Confounding

1
Confounding

• A confusion of effects that occurs when the
  effect of an extraneous factor is mistaken for or
  mixed with the actual exposure effect
• Occurs when disease risk factors are unevenly
  distributed across exposure groups, making these
  groups incomparable with respect to factors that
  influence disease frequency

2
Confounding

• A confounder can
• create the appearance of an association when the
  true association is null
• create the appearance of a null association when
  there is a true association
• bias the measure of a true effect toward or away
  from the null value
• reverse the direction of a true association

3
Confounding

• A confounder, considered in isolation, must
  fulfill 3 conditions
• a risk factor for disease in the unexposed
• associated with exposure in the population from
  which cases arose
• not an intermediate step in the causal pathway
  between exposure and disease
• Valid identification of confounders is done in
  the multivariate context, considering all
  potential confounders, because confounding
  influences can be altered (heightened, lessened
  or canceled) by the presence of other confounders

4
Confounding

• Control of confounding
• in study design
• randomization - only achieved in intervention
  studies unique strength is the ability to
  control confounding
• restriction - establish inclusion/exclusion
  criteria to limit selection of individuals that
  fall in a specific category of the confounder
• matching - primarily used in case-control
  studies removes the effect by making groups
  equivalent in terms of a particular confounding
  variable

5
Confounding

• Control of confounding
• in analysis
• stratified analysis - determining an estimate of
  the association within homogeneous categories
  (e.g., sex, age groups)
• multivariate analysis - allows for efficient
  estimation of measures of association while
  controlling for a number of potential confounding
  variables simultaneously normally done with
  regression modeling

6
Confounding

• Confounding
• F
• D
• E
• F is the confounder
• E is confounded

Causal association Non-causal association
7
Confounding

• Non-confounding
• F
• D
• E
• F is not associated with E but both are
  independent risk factors (no correlation)

Causal association Non-causal association
8
Confounding

• Non-confounding
• F
• D
• E
• F is not a risk factor but is a correlate of E
• Adjusting for F would introduce confounding

Causal association Non-causal association
9
Confounding

• If risk factors is a confounder, then control
  in some appropriate way changes meaningfully the
  disease-risk factor association
• If RRcrude Rradjusted, then no confounding
• If RRcrude ? Rradjusted, then confounding
  present

10
Confounding

• In addition to the counterfactual approach to the
  concept of confounding, what are complementary
  ways to view confounding?
• A confusion of effects
• The apparent effect of the exposure is distorted
  because the effect of an extraneous factor is
  mistaken for or mixed with the actual exposure
  effect
• A distortion of the exposure effect that results
  when comparison groups differ on the distribution
  of factors that affect disease frequency other
  than the exposure

11
Conditions for a variable to be a confounder

• Is it a risk factor for disease?
• A confounder must be a disease risk factor (a
  cause or marker for a cause) within the reference
  level of the exposure under study, that is, it
  must be a risk factor independent of any
  association with exposure
• Confounding is determined by the actual
  confounder-disease relation in the source
  population, not the apparent relation observed in
  the data
• When prior knowledge is inadequate, study data
  may serve as a guide to the relation between a
  potential confounder and disease, particularly
  high quality data from large studies (with
  minimal sampling error)

12
Conditions for a variable to be a confounder

• Is it associated with exposure in the population
  from which cases arose?
• Cohort study
• A confounder must be associated with exposure
  among subjects at the start of follow-up
• The relation between the potential confounder and
  exposure can be evaluated from study data prior
  information from other populations is not relevant

13
Conditions for a variable to be a confounder

• Is it associated with exposure in the population
  from which cases arose?
• Case-control study
• A confounder must be associated with exposure in
  the population from which cases arose (source
  population in Rothman Greenland terminology)
• The relation between a potential confounder and
  exposure should be assessed ideally in the source
  population, but this is seldom possible
• If the control series is large and represents the
  source population (no selection bias), it will
  provide a reasonable estimate of the association
  between the potential confounder and exposure

