Confounding in epidemiology

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Confounding in epidemiology
Maura Pugliatti, MD, PhDAssociate Professor of
NeurologyDept. of Clinical and Experimental
Medicine, Unit of Clinical NeurologyUniversity
of Sassari, Italy 1st International Course of
Neuroepidemiology Chisinau, Moldova, 24-28 Sept.
2012
2
Definitions

• Confounding, the situation in which an apparent
  effect of an exposure on risk is explained by its
  association with other factors, is probably the
  most important cause of spurious associations in
  observational epidemiology
• BMJ Editorial The scandal of poor
  epidemiological research BMJ 2004329868-869

Bias of the estimated effect of an exposure on
an outcome, due to the presence of a common cause
of the exposure and the outcome Porta, 2008
3
Overview

• Causality central concern of epidemiology
• Confounding central concern when establishing
  causality
• Four approaches to understand confounding
• Avoiding and controlling for confounding is
  essential in health research

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Causality

• Main application of epidemiology
• to identify etiologic (causal) associations
  between exposure(s) and outcome(s)

?
Exposure
Outcome
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Key biases in identifying causal effects
Causal Effect
Random Error
Confounding
Information bias (misclassification)
Selection bias
Bias in inference
Reporting publication bias
Bias in knowledge use
RRcausal truth
RRassociation
Adapted from Maclure, M, Schneeweis S.
Epidemiology 200112114-122.
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Confounding four approaches

• Mixing of effects
• Based on a priori criteria (classical approach)
• Data-based criteria
• Counterfactual and non-comparability approaches
• Overlapping

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• Confounding is confusion, or mixing, of effects
  the effect of the exposure is mixed together with
  the effect of another variable, leading to bias

Latin confundere to mix together
Rothman KJ. Epidemiology. An introduction.
Oxford Oxford University Press, 2002
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• Association between birth order and Down Syndrome

Data from Stark and Mantel (1966)
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Association between maternal age and Down
Syndrome
Data from Stark and Mantel (1966)
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Association between maternal age and Down
Syndrome, stratified by birth order
Data from Stark and Mantel (1966)
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A factor is a confounder if 3 criteria are met
C

• 1. A confounder must be causally or non-causally
  associated with the exposure in the source
  population (study base) being studied

E
2. A confounder must be a causal risk factor (or
a surrogate measure of a cause) for the disease
in the unexposed cohort and
C
D
3. A confounder must not be an intermediate cause
(not an intermediate step in the causal pathway
between the exposure and the disease)
X
D
C
E
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Confounder C
Szklo M, Nieto JF. Epidemiology Beyond the
basics. Aspen Publishers, Inc., 2000. Gordis L.
Epidemiology. Philadelphia WB Saunders, 4th
Edition.
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Confounder parent of the exposure not
daughter of the exposure!!!
Exposure
Disease
E
D
Confounder
C
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Confounding factor Maternal Age
C
Birth Order Down Syndrome
D
E
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Simple causal graphs
Maternal age (C) can confound the association
between multivitamin use (E) and the risk of
certain birth defects (D)
Hernan MA, et al. Causal knowledge as a
prerequisite for confounding evaluation an
application to birth defects epidemiology. Am J
Epidemiol 2002155176-84.
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Complex causal graphs
History of birth defects (C) may increase the
chance of periconceptional vitamin intake (E). A
genetic factor (U) could have been the cause of
previous birth defects in the family, and could
again cause birth defects in the current
pregnancy (D)
Hernan MA, et al. Causal knowledge as a
prerequisite for confounding evaluation an
application to birth defects epidemiology. Am J
Epidemiol 2002155176-84.
18
More complicated causal graphs
Physical Activity
Smoking
A
B
BMI
C
U
E
D
Bone fractures
Calcium supplementation
Source Hertz-Picciotto
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• A factor is a confounder if
• a) the effect measure is homogeneous across the
  strata defined by the confounder and
• b) the crude and common stratum-specific
  (adjusted) effect measures are unequal (lack of
  collapsibility)
• Usually evaluated using 2x2 tables, and simple
  stratified analyses to compare crude effects with
  adjusted effects

