1 Confounding and Interaction: Part II Confounder vs. intermediary variables Factors to be...
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Transcript of 1 Confounding and Interaction: Part II Confounder vs. intermediary variables Factors to be...
1
Confounding and Interaction: Part II
Confounder vs. intermediary variables
Factors to be considered as potential confounders in designing a study
Methods to reduce confounding
– during study design:
» Randomization
» Restriction
» Matching
– during study analysis:
» Stratified analysis
Interaction
– What is it? How to detect it?
– Additive vs. multiplicative interaction
– Comparison with confounding
– Statistical testing for interaction
– Implementation in Stata
2
Exercise and CAD
HDL is associated with exercise
HDL is associated with CAD
When evaluating the relationship between exercise and CAD, is HDL a confounder or an intermediary?
ExerciseExercise
CADCAD
HDLHDL
HDLHDL
3
It depends on the pathway under investigation
If interest is in a pathway other than through HDL, then HDL is a confounder
Here, HDL is extraneous to pathway under study
Confounding factors are extraneous factors
ExerciseExercise
CADCAD
not yet specified
mechanism
not yet specified
mechanismHDLHDL ??
4
Exercise and CAD If pathway under study goes thru HDL, then HDL is
an intermediary variable.
e..g., Does exercise influence CAD risk in a newly studied population (elderly Asians)?
Hence, classification of HDL as confounder or intermediary depends upon the biological pathway under investigation and the research question
ExerciseExercise
CADCAD
HDLHDLHDL is not a confounder
here
HDL is not a confounder
here
5
What is NOT a Confounder?
Variables that are the RESULT of the disease, regardless of their association with the exposure are NOT confounders
ConfounderConfounder
DD
6
Lung CA
Lung CA
SmokingSmoking
CoughCough??
Cough is not a confounder.
Do not adjust for it!
Cough is not a confounder.
Do not adjust for it!
7
When Planning a Study, Which Factors Should be Considered as
Potential Confounders?
Any factor for which prior evidence indicates it is a confounder
and
In newer research areas:
– factors known to be associated with the disease and which may be associated with exposure
When in doubt, plan on measuring ALL factors associated with the disease
– i.e. If you don’t, you may regret it later
8
Seeking cause of high Marin cancer rates Activists canvass residents to search for trendsSunday, November 10, 2002
Thousands of volunteers scattered across Marin County under baleful skies Saturday in an unprecedented grassroots campaign against the region's soaring cancer rate.
Armed with surveys, some 2,000 volunteers went door to door in every neighborhood in the county, asking people whether they or anyone in their household has ever been diagnosed with cancer in Marin. The volunteers hope to collect enough money to hire an epidemiologist to analyze the data for use in future studies.
9
Preventing or Managing Confounding
ConfounderConfounder
DD
ANOTHER PATHWAY TO
GET TO THE DISEASE
ANOTHER PATHWAY TO
GET TO THE DISEASE
11
Methods to Prevent or Manage Confounding
By prohibiting at least one “arm” of the exposure- confounder - disease structure, confounding is precluded
12
Randomization to Reduce Confounding
Definition: random assignment of subjects to exposure (e.g., treatment) categories
All subjects Randomize
One of the most important inventions of the 20th Century!
Exposed
Unexposed
14
Randomization to Reduce Confounding
Definition: random assignment of subjects to exposure (or treatment) categories
All subjects Randomize
Applicable only for intervention (experimental) studies
Special strength of randomization is its ability to control the effect of confounding variables about which the investigator is unaware
Does not, however, eliminate confounding!
Exposed
Unexposed
15
Restriction to Reduce Confounding
AKA Specification
Definition: Restrict enrollment to only those subjects who have a specific value/range of the confounding variable
– e.g., when age is confounder: include only subjects of same narrow age range
17
Restriction to Reduce Confounding
Advantages:
– conceptually straightforward
Disadvantages:
– may limit number of eligible subjects
– inefficient to screen subjects, then not enroll
– “residual confounding” may persist if restriction categories not sufficiently narrow (e.g. “decade of age” might be too broad)
– limits generalizability– not possible to evaluate the relationship of
interest at different levels of the restricted variable (i.e. cannot assess interaction)
18
Matching to Reduce Confounding
Definition: only unexposed/non-case subjects are chosen who match those of the reference group (either exposed or cases) in terms of the confounder in question
– Results in the same distribution of the potential confounder as seen in the exposed/cases
19
Matching to Reduce Confounding
Mechanics depends upon study design:
– e.g. cohort study: unexposed subjects are “matched” to exposed subjects according to their values for the potential confounder.