14
Conditions for a variable to be a confounder

• Is it an intermediate step in the causal pathway
  between exposure and disease?
• A factor that represents an intermediate step in
  the exposure-disease pathway is an intervening
  variable
• Adjusting a relative risk estimate for an
  intervening variable creates bias by removing the
  exposure effect that operates through the
  intervening factor
• An intervening variable cannot be distinguished
  statistically from a confounder
• Knowledge of biological mechanisms must be used
  to distinguish intervening variables from
  confounders

15
Design features for preventing confounding

• Randomization
• Confounding can occur in studies that randomly
  allocate exposure, though to a lesser extent than
  in nonrandomized studies it tends to be
  negligible in very large well-conducted
  randomized studies
• Randomization does not guarantee no association
  between the exposure and extraneous risk factors
• A probabilistic procedure that can leave some
  association between exposure and extraneous
  factors, especially if the sample is small

16
Design features for preventing confounding

• Restriction
• A variable cannot produce confounding if it is
  prohibited from varying, for example, when all
  study subjects fall into the same category of a
  potential confounder
• Restricting eligibility of study subjects by
  admitting only those falling into specified
  categories (often a single category) can prevent
  confounding

17
Design features for preventing confounding

• Restriction - potential limitations
• May reduce the number of available eligible
  subjects resulting in a diminished study group
  in this case, the advantages of restriction must
  be weighed against the disadvantages of a smaller
  study group
• May limit generalizability if the effect under
  study varies in important ways across the
  variables used for restriction
• However, a study that tries to encompass a
  heterogeneous sample of a general population can
  produce imprecise and ambiguous estimates across
  subgroups
• Therefore, preferable to obtain a less ambiguous
  result regarding the existence of an effect from
  a restricted study group and examine the effect
  in other groups in another study

18
What contributes to residual confounding?

• Misclassification of the confounder (measurement
  error)
• Use of a surrogate for the confounder (to the
  extent that the surrogate misrepresents the
  confounder)
• Use of overly broad confounder categories (such
  that disease risk is heterogeneous within
  categories)

19
What contributes to residual confounding?

• Misclassification of the confounder (measurement
  error)
• Use of a surrogate for the confounder (to the
  extent that the surrogate misrepresents the
  confounder)
• Use of overly broad confounder categories (such
  that disease risk is heterogeneous within
  categories)

20
Selection of confounding categories

• Concerns that are general to categorizing any
  variables for stratified analysis
• Create categories such that no important
  confounding by the variable being categorized can
  occur within categories
• Chose category boundaries to insure that risk
  will not change profoundly within categories
• Categories based on percentiles can do poorly in
  this regard because they are based on how the
  confounder is distributed in the study sample
  rather than on creating categories of homogenous
  disease risk

21
Selection of confounders to control for

• Decisions regarding whether or not to adjust for
  potential confounding variables will depend on a
  combined assessment of
• prior knowledge
• observed associations in the data
• sample size considerations

22
Selection of confounders to control for

• Generally look for empirical evidence of
  confounding in data obtained from study
  populations
• however, observations in such data may reflect
  selection and information bias affecting observed
  confounder-disease-exposure associations in a
  similar way to how these biases affect observed
  exposure-disease associations
• Therefore, it is necessary to rely on prior
  knowledge of relevant associations in source
  populations

23
Selection of confounders to control for

• If a variable is a known confounder but does not
  appear to be one in the data, this should create
  uncertainty regarding the validity of the data
• Adjusting for this factor may not change the
  relative risk point estimate, but it may
  influence the standard error for this estimate,
  thus appropriately reflecting our uncertainty
• Even if no changes result from adjusting for this
  factor, adjustment may be required for
  knowledgeable reviewers to trust the results

24
Selection of confounders to control for

• If prior knowledge suggests a variable should not
  be a confounder but it appears to be one in the
  data, the confounding may have been introduced by
  the study methods (eg., as a result of matching
  in a case-control design)
• In this case it would be appropriate to adjust
  for this factor providing it meets the criteria
  for a confounder

25
Selection of confounders to control for

• When prior knowledge regarding exposure-covariate
  associations is insufficient and the number of
  covariates to consider is small, it may be
  desirable to adjust for all variables that appear
  to be important risk factors for the outcome