Collapsibility is equality of stratum-specific
measures of effect with the crude (collapsed),
unstratified measure Porta, 2008, Dictionary
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Crude vs. Adjusted Effects

• Crude does not take into account the effect of
  the confounder
• Adjusted accounts for the confounder
• Mantel-Haenszel method estimator
• Multivariate analyses (e.g. logistic regression)
• Confounding is likely when
• RRcrude / RRadjusted
• ORcrude / ORadjusted

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Stratified Analysis
Crude 2 x 2 table Calculate Crude OR (or
RR) Stratify by Confounder Calculate ORs
for each stratum If stratum-specific ORs are
similar, calculate adjusted OR (e.g. MH)
Crude
ORCrude
Stratum 1
Stratum 2
OR1
OR2
If Crude OR Adjusted OR, confounding is unlikely
If Crude OR / Adjusted OR, confounding is likely
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• Ideal causal contrast between exposed and
  unexposed groups
• A causal contrast compares disease frequency
  under two exposure distributions, but in one
  target population during one etiologic time
  period
• If the ideal causal contrast is met, the observed
  effect is the causal effect

Maldonado Greenland, Int J Epi 200231422-29
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Ideal counterfactual comparison to determine
causal effects
Exposed cohort
Iexp
Initial conditions are identical in the exposed
and unexposed groups, except for presence of
exposure (cause)
Unexposed cohort
Iunexp
RRcausal Iexp / Iunexp
Maldonado Greenland, Int J Epi 200231422-29
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What happens in reality?
Exposed cohort
Iexp
Unexposed cohort
Iunexp
Substitute, unexposed cohort
Isubstitute
RRassoc Iexp / Isubstitute
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In this case
RRcausal Iexp / Iunexp
IDEAL
RRassoc Iexp / Isubstitute
ACTUAL
Confounding is present if the substitute
population represents imperfectly what the target
would have been like under the counterfactual
condition
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Simulating the counter-factual comparisonExperim
ental Studies Randomized Clinical Trials
compare rates
Randomization helps to make the groups
comparable (i.e. similar initial conditions)
with respect to known and unknown
confounders Confounding is unlikely at
randomization - time t0
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Simulating the counter-factual comparisonObserva
tional Studies Cohort studies, case-control
studies
compare rates
PRESENT
FUTURE
In observational studies, because exposures are
not assigned randomly, attainment of
exchangeability is impossible initial
conditions are likely to be different and the
groups may not be comparable
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ConfoundingObservational studies vs randomized
trials

• Example
• Aspirin to reduce cardiovascular mortality

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Confounding adjustment and controls

• Control at the design stage
• Randomization
• Restriction
• Matching
• Control at the analysis stage
• Conventional approaches
• Stratified analyses
• Multivariate analyses
• Newer approaches
• Graphical approaches using DAGs
• Propensity scores
• Instrumental variables
• Marginal structural models

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• Options at the design stage
• Randomization
• Reduces potential for confounding by generating
  groups that are fairly comparable with respect to
  known and unknown confounding variables
• Restriction
• Eliminates variation in the confounder (e.g. only
  recruiting one gender)
• Matching
• Involves selection of a comparison group that is
  forced to resemble the index group with respect
  to the distribution of one or more potential
  confounders

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Randomization

• Randomization
• Only for intervention studies
• Definition random assignment of study subjects
  to exposure categories
• To control/reduce the effect of confounding
  variables about which the investigator is unaware
  (i.e. both known and unknown confounders get
  distributed evenly because of randomization)
• Randomization does not always eliminate
  confounding
• Covariate imbalance in small trials
• Maldistribution of potentially confounding
  variables after randomization (Table I Baseline
  characteristics in the randomized trial)

