Bias, Confounding,

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Spring 2008

• Bias, Confounding,
• and Effect Modification
• STAT 6395

Filardo and Ng
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Confounding

• Suppose we have observed an association between
  an exposure and disease in a cohort study or
  case-control study that
• We are confident was not a biased result due to
  a flaw in the design or execution of the study

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Confounding

• Suppose we have observed an association between
  an exposure and disease in a cohort study or
  case-control study that
• We are confident was not a random association
  due to chance variation (95 confidence interval
  for the estimate does not include 1.0)

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Confounding

• Suppose we have observed an association between
  an exposure and disease in a cohort study or
  case-control study that
• How do we now distinguish between a noncausal
  association due to confounding and a causal
  association?

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Hypothetical example of confounding comparison
of prostate cancer mortality rate in 2 geographic
areas

• The exposure of interest is geographic area
• Annual mortality rate from prostate cancer
• Region A 50 per 100,000
• Region B 20 per 100,000
• Relative risk 50/20 2.5
• Do these data show that living in Region A is a
  risk factor for prostate cancer?

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Prostate cancer mortality rate in 2 geographic
areas
per 100,000 per year Unadjusted (crude) RR
50/20 2.5 Age-adjusted RR 66.25/85 0.78
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Age as a confounder

• The large discrepancy between the age-adjusted
  RR (0.78) and the unadjusted RR (2.5) means that
  age confounded the observed association between
  geographic area and prostate cancer mortality

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Age as a confounder

• Age was a confounder because
• Age is a ? risk factor for prostate cancer
• Age was ? associated with geographic region
• Age is not ?? an intermediate step in a causal
  pathway between residence in a geographic region
  and prostate cancer mortality

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Age as a confounder

• Age is a common confounder in observational
  epidemiology because it is associated with many
  diseases and many exposures
• As distinct from a biased association, which is
  erroneous, the confounded association between
  geographic region and prostate cancer mortality,
  though not causal, is real

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Causal association (?)
Geographic area
Prostate cancer
RR(unadj)2.5 RR(adj)0.78
association
association
Age
Age confounded the relationship between
geographic area and prostate cancer
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Case-control study alcohol consumption and lung
cancer
OR(unadj) (390x175)/(325x110) 1.91
Note 90 of the 500 cases in the study were
smokers 25 of the 500 controls in the
study were smokers 80 of the smokers
drank
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Case-control study alcohol consumption and lung
cancer table for Smokers
OR (360x25)/(100x90) 1.00
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Case-control study alcohol consumption and lung
cancer table for NON Smokers
OR (30x150)/(225x20) 1.00
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Smoking ? and lung cancer
OR (450x375)/(125x50) 27.0
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Alcohol consumption ? and smoking
OR (460x170)/(255x115) 2.67
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Alcohol consumption and lung cancer (summary)

• Unadjusted OR 1.91
• Stratify by smoking status (2 strata -- smokers
  and nonsmokers)
• OR 1 for the relationship between alcohol
  consumption and lung cancer among both smokers
  and non smokers
• Smoking-adjusted OR (weighted average of the
  stratum-specific ORs) 1.00

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Smoking confounded the relationship between
alcohol consumption and lung cancer

• Large discrepancy between the smoking-adjusted
  OR (1.00) and the unadjusted OR (1.91) shows
  smoking was a confounder

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Smoking confounded the relationship between
alcohol consumption and lung cancer

• Smoking was a confounder because
• Smoking is ? a strong risk factor for lung cancer
• Smoking is ? associated with alcohol consumption
• Smoking is not ?? an intermediate step in a
  causal pathway between alcohol consumption and
  lung cancer

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Causal association NO
Alcohol consumption
Lung cancer
OR(unadj)1.91 OR(adj)1.00
association
association
Smoking
Smoking confounded the relationship between
alcohol consumption and lung cancer
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Confounding definition

• Confounding is a distortion of the association
  between exposure and outcome brought about by the
  association of another, extraneous exposure
  (confounder) with both the disease and the
  exposure of interest

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Confounding definition

• As distinct from a biased association, which is
  erroneous, a confounded association, though not
  causal, is real

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Properties of confounders

• A confounder must be associated with the
  exposure under study

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Properties of confounders
Causal association (?)
Lung cancer
Alcohol consumption
RR(unadj) RR(adj)

? association
Electomagnetic fields
Exposure to electromagnetic fields cannot
confound the relationship between alcohol
consumption and lung cancer
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Properties of confounders

• For an extraneous exposure to be a confounder,
  it is necessary, but not sufficient to just be
  associated with the exposure of interest

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Properties of confounders
Causal association (?)
Lung cancer
Alcohol consumption
RR(unadj) RR(adj)

association
Read meat
Red meat consumption cannot confound the
relationship between alcohol consumption and lung
cancer
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Properties of confounders

