (Interaction)
Question: How do we know which variables to consider as potential
confounders or effect modifiers?
Answer:
 Clinical Knowledge
 Biological Knowledge
 Common sense
Note: It is impossible to think of every possible confounder or effect
modifier. Therefore, we will practically never be able to determine
the “true” OR.
Difference between effect modification and confounding
Example of effect modification
Assume we conducted a case-control study to explore the association
between asbestos exposure and lung cancer.
Further assume we got the following results:
For the entire study population: OR asbestos, lung cancer = 25
Among smokers:
OR asbestos, lung cancer = 35
Among non-smokers:
OR asbestos, lung cancer = 15
The effect of asbestos exposure on lung cancer depends on whether
or not the person smokes. It is much stronger for smokers than for
non-smokers.
Difference between effect modification and confounding
Example of effect modification
Assume we conducted a case-control study to explore the association between
playing card and lung cancer.
Further assume we got the following results:
For the entire study population: OR card, lung cancer = 3
Among old people:
OR card, lung cancer = 1
Among non-smokers:
OR card, lung cancer = 1
The effect of playing card on lung cancer does Not depend on age; it is the
same for old and for young people. Playing card does not affect the risk of
developing lung cancer differently in old and in young people.
Difference between effect modification and confounding
Example of effect modification
Comparing card players to persons who do not play card means
comparing a group of mostly old persons to a group of many young
persons. Thus, when only the crude effect is considered, we do
not know whether the apparent association is due to playing card
or due to age. By separating people into old and young persons,
we can “untangle” the effects.
Summary Odds Ratios
We are interested in the association between a risk factor (RF) and a
disease (D). We stratify by smoking status to determine whether
smoking is a confounder or an effect modifier.
We find that the risk factor-disease OR’s in the two strata are almost
identical (i.e. 2.0 and 2.1), but are different from the crude OR (i.e.
1.2). We conclude that smoking is a confounder. Which OR
should we report as the OR for the risk factor-disease association?
 Reporting the crude OR would mean reporting a biased result.
 Reporting the two stratum specific OR’s would unnecessarily
complicate the report.
Summary Odds Ratios
Instead we calculate a summary odds ratio, i.e. a weighted average of
the two stratum specific odds ratios.
A commonly used summary odds ratio is the Mantel-Heanszel odds
ratio. Let k be the stratum number, and K the total number of
strata.
Then OR MH = Σ (ak dk)/nk
Σ (bk ck)/nk
Example
D
D
Total
RF
432
1000
1432
Crude
RF
400
1004
1404
OR = 0.59
Total
832
2004
2838
Stratum 2
Stratum 1
D
D
Total
RF
152
120
272
RF
240
284
Total
392
404
OR = 1.5
D
D
Total
RF
280
880
1160
524
RF
160
720
880
796
Total
440
1600
2040
OR = 1.43
The two stratum specific odds ratio are similar to each other and different from
the crude odds ratio. Thus, we can calculate a summary odds ratio.
Summary Odds Ratios
Then OR MH = Σ (ak dk)/nk = (a1d1)/n1 + (a2d2)/n2
Σ (bk ck)/nk (b1c1)/n1 + (b2c2)/n2
= (152x284)/796 + (280x720)/2040 = 1.45
(120x240)/796 + (880x160)/2040
Note: When the stratum specific ORs are different from each other we
conclude that effect modification is present. In this case we Do Not
calculate a summary OR, but report the two stratified ORs.
Summary Odds Ratios
How do we determine whether stratum specific ORs are different?
 We can use a significant test (i.e. the Breslow-Day test).
 We can calculate the confidence intervals of the stratum specific OR’s
and check whether CI1 includes OR2 and vice versa.
95% CI = exp (ln OR) + 1.96 √1/a + 1/b + 1/c + 1/d )
 We can use biological criteria to make the decision.
Example
95% CI for the OR in stratum 1= exp (ln 1.5) +1.96 √1/152 + 1/120 + 1/240 + 1/284 )
= exp (0.41 + 0.29) or (1.13, 2.01); 95% CI includes 1.43
95% CI for the OR in stratum 2= exp (ln 1.43) +1.96 √1/280 + 1/880 + 1/160 + 1/720 )
= exp (0.36 + 0.22) or (1.15, 1.79); 95% CI includes 1.5
Summary Odds Ratios
Thus, the stratum specific ORs not significantly different and a
summary OR is appropriate.
Note:
Both stratum specific ORs are significantly different from the crude OR
(1.08). If they were not and biological criteria did not dictate
stratification, we could report the crude rather than the summary
OR.
Reference


Annette Bachand, Introduction to Epidemiology: Colorado
State University, Department of Environmental Health
Leslie Gross Portney and Mary P. Watkins (2000).
Foundations of Clinical Research: Applications to Practice.
Prentice-Hall, Inc. New Jersey, USA