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Randomization breaks any links between treatment
and prognostic factors
Confounder
C
Randomization X
Exposure Disease (outcome)
D
E
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Restriction

• The distribution of the potential confounding
  factors does not vary across exposure or disease
  categories
• An investigator may restrict study subjects to
  only those falling with specific level(s) of a
  confounding variable
• Advantages of restriction
• straightforward, convenient, inexpensive (but,
  reduces recruitment!)
• Disadvantages of restriction
• Limits number of eligible subjects
• Limits ability to generalize the study findings
• Residual confounding
• Impossible to evaluate the relationship of
  interest at different levels of the confounder

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Matching

• Matching is commonly used in case-control studies
  
• Match on strong confounder
• Types
• Pair (individual) matching
• Frequency matching
• The use of matching usually requires special
  analysis techniques (e.g. matched pair analyses
  and conditional logistic regression)

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Matching

• Disadvantages of matching
• Finding appropriate control subjects difficult
  and expensive and limit sample size
• Confounder used to match subjects cannot be
  evaluated with respect to the outcome/disease
• Matching does not control for confounders other
  than those used to match
• The use of matching makes the use of stratified
  analysis very difficult
• Matching is most often used in case-control
  studies (prohibitive in a large cohort study)
• In a case-control study, matching may even
  introduce confounding

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Controlling ConfoundingAt the analysis
stageConventional approaches
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Confounding control at the analysis stage

• Confounding is one type of bias that can be
  adjusted in the analysis (unlike selection and
  information bias)
• Options at the analysis stage
• Stratification
• Multivariate methods
• To control for confounding in the analyses,
  confounders must be measured in the study

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Stratification

• Produce groups within which the confounder does
  not vary
• Evaluate the exposure-disease association within
  each stratum of the confounder

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Source www.epiet.org
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Stratified Analysis
Crude 2 x 2 table Calculate Crude OR (or
RR) Stratify by Confounder Calculate ORs
for each stratum If stratum-specific ORs are
similar, calculate adjusted OR (e.g. MH)
Crude
ORCrude
Stratum 1
Stratum 2
OR1
OR2
If Crude OR Adjusted OR, confounding is unlikely
If Crude OR / Adjusted OR, confounding is likely
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Direction of Confounding

• Confounding pulls the observed association away
  from the true association
• It can either exaggerate/over-estimate the true
  association (positive confounding)
• Example
• ORcausal 1.0
• ORobserved 3.0
• or
• It can hide/under-estimate the true association
  (negative confounding)
• Example
• ORcausal 3.0
• ORobserved 1.0

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Multivariate Analysis

• Stratified analysis works best only in the
  presence of 1 or 2 confounders
• If the number of potential confounders is large,
  multivariate analyses offer the only real
  solution
• Can handle large numbers of confounders
  (covariates) simultaneously
• Based on statistical regression models
• E.g. logistic regression, multiple linear
  regression
• Always done with statistical software packages

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Residual confounding

• Confounding that can persist, even after
  adjustment
• Unmeasured confounding
• Some variables were actually not confounders
• Confounders were measured with error (eg.,
  misclassification)
• Categories of the confounder improperly defined

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Effect modification and interaction
Maura Pugliatti, MD, PhDAssociate Professor of
NeurologyDept. of Clinical and Experimental
Medicine, Unit of Clinical NeurologyUniversity
of Sassari, Italy 1st International Course of
Neuroepidemiology Chisinau, Moldova, 24-28 Sept.
2012
46
Definition

• Biological interaction
• Effect modification (effect-measure
  modification)
• Heterogeneity of effects
• Subgroup effects
• Statistical Interaction
• Deviation from a specified model form (additive
  or multiplicative)

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Biological interaction the interdependent
operation of two or more biological causes to
produce, prevent or control an effectPorta,
Dictionary, 2008
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Multicausality and interdependent effects