» e.g. matching on race
One unexposedblack enrolled for each exposedblack
One unexposedasian enrolled for each exposedasian
– e.g. case-control study: non-diseased controls are “matched” to diseased cases
» e.g. matching on age
One controlage 50 enrolled for each caseage 50
One controlage 70 enrolled for each caseage 70
21
Advantages of Matching1. Useful in preventing confounding by factors which
would be difficult to manage in any other way
– e.g. “neighborhood” is a nominal variable with multiple values. (complex nominal variable)
– e.g. Cohort study of the effect of stop light cameras in preventing MVA’s
» Exposed: cars going thru stop lights with camera
» Unexposed: cars going thru stop lights without camera
» Potential confounder: ambient driving practices in the neighborhood
» Relying upon random sampling of unexposed cars without attention to neighborhood may result in (especially in a small study) choosing no unexposed cars from some of the neighborhoods seen in the exposed group
» Even if all neighborhoods seen in the exposed group were represented in the unexposed group, adjusting for neighborhood with “analysis phase” strategies are problematic
22
Advantages of Matching
2. By ensuring a balanced number of cases and controls (in a case-control study) or exposed/unexposed (in a cohort study) within the various strata of the confounding variable, statistical precision is increased
23
Smoking, Matches, and Lung Cancer
Lung Ca No Lung CaMatches 820 340No Matches 180 660
Lung CaNo
Lung CAMatches 810 270No Matches 90 30
900 300
B. Controls matched on smoking
A. Random sample of controls
Crude
Non-SmokersSmokers
OR crude = 8.8
OR CF+ = ORsmokers = 1.0 OR CF- = ORnon-smokers = 1.0
ORadj= 1.0 (0.75 to 1.34)
Lung CaNo
Lung CAMatches 10 70No Matches 90 630
100 700
Stratified
Smokers Non-Smokers
OR CF+ = ORsmokers = 1.0 OR CF- = ORnon-smokers = 1.0
ORadj= 1.0 (0.69 to 1.45)
Lung CaNo
Lung CAMatches 810 810No Matches 90 90
900 900
Lung CaNo
Lung CAMatches 10 10No Matches 90 90
100 100
24
Disadvantages of Matching
1. Finding appropriate matches may be difficult and expensive and limit sample size (e.g., have to throw out a case if cannot find a control). Therefore, the gains in statistical efficiency can be offset by losses in overall efficiency.
2. In a case-control study, factor used to match subjects cannot be itself evaluated as a risk factor for the disease. In general, matching decreases robustness of study to address secondary questions.
3. Decisions are irrevocable - if you happened to match on an intermediary, you likely have lost ability to evaluate role of exposure in question.
4. If potential confounding factor really isn’t a confounder, statistical precision will be worse than no matching.
25
Stratification to Reduce Confounding
Goal: evaluate the relationship between the exposure and outcome in strata homogeneous with respect to potentially confounding variables
Each stratum is a mini-example of restriction!