• A confounder must also be a risk factor for the
  disease

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Properties of confounders
Causal association NO
Alcohol consumption
Lung cancer
OR(unadj)1.91 OR(adj)1.00
association
association
Smoking
Smoking confounds the relationship between
alcohol consumption and lung cancer
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Properties of confounders

• A confounder cannot ?? be an intermediate
  variable in the causal pathway between the
  exposure of interest and the disease

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Properties of confounders
Willingness to get HIV testing
A Predictors / Confounders
HIV-related knowledge
Direct effect on HIV-related knowledge Direct
effect on willingness to get HIV testing
Mediated effect of A on willingness to get HIV
testing
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Properties of confounders
Causal association ?
Exposure
Disease
/ - association
/ - association
Confounder
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Avoiding confounding with appropriate study design

• Randomization
• Restriction
• Matching

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Randomization

• done in experimental studies ONLY
• Subjects are randomly allocated between n groups
  ...ensuring that known and unknown potential
  confounder distributions are similar across groups

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Restriction

• Restrict the selection criteria for subjects
  to a single category of an exposure that is a
  potential confounder
• in the cohort study of alcohol consumption and
  lung cancer, restrict the cohort to persons who
  have never smoked.
• Enhances internal validity, but could hurt
  external validity

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Matching

• In a case-control study, selection of controls
  who are identical to, or nearly identical to, the
  cases with respect to the distribution of one or
  more potential confounding factors
• Matching is intuitively appealing, but its
  implications, particularly in case-control
  studies, are much more complicated than one might
  at first suppose

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Assessing the presence of confounding during
analysis

• Is the potential confounder related to both the
  exposure and the disease?
• Stratification Is the unadjusted OR or RR
  similar in magnitude to the ORs or RRs observed
  within strata of the potential confounder?
• Adjustment Is the unadjusted OR or RR similar
  in magnitude to the OR or RR adjusted for the
  presence of the potential confounder?

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Assessing the presence of confounding during
analysis

• Is the potential confounder related to both the
  exposure and the disease?
• Confounding is judged to occur when the adjusted
  and unadjusted values differ meaningfully.

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Pandey DK et al. Dietary vitamin C and
beta-carotene and risk of death in middle-aged
men. The Western Electric study.

• Concurrent cohort study
• Hypothesis intake of vitamin C and beta carotene
  (both anti-oxidants) are protective against
  all-cause mortality
• Potential confounder cigarette smoking

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Unadjusted mortality rates and RRs according to
vitamin C/beta-carotene intake index
deaths per 1,000 person-years
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Percentage distribution of vitamin
C/beta-carotene intake index by smoking status at
baseline
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Mortality rates and RRs by current smoking at
baseline
deaths per 1,000 person-years
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Mortality rates and RRs for vitamin
C/beta-carotene intake index, stratified by
current smoking at baseline
deaths per 1,000 person-years
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Unadjusted and smoking-adjusted mortality RRs
according to vitamin C/beta carotene intake index
Adjusted for smoking using the direct method
with the total cohort as the standard population
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Vitamin C/ beta-carotene
Causal association (?)
Mortality
Medium intake RR(unadj)0.82 RR(adj)0.85 High
intake RR(unadj)0.79 RR(adj)0.81
- association
association
Smoking
Smoking did not confound the association between
vitamin C/beta carotene intake and all-cause
mortality
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Methods of adjusting for (controlling for)
confounding in the analysis

• Adjustment methods based on stratification
• Mathematical models (multivariable analysis)

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Adjustment methods based on stratification

• Stratify by the confounder
• Calculate a single estimate of effect across the
  strata (adjusted OR or adjusted RR), which is a
  weighted average of the RRs or ORs across the
  strata

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Adjustment methods based on stratification

• Stratify by the confounder
• Calculate the RR or OR for the association
  between the exposure and disease within each
  stratum of the confounder

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3 methods of obtaining a weighted average

• Direct adjustment (used in cohort studies) --
  weights are based on the distribution of the
  confounder in a standard population

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3 methods of obtaining a weighted average

• Indirect adjustment (mainly used in occupational
  retrospective cohort studies) -- weights are
  based on the distribution of the confounder in
  the study population

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3 methods of obtaining a weighted average

• Mantel-Haenszel method (most common adjustment
  method based on stratification used in
  case-control or cohort studies) -- weights are
  approximately proportional to the reciprocals of
  the variances of the ORs or RRs within each
  stratum

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Shapiro S et al. Oral-contraceptive use in
relation to myocardial infarction a case-control
study

• Hypothesis recent use of oral contraceptives is
  associated with risk of myocardial infarction
• Cases 234 premenopausal women with a definite
  first myocardial infarction (median age 43)
• Controls 1,742 premenopausal women admitted for
  musculoskeletal conditions, trauma, abdominal
  conditions, and many miscellaneous conditions
  (median age 36)