• Disease processes tend to be multifactorial
  multicausality
• The one-variable-at-a-time perspective has
  several limitations
• Confounding and effect modification
  manifestations of multicausality

Schoenbach, 2000
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Effect modification and statistical interaction

• Two definitions (related)
• Based on homogeneity or heterogeneity of effects
• Interaction occurs when the effect of a risk
  factor (X) on an outcome (Y) is not homogeneous
  in strata formed by a third variable (Z, effect
  modifier)
• Differences in the effect measure for one factor
  at different levels of another factor Porta,
  2008
• This is often called effect modification
• Based on the comparison between observed and
  expected joint effects of a risk factor and a
  third variable
• Interaction occurs when the observed joint
  effects of the risk factor (X) and third variable
  (Z) differs from that expected on the basis of
  their independent effects
• This is often called statistical interaction

Szklo Nieto, Epidemiology Beyond the basics.
2007
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Definition based on homogeneity or heterogeneity
of effects

• Effect of exposure on the disease is modified
  depending on the value of a third variable
• the effect modifier

Effect modifier
Exposure
Disease
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Stratified Analysis
Crude 2 x 2 table Calculate Crude OR (or
RR) Stratify by Confounder Calculate ORs
for each stratum
Crude
ORCrude
Stratum 1
Stratum 2
OR1
OR2
If stratum-specific ORs are the same or similar,
calculate adjusted OR (e.g. MH)
If stratum-specific ORs are not similar,
calculate adjusted OR (e.g. MH)
Effect modification is present. Report
Stratum-specific OR
If Crude OR / Adjusted OR, confounding is
likely. Report Adjusted OR
If Crude OR Adjusted OR, confounding is
unlikely. Report Crude OR
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Confounding vs. interaction

• Confounding is a problem we want to eliminate
  (control or adjust for) in our study
• Comparing crude vs. adjusted effect estimates
• Interaction is a natural occurrence that we want
  to describe and study further
• Comparing stratum-specific estimates

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Heterogeneity of effects

• Can occur at the level of
• Individual study within subgroups of a single
  study or trial
• Seen in subgroup or stratified analyses within a
  study
• Across studies if several studies are done on
  the same topic, the effect measures may vary
  across studies
• Seen in meta-analyses (across trials)

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Definition based on the comparison between
observed and expected joint effects of a risk
factor and a third variable Deviation from
additive or multiplicative joint effectsThis is
often called statistical interaction
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Observed vs expected joint effects of a risk
factor and a third variable
No interaction
Positive interaction
Negative interaction
Szklo Nieto, Epidemiology Beyond the basics.
2007
56
Deviation from additive or multiplicative joint
effects

• Interaction on an additive scale (additive
  interaction)
• Effect measure modification when risk difference
  is used as measure of effect
• Additive statistical model
• Linear regression y a b1x1 b2x2
• Interaction on a multiplicative scale
  (multiplicative interaction)
• Effect measure modification when risk ratio is
  used as measure of effect
• Multiplicative statistical model
• Logistic regression

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Additive or multiplicative model?

• The additive model underpins the methods for
  assessing biological interaction
• Interaction here is a departure from additivity
  of disease rates (risk difference is the key
  measure)
• Risk difference scale is of greatest public
  health importance (based on attributable risk)
• Many of the models used in epidemiology are
  inherently multiplicative (e.g. logistic
  regression)
• Vast majority of epi analyses implicitly use the
  multiplicative scale (risk ratio is the key
  measure)
• Because most epi studies report RR and OR
  estimates and use regression models such as
  logistic and survival analyses these models
  inherently use ratio measures and are therefore
  multiplicative

Ahlbom A et al. Eur J Epi 2005
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Why is interaction/effect modification important?

• Better understanding of causation
• Identification of high-risk groups
• Target interventions at specific subgroups