26
Selection of confounders to control for

• When a large number of potential confounders must
  be considered, the change-in-estimate variable
  selection strategy (include the variable if it
  results in a specified degree of change in point
  or interval estimates) has been shown in
  simulation studies to produce more valid results
  for confounder detection than strategies that
  rely on p-values, unless the significance level
  for the p-value is raised to 0.2 or higher

27
Selection of confounders to control for

• Variable selection decisions are made ideally
  when controlling for other potential confounders
• When many variables must be evaluated a backward
  selection strategy may be useful (as described in
  RG, p. 257), but such a strategy can produce
  extremely confounded results unless the
  alpha-levels for deletion and retention are set
  much higher than 0.05
• If data are too sparse to adjust for all
  potential confounders at once, a forward
  selection strategy may be necessary
• Whatever the approach (usually there is more than
  one), criterion for selection should be explicit
  and consistently applied

28
Confounding
Example 2 strong upward bias due to confounding
(positive confounding) Example 3 association
masked by confounding (negative confounding)
29
Confounding
Example 1 3 bias due to confounding and
interaction
30
Effect-measure modification

• Effect-measure modification occurs when the size
  of a causal effect differs in different targets
• Unlike confounding, it is a reflection of nature
  rather than a bias
• Effect-measure modifier is a variable that
  modifies the size of an effect measure, that is,
  the effect measure differs across levels, or
  strata, of the variable
• Heterogeneity or modification of an effect
  measure describes variation of exposure effect
  across strata of a modifier
• Homogeneity, constancy or uniformity of an effect
  measure across strata of another variable
  describes lack of effect measure modification by
  that variable

31
Effect-measure modification

• Why is the term "effect-measure modification"
  preferable to the more frequently used term
  "effect modification"?
• If the exposure has any effect on a disease
  frequency measure, at most one of the ratio or
  difference measures of effect can be uniform
  across strata of the modifying factor (that is,
  either the absolute or the relative effect can be
  uniform across strata, but not both), thus it is
  most appropriate to refer to this concept as
  modification of the effect measure rather than
  the effect

32
Effect-measure modification

• Effect-measure modification distinguished from
  confounding
• Confounding occurs when the effect of the
  exposure of interest is confused with the effect
  of an extraneous factor effect-measure
  modification occurs when the effect of the
  exposure of interest is modified by another
  factor
• Confounding is a bias to prevent or remove from
  an effect estimate effect-measure modification
  is a property of the effect under study and thus
  a finding to be reported

33
Effect-measure modification

• Synonymous with
• Interaction
• Heterogeneity of effect
• Departure from additivity of effects on the
  chosen outcome scale
• Absence of effect-measure modification
• Absence of interaction
• Homogeneity or uniformity of effect
• Additivity of effects on the chosen outcome scale

34
Effect measure modificationNon-uniformity of
stratum-specific estimates of effect
Ex. 1, 2, 3 no association in one stratum but
strong affect in the other strong interaction,
confounding irrelevant strata specific effects
should be presented Ex. 2 3 strong interaction
with cross-over
35
Effect-measure modification

• Synonymous with
• Interaction
• Heterogeneity of effect
• Departure from additivity of effects on the
  chosen outcome scale
• Absence of effect-measure modification
• Absence of interaction
• Homogeneity or uniformity of effect
• Additivity of effects on the chosen outcome scale

36
Additivity of effects

• Departures from additivity of risk differences
• superadditivity or subadditivity
• imply the presence of biologic interaction types
  (individuals for which two exposures are
  synergistic or antagonistic), whether factors
  under study are causal or preventive
• definitions of response types and biologic
  interactions are specific to the particular
  outcome measure under study

37
Assessing additivity or multiplicativity of
effects in stratified analysis

• For additive effects (no interaction on the
  additive scale)
• The difference measure (incidence rate or
  incidence proportion difference) associated with
  exposure is uniform across strata of the
  stratification variable
• The difference measure for the joint effect of
  two factors equals the sum of the difference
  measures for the two independent effects
• The ratio measure (rate or risk ratio) for the
  joint effect of two factors is equal to the sum
  of the ratio measures for the independent effects
  minus 1
• Assuming the OR approximates the rate or risk
  ratio, the same relationship will hold for the OR