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Hospital-based case-control study
OR(unadj) (29x1607)/(135x205) 1.7
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Age is a likely confounder

• Age is ? a risk factor for myocardial infarction
• Age is ? negatively associated with oral
  contraceptive use

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Assess for confounding by age

• Perform a stratified analysis by age
• Compare the Mantel-Haenszel adjusted OR with the
  unadjusted OR
• Mantel-Haenszel age-adjusted OR 4.0
• Unadjusted OR 1.7

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Limitations of adjustment methods based on
stratification

• There is often more than one potential confounder
• Allow adjustment only for categorical variables
  continuous variables must be categorized
• Stratification methods are usually limited to
  adjustment for one or two confounders with a
  small number of categories each

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Multivariable models

• Simultaneous adjustment for multiple potential
  confounders, including continuous variables
• Potential confounders are included as variables
  in the model along with the exposure under study
• Commonly used models
• Logistic regression case-control and cohort
  studies
• Cox proportional hazards model cohort studies
• Poisson regression cohort studies

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Effect Modification (Interaction) - Oral
contraceptives and myocardial infarction example

• Definition variation in the magnitude of the
  association between an exposure and a disease
  (variation in the RR or OR) across strata of
  another exposure
• Are the odds ratios regarding the association
  between OC use and MI heterogeneous across the
  smoking status strata?

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Oral contraceptives and myocardial infarction
stratified analysis by smoking
Effect modification has an underlying biologic
basis it is not merely a statistical phenomonon.
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Other effect modification examples

• Menopausal status modifies the association
  between obesity and breast cancer
• The association between gender and hip fracture
  is modified by age
• Nutrition modifies the association between HIV
  infection and progression of latent tuberculosis
  infection to active tuberculosis

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Effect modification example Lyon et al. Smoking
and carcinoma in situ of the uterine cervix
OR(unadj) (130x198)/(45x87) 6.6
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Effect modification example Lyon et al. Smoking
and carcinoma in situ of the uterine cervix
OR(unadj) (130x198)/(45x87)
6.6 Mantel-Haenszel age-adjusted OR 6.3 p-value
for heterogeneity lt0.01
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Confounding vs. Effect Modification

• Confounding Confounding is a distortion of the
  RR or OR that should be adjusted for
• Effect modification Effect modification is a
  property of a putative causal association.
• It is a finding to be detected and estimated, not
  a bias to be avoided or confounding to be
  adjusted for
• An effect modifier may or may not itself be a
  confounder

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Confounding vs. Effect Modification cohort study
example

• The unadjusted RR for the association between
  Exposure A and Disease X is 9.7
• How does age affect the relationship between
  Exposure A and Disease X? 4 hypothetical scenarios

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Confounding vs. Effect Modification cohort study
example
Iexp(A) /Inonexp(A) RR(unadj) 9.7 RR (adj)
10.1
Age is neither a confounder nor an effect modifier
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Confounding vs. Effect Modification cohort study
example
Iexp(A) /Inonexp(A) RR(unadj) 9.7 RR(adj)
10.1
Age is an effect modifier, but not a confounder
Note When there is effect modification, we
cannot summarize the relationship between
Exposure A and Disease X with a single number
RR(adj)
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Confounding vs. Effect Modification cohort study
example
Iexp(A) /Inonexp(A) RR(unadj) 9.7 RR(adj) 4.3
Age is a confounder, but not an effect modifier
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Confounding vs. Effect Modification cohort study
example
Iexp(A) /Inonexp(A) RR(unadj) 9.7 RR(adj)
4.3
Age is a confounder and an effect modifier
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Case-control study of alcohol consumption,
smoking, and oral cancer
OR(unadj) (80x125)/(40x40) 6.25
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Case-control study of alcohol consumption,
smoking, and oral cancer
OR(unadj) (84x120)/(45x36) 6.22
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Case-control study of alcohol consumption,
smoking, and oral cancer
Unadjusted OR 6.25 ? Smoking-adjusted OR
4.0 Smoking is a confounder of the relationship
between alcohol consumption and oral cancer and
no effect modification
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Case-control study of alcohol consumption,
smoking, and oral cancer
Unadusted OR 6.22 ? Alcohol-adjusted OR
4.0 Alcohol consumption is a confounder of the
relationship between smoking and oral cancer and
no effect modification
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ORs for the joint effect of smoking and alcohol
consumption on risk of oral cancer
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Assessment of effect modification (summary)

• Stratify by the potential effect modifier
• Calculate the RR or OR for the association
  between the exposure and disease within each
  stratum of the potential effect modifier

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Assessment of effect modification (summary)

• Assess the degree of heterogeneity of the RRs or
  ORs across the strata by inspection
• Calculate a p-value for heterogeneity however,
  remember that formal test for heterogeneity are
  conservative and they might fail to detect effect
  modification