1. Confounding in epidemiology
Maura Pugliatti, MD, PhD Associate Professor of Neurology Dept. of Clinical and Experimental Medicine, Unit of Clinical Neurology University of Sassari, Italy 1st International Course of Neuroepidemiology
Chisinau, Moldova, 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 2004;329:
“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

4. Main application of epidemiology:
Causality
Main application of epidemiology:
to identify etiologic (causal) associations between exposure(s) and outcome(s) ?
Exposure
Outcome

5. Adapted from: Maclure, M, Schneeweis S. Epidemiology 2001;12:114-122.
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 2001;12:

6. Confounding: four approaches
“Mixing of effects”
Based on a priori criteria (classical approach)
Data-based criteria
“Counterfactual” and non-comparability approaches
Overlapping

7. “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

8. Association between birth order and Down Syndrome
Data from Stark and Mantel (1966)

9. Association between maternal age and Down Syndrome
Data from Stark and Mantel (1966)

10. Association between maternal age and Down Syndrome,
stratified by birth order
Data from Stark and Mantel (1966)

11. X C E C D E C D A factor is a confounder if 3 criteria are met:
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 E C D

12. Confounder C E D C E D Exposure Disease (outcome) Intermediate cause
Szklo M, Nieto JF. Epidemiology: Beyond the basics. Aspen Publishers, Inc., 2000.
Gordis L. Epidemiology. Philadelphia: WB Saunders, 4th Edition.

13. Confounder:
‘parent’ of the exposure not ‘daughter’ of the exposure!!!
Exposure
Disease E D
Confounder C

15. Confounding factor:
Maternal Age C
Birth Order Down Syndrome D E

16. Simple causal graphs E D C
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 2002;155:

17. Complex causal graphs E D C U
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 2002;155:

18. Calcium supplementation
More complicated causal graphs
Physical Activity
Smoking A B
BMI C U E D
Bone fractures
Calcium supplementation
Source: Hertz-Picciotto

19. 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

20. 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

21. Stratified Analysis Crude Crude 2 x 2 table Calculate Crude OR (or RR)
Stratify by Confounder
Calculate OR’s
for each stratum
If stratum-specific OR’s are similar,
calculate adjusted OR (e.g. MH)
ORCrude
Stratum 1
Stratum 2
OR1
OR2
If Crude OR =/= Adjusted OR,
confounding is likely
If Crude OR = Adjusted OR, confounding is unlikely

22. 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 2002;31:422-29

23. 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 2002;31:422-29

24. Isubstitute Iexp Iunexp RRassoc = Iexp / Isubstitute
What happens in reality?
Exposed
cohort
Iexp
Unexposed
cohort
Iunexp
Substitute, unexposed
cohort
Isubstitute
RRassoc = Iexp / Isubstitute

25. RRcausal = Iexp / Iunexp
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”

26. Untreated individuals
Simulating the counter-factual comparison: Experimental Studies: Randomized Clinical Trials
Disease +
Treated individuals
Disease -
Randomization
Eligible population
compare rates
Disease +
Untreated individuals
Disease -
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

27. Simulating the counter-factual comparison: Observational Studies: Cohort studies, case-control studies
Disease +
Exposed cohort
Disease -
compare rates
Disease +
Unexposed cohort
Disease -
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

28. Confounding: Observational studies vs randomized trials
Example:
Aspirin to reduce cardiovascular mortality

29. 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 29

30. 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 30

31. 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)

32. X C D E Randomization breaks any links
between treatment and prognostic factors
Confounder C
Randomization X
Exposure Disease (outcome) D E 32

33. 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

34. 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)

35. 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

36. Controlling Confounding: At the analysis stage Conventional approaches

37. 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 37

38. Stratification
Produce groups within which the confounder does not vary
Evaluate the exposure-disease association within each stratum of the confounder 38

39. Source: 39

40. Stratified Analysis Crude Crude 2 x 2 table Calculate Crude OR (or RR)
Stratify by Confounder
Calculate OR’s
for each stratum
If stratum-specific OR’s are similar,
calculate adjusted OR (e.g. MH)
ORCrude
Stratum 1
Stratum 2
OR1
OR2
If Crude OR =/= Adjusted OR,
confounding is likely
If Crude OR = Adjusted OR, confounding is unlikely

41. 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)
ORcausal = 3.0
ORobserved = 1.0 41

42. 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 42

43. 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 43

45. Effect modification and interaction
Maura Pugliatti, MD, PhD Associate Professor of Neurology Dept. of Clinical and Experimental Medicine, Unit of Clinical Neurology University of Sassari, Italy 1st International Course of Neuroepidemiology
Chisinau, Moldova, Sept. 2012 45

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)

47. Biological interaction “the interdependent operation of two or more biological causes to produce, prevent or control an effect” [Porta, Dictionary, 2008]

48. 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

49. 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”
[deviation from some specified model]
Szklo & Nieto, Epidemiology: Beyond the basics. 2007

50. 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

51. Stratified Analysis Crude Crude 2 x 2 table Calculate Crude OR (or RR)
Stratify by Confounder
Calculate OR’s
for each stratum
ORCrude
Stratum 1
Stratum 2
OR1
OR2
If stratum-specific OR’s are the same or similar, calculate adjusted OR (e.g. MH)
If stratum-specific OR’s 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

52. 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

53. 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)

54. 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 effects This is often called “statistical interaction”

55. Szklo & Nieto, Epidemiology: Beyond the basics. 2007
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:

57. 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

58. Why is interaction/effect modification important?
Better understanding of causation
Identification of “high-risk” groups
Target interventions at specific subgroups