38
Assessing additivity or multiplicativity of
effects in stratified analysis

• For multiplicative effects (no interaction on the
  multiplicative scale)
• The ratio measure (incidence rate or incidence
  proportion ratio) associated with exposure is
  uniform across strata of the stratification
  variable
• The ratio measure for the joint effect of two
  factors equals the product of the ratio measures
  for the two independent effects
• Assuming the OR approximates the rate or risk
  ratio, the same relationship will hold for the OR

39
Interaction (from KKM, Ch 19)

• Assessment of interaction is model dependent
• Consider two factors A B, with A1, B1
  presence and A0, B0 absence
• Probability of developing disease given exposure
  to A and B
• R11 pr(D A1B1) R10 pr(D A1B0)
• R01 pr(D A0B1) R00 pr(D A0B0)
• Corresponding risk ratios
• RR11 RR11 / R00
• RR10 RR10 / R00
• RR01 RR01 / R00

40
Interaction (from KKM, Ch 19)

• No interaction on the additive scale
• (RR11 - 1) (RR10 1) (RR01 1)
• (RR11 RR00) (RR10 RR00) (RR01 RR00)
• No interaction on the multiplicative scale
• RR11 RR10 ? RR01

41
Interaction (from KKM, Ch 19)

• Example Cohort study of 100 individuals in each
  of four exposure categories
• R11 40/100 0.40
• R10 R01 20/100 0.20
• R00 10/100 0.10
• Estimated risk ratios
• RR11 0.40/0.10 4.00
• RR10 RR01 0.20/0.10 2.00

42
Interaction (from KKM, Ch 19)

• Evidence of interaction
• Multiplicative scale
• RR11 RR10 ? RR01 (0.40 0.20 ? 0.20)
• Therefore no interaction on multiplicative scale
• Additive scale
• RR11 RR00 0.40 - 0.10 ? 0.30
• (RR10 RR00) (RR01 RR00) (0.20 0.10)
  (0.20 0.10) 0.20
• (RR11 RR00) ? (RR10 RR00) (RR01 RR00)
• Reflects a deviation from additivity
• Therefore evidence of interaction on additive
  scale

43
Ambiguity of the term interaction

• The terms effect-measure modification and
  statistical interaction are logically
  equivalent
• The presence or absence of interaction is
  determined by the scale or measure of the
  outcome, thus absence of interaction on one scale
  implies presence of interaction on many other
  scales
• Preferable phrases for no interaction
• No risk-ratio heterogeneity was detected, or, no
  departure from risk-ratio multiplicativity was
  detected
• No risk difference heterogeneity was detected,
  or, no departure from risk-difference additivity
  was detected

44
Effect measure modification and interaction

• How is effect-measure modification different from
  confounding?
• confounding is a bias to prevent or remove from
  an effect estimate
• effect-measure modification is a property of the
  effect under study and thus a finding to be
  reported
• What is the relationship between effect-measure
  modification and statistical interaction?
• The terms are logically equivalent

45
Counterfactual and sufficient cause approach to
conceptualizing interaction

• In theory (that is, conceptually, though not by
  observation), the counterfactual causal response
  type (the original 4 doomed, causal,
  preventive, immune multiplied by all of the
  combinations of synergy and antagonism) for any
  individual can be defined by their risk status
  for sufficient causes (see RG, p. 338)

46
Inappropriateness of inferring biologic
interaction from statistical interaction

• Methods for drawing conclusions about biologic
  interactions from epidemiologic data have limited
  utility because
• Tests for nonadditivity have very little power at
  typical study sizes and corresponding estimates
  of departures from additivity have little
  precision
• Simple assumptions become difficult to justify
  when the two factors of interest are continuous
  variables
• One can never infer that a particular type of
  interaction is absent and inferring presence of
  interaction requires untestable assumptions about
  the absence of other response types

47
Biologic (causal) interaction
Source Table 18-2, pg 333, RG