CF = confounding factor
Disease No DiseaseExposedUnexposed
Crude
Dis NoDis
Exp
Unexp
Dis NoDis
Exp
Unexp
Dis NoDis
Exp
Unexp
Stratified
CF Level I CF Level 3CF Level 2
26
Smoking, Matches, and Lung Cancer
Lung Ca No Lung CaMatches 820 340No Matches 180 660
Lung CaNo
Lung CAMatches 810 270No Matches 90 30
Stratified
Crude
Non-SmokersSmokersOR crude
OR CF+ = ORsmokers OR CF- = ORnon-smokers
ORcrude = 8.8
ORsmokers = 1.0
ORnon-smoker = 1.0
Lung CaNo
Lung CAMatches 10 70No Matches 90 630
27
Stratifying by Multiple Potential Confounders
Potential Confounders: Race and Smoking
To control for multiple confounders simultaneously, must construct mutually exclusive and exhaustive strata:
White Black Latino
Smokers Non-smokers
CrudeCAD No CAD
ChlamydiaNo chlamydia
28
Stratifying by Multiple Potential Confounders
Crude
Stratifiedwhite smokers
latino non-smokers
black non-smokers
CAD NoCAD
Chlamydia
NoChlamydia
white non-smokers
black smokers latino smokers
CAD No CADChlamydiaNo chlamydia
CAD NoCAD
Chlamydia
NoChlamydia
CAD NoCAD
Chlamydia
NoChlamydia
CAD NoCAD
Chlamydia
NoChlamydia
CAD NoCAD
Chlamydia
NoChlamydia
CAD NoCAD
Chlamydia
NoChlamydia
29
Summary Estimate from the Stratified Analyses
Goal: Create an unconfounded (“adjusted”) estimate for the relationship in question
– e.g. relationship between matches and lung cancer after adjustment (controlling) for smoking
Process: Summarize the unconfounded estimates from the two (or more) strata to form a single overall unconfounded “summary estimate”
– e.g. summarize the odds ratios from the smoking stratum and non-smoking stratum into one odds ratio
30
Smoking, Matches, and Lung Cancer
Lung Ca No Lung CaMatches 820 340No Matches 180 660
Lung CaNo
Lung CAMatches 810 270No Matches 90 30
Stratified
Crude
Non-SmokersSmokersOR crude
OR CF+ = ORsmokers OR CF- = ORnon-smokers
ORcrude = 8.8 (7.2, 10.9)
ORsmokers = 1.0 (0.6, 1.5)
ORnon-smoker = 1.0 (0.5, 2.0)
Lung CaNo
Lung CAMatches 10 70No Matches 90 630
31
Smoking, Caffeine Use and Delayed Conception
Delayed Not DelayedSmoking 26 133No Smoking 64 601
DelayedNot
DelayedSmoking 15 61No Smoking 47 528
Stratified
Crude
No Caffeine Use
Heavy Caffeine Use
RR crude = 1.7
RRno caffeine use = 2.4
DelayedNot
DelayedSmoking 11 72No Smoking 17 73
RRcaffeine use = 0.7
32
Underlying Assumption When Forming a Summary of the Unconfounded
Stratum-Specific Estimates
If the relationship between the exposure and the outcome varies meaningfully (in a clinical/biologic sense) across strata of a third variable, then it is not appropriate to create a single summary estimate of all of the strata
i.e. the assumption is that no statistical interaction is present
33
Statistical Interaction
Definition
– when the magnitude of a measure of association (between exposure and disease) meaningfully differs according to the value of some third variable
Synonyms
– Effect modification
– Effect-measure modification
– Heterogeneity of effect
Proper terminology
– e.g. Smoking, caffeine use, and delayed conception
» Caffeine use modifies the effect of smoking on the risk ratio for delayed conception.
» There is interaction between caffeine use and smoking in the risk ratio for delayed conception.
» Caffeine is an effect modifier in the relationship between smoking and delayed conception.
34
No Interaction
0.05
0.150.15
0.45
0.01
0.1
1
10
Unexposed Exposed
Ris
k o
f D
ise
as
e
Third Variable Present
Third Variable Absent
Interaction
0.05
0.150.08
0.9
0.01
0.1
1
10
Unexposed Exposed
Ris
k o
f D
ise
as
e
Third Variable Present
Third Variable Absent
35
Qualitative Interaction
0.180.13
0.08
0.2
0.01
0.1
1
10
Unexposed Exposed
Ris
k o
f D
ise
as
e
Third Variable Present
Third Variable Absent
36
Interaction is likely everywhere
Susceptibility to infections
– e.g.,
» exposure: sexual activity
» disease: HIV infection
» effect modifier: chemokine receptor phenotype
Susceptibility to non-infectious diseases
– e.g.,
» exposure: smoking
» disease: lung cancer
» effect modifier: genetic susceptibility to smoke
Susceptibility to drugs
» effect modifier: genetic susceptibility to drug
But in practice to date, difficult to document
37
Smoking, Caffeine Use and Delayed Conception:
Additive vs Multiplicative Interaction
Delayed Not DelayedSmoking 26 133No Smoking 64 601
DelayedNot
DelayedSmoking 15 61No Smoking 47 528
Stratified
Crude
No Caffeine Use
Heavy Caffeine Use
RR crude = 1.7
RD crude = 0.07
RRno caffeine use = 2.4
RDno caffeine use = 0.12
DelayedNot
DelayedSmoking 11 72No Smoking 17 73
RRcaffeine use = 0.7
RDcaffeine use = -0.06
RD =
Risk Difference = Risk exposed - Risk Unexposed
38
Additive vs Multiplicative Interaction
Assessment of whether interaction is present depends upon the measure of association
– ratio measure (multiplicative interaction) or difference measure (additive interaction)
– Hence, the term effect-measure modification
Absence of multiplicative interaction typically implies presence of additive interaction
0.05
0.150.15
0.45
0.01
0.1
1
Unexposed Exposed
Ris
k o
f D
ise
as
e
Additive interaction present
39
Additive vs Multiplicative Interaction
Absence of additive interaction typically implies presence of multiplicative interaction
0.05
0.150.150.25
0.01
0.1
1
Unexposed Exposed
Ris
k o
f D
ise
as
e
Multiplicative interaction present
40
Additive vs Multiplicative Interaction
Presence of multiplicative interaction may or may not be accompanied by additive interaction
0.1
0.20.2
0.6
0.01
0.1
1
Unexposed Exposed
Ris
k o
f D
ise
as
e
0.1
0.2
0.05
0.15
0.01
0.1
1
Unexposed Exposed
Ris
k o
f D
ise
as
e
Additive interaction present
No additive interaction
41
Additive vs Multiplicative Interaction
Presence of additive interaction may or may not be accompanied by multiplicative interaction
0.1
0.20.2
0.6
0.01
0.1
1
Unexposed Exposed
Ris
k o
f D
ise
as
e
0.1
0.3
0.05
0.15
0.01
0.1
1
Unexposed Exposed
Ris
k o
f D
ise
as
e Multiplicative interaction absent
Multiplicative interaction present
42
Additive vs Multiplicative Interaction
Presence of qualitative multiplicative interaction is always accompanied by qualitative additive interaction
Qualitative Interaction
0.18
0.13
0.08
0.2
0.01
0.1
1
Unexposed Exposed
Ris
k o
f D
ise
as
e
Third Variable Present
Third Variable Absent
43
Additive vs Multiplicative Scales
Additive measures (e.g., risk difference):
– readily translated into impact of an exposure (or intervention) in terms of number of outcomes prevented
» e.g. 1/risk difference = no. needed to treat to prevent (or avert) one case of disease
or no. of exposed persons one needs to take the exposure away from to avert one case of disease
– gives “public health impact” of the exposure
Multiplicative measures (e.g., risk ratio)
– favored measure when looking for causal association
44
Additive vs Multiplicative Scales
Causally related but minor public health importance
– RR = 2
– RD = 0.0001 - 0.00005 = 0.00005
– Need to eliminate exposure in 20,000 persons to avert one case of disease
Causally related but major public health importance
– RR = 2
– RD = 0.2 - 0.1 = 0.1
– Need to eliminate exposure in 10 persons to avert one case of disease
Disease No DiseaseExposed 10 99990Unexposed 5 99995
Disease No DiseaseExposed 20 80Unexposed 10 90
45
Smoking, Family History and Cancer:
Additive vs Multiplicative Interaction
Cancer No CancerSmoking 50 150No Smoking 25 175
CancerNo
CancerSmoking 10 90No Smoking 5 95
Stratified
Crude
Family History Absent
Family History Present
RRno family history = 2.0
RDno family history = 0.05
CancerNo
CancerSmoking 40 60No Smoking 20 80
RRfamily history = 2.0
RDfamily history = 0.20
• No multiplicative interaction but presence of additive interaction
• If goal is to define sub-groups of persons to target:
- Rather than ignoring, it is worth reporting that only 5 persons with a family history have to be prevented from smoking to avert one case of cancer
46
Confounding vs Interaction
Confounding
– An extraneous or nuisance pathway that an investigator hopes to prevent or rule out
Interaction
– A more detailed description of the “true” relationship between the exposure and disease
– A richer description of the biologic system
– A finding to be reported, not a bias to be eliminated
47
When Assessing the Association Between an Exposure and a Disease,
What are the Possible Effects of a Third Variable?
EM+
_Confounding:
ANOTHER PATHWAY TO
GET TO THE DISEASE
Confounding:
ANOTHER PATHWAY TO
GET TO THE DISEASE
Effect Modifier (Interaction):
MODIFIES THE EFFECT OF THE EXPOSURE
D
I C Intermediary
Variable
No Effect
48
Smoking, Caffeine Use and Delayed Conception
Delayed Not DelayedSmoking 26 133No Smoking 64 601
DelayedNot
DelayedSmoking 15 61No Smoking 47 528
Stratified
Crude
No Caffeine Use
Heavy Caffeine Use
RR crude = 1.7
RRno caffeine use = 2.4
DelayedNot
DelayedSmoking 11 72No Smoking 17 73
RRcaffeine use = 0.7
RR adjusted = 1.4 (95% CI= 0.9 to 2.1)
Here, adjustment is contraindicated!
49
Chance as a Cause of Interaction?
Down’s No Down’sSpermicide Use 4 109No Spermicide 12 1145
Down’sNo
Down’sSpermicide 3 104No Spermicide 9 1059
Stratified
Crude
Age > 35Age < 35
OR crude = 3.5
ORage >35 = 5.7
Down’sNo
Down’sSpermicide 1 5No Spermicide 3 86
ORage <35 = 3.4
50
Statistical Tests of Interaction: Test of Homogeneity (heterogeneity)
Null hypothesis: The individual stratum-specific estimates of the measure of association differ only by random variation
– i.e., the strength of association is homogeneous across all strata
– i.e., there is no interaction
A variety of formal tests are available with the general format, following a chi-square distribution:
where:
– effecti = stratum-specific measure of assoc.
– var(effecti) = variance of stratum-specifc m.o.a.
– summary effect = summary adjusted effect
– N = no. of strata of third variable
For ratio measures of effect, e.g., OR, log transformations are used:
The test statistic will have a chi-square distribution with degrees of freedom of one less than the number of strata
i i
iN effect
effectsummaryeffectsquarechi
)var(
) ( 2
1
51
Interpreting Tests of Homogeneity
If the test of homogeneity is “significant”, this is evidence that there is heterogeneity (i.e. no homogeneity)
– i.e., interaction may be present
The choice of a significance level (e.g. p < 0.05) is somewhat controversial.
– There are inherent limitations in the power of the test of homogeneity
» p < 0.05 is likely too conservative
– One approach is to declare interaction for p < 0.20
» i.e., err on the side of assuming that interaction is present (and reporting the stratified estimates of effect) rather than on reporting a uniform estimate that may not be true across strata.
52
Tests of Homogeneity with Stata
1. Determine crude measure of association
e.g. for a cohort study
“cs outcome-variable exposure-variable”
for smoking, caffeine, delayed conception:
-exposure variable = smoking
-outcome variable = delayed
-third variable = caffeine
“cs delayed smoking”
2. Determine stratum-specific estimates by levels of third variable
“cs outcome-var exposure-var, by(third-variable)”
e.g. cs delayed smoking, by(caffeine)
53
. cs delayed smoking
| smoking | | Exposed Unexposed | Total
-----------------+------------------------+----------
Cases | 26 64 | 90
Noncases | 133 601 | 734
-----------------+------------------------+----------
Total | 159 665 | 824
| |
Risk | .163522 .0962406 | .1092233
| Point estimate | [95% Conf. Interval]
|------------------------+----------------------
Risk difference | .0672814 | .0055795 .1289833
Risk ratio | 1.699096 | 1.114485 2.590369
– +----------------------------------------------- chi2(1) = 5.97 Pr>chi2 = 0.0145
. cs delayed smoking, by(caffeine)
caffeine | RR [95% Conf. Interval] M-H Weight
-----------------+-------------------------------------------------
no caffeine | 2.414614 1.42165 4.10112 5.486943
heavy caffeine | .70163 .3493615 1.409099 8.156069
-----------------+-------------------------------------------------
Crude | 1.699096 1.114485 2.590369
M-H combined | 1.390557 .9246598 2.091201
-----------------+-------------------------------------------------
Test of homogeneity (M-H) chi2(1) = 7.866 Pr>chi2 = 0.0050
54
Declare vs Ignore Interaction?
Relative Risks for aGiven Exposure and
Disease
Potential Effect ModifierPresent Absent
P value forheterogeneity
Declare orIgnore
Interaction
2.3 2.6 0.45 Ignore
2.3 2.6 0.001 Ignore
2.0 20.0 0.001 Declare
2.0 20.0 0.20 Declare
2.0 20.0 0.30 +/-
3.0 4.5 0.30 Ignore
3.0 4.5 0.001 +/-
0.5 3.0 0.001 Declare
0.5 3.0 0.20 Declare
0.5 3.0 0.30 +/-