What is Confounding?
–Confounding is bias in the estimation of the effect of exposure on disease occurrence, due to a lack of comparability between exposed and unexposed population.
–Occurs when the substitute population is NOT equivalent to the counterfactual condition.
(AKA, the substitute population does not show the outcome in the exposed population WITHOUT the exposure.)
How do we Identify and Control for Empirical Manifestations of Confounding?
Practically, there is no empirical method for directly examining the correctness of the comparability assumption
We search for differences in the distributions of risk factors among the exposure groups = confounding variables
Interaction
Example : smoking, lung cancer, and asbestos
Occurs when the association between the exposure and the disease varies by levels of a third factor
ie when the magnitude of effect is “modified” by varying levels of a 3rd factor
Ex: the association btwn smoking + lung cancer varies by exposure to asbestos.
—(risk is much higher and smoking + asbestos exposures are present together)
Example of Confounding
smoking, lung cancer, and age
If smokers are older than non-smokers, how would we know whether the observed association between smoking + lung cancer is due to smoking or to age?
(if we have adequately measured confounders in all subjects, we can correct or control for their distorting effect in the analysis)
Comparability-based confounding
The observed value of the outcome measure in the exposed group is compared with the expected value that would have been observed in the exposure group if it had not been exposed.
The unexposed group’s actual outcome is used as a proxy for the exposed group’s unobserved value. When the two groups experiences differ, the groups are noncomparable
=confounding occurs
Collapsibility-based confounding
Confounding is a failure of the estimate for an adjusted effect parameter to equal the estimate for the crude parameter that is obtained when a covariate is ignored (collapsed).
Confounding is equated with non-collapsibility (or change in the estimated parameter)
Properties of a Confounder
- A confounder must be the cause of the disease
- A confounder must be associated with the exposure in the base population
- A confounder must not be affected by the exposure or the disease
Property 1:
A Confounder must be the cause of the disease
Meaning?
Covariate must be a risk factor for the disease in the unexposed base population.
OR, it can be a marker for another, often unmeasured risk factor.
Meaning: the association can be observed in the unexposed group in both cohort and case-control studies.
C is not a confounder if:
- -its association with D is due to chance/bias
- -association is due to the effect of D on C
- -the effect of C on D in the base pop. is not independent of the exposure
Property 2:
A confounder must be associated with the exposure in the base population
Covariate must be associated with exposure status in the total base population.
- -Cohort study: association can be observed in the total sample.
- -Case-control study: association can be observed in controls, assuming that it reflects the association in the base population.
- C-E association should be known prior to study, or else we may have to assume that the observed C-E association reflects this association in the base population
Property 1 and 2 depend on:
–Prior knowledge of covariate associations or effects in the base population, which may conflict with associations observed in the data
Property 3:
A confounder must not be affected by the exposure or the disease
C is not a confounder if its association with E in the base population is due entirely to the effect of E on C –even if C is a proxy/risk factor for D
C is not a confounder if:
- C is an intermediate variable in the causal pathway between E + D
- both C + D are affected by the same unmeasured risk factors and C is affected by E
- both C and D are affected by another unmeasured risk factor
*often requires prior knowledge
Positive v Negative Confounding
When X is a Risk Factor:
- -If Ba* Bb are > 0, bias is away from the null (positive)
- -If Ba* Bb < 0, bias is toward the null (negative)
When X is a Protective Factor:
- -If Ba* Bb > 0, bias is toward the null (negative)
- -If Ba* Bb <0, bias is away from the null (positive)
Positive confounding: crude OR/RR > Adjusted OR/RR
Negative confounding: crude OR/RR < Adjusted OR/RR
Stratification Methods:
Mantel-Haenszel method
- Stratify data by the level (i) of a confounder
- Calculate a weighted average of the stratum specific estimates (adjusting)
- Compare crude vs. adj estimates
Advantages and Disadvantages of Stratification Methods
Advantage:
-easy to understand and compute
Disadvantage:
- cannot handle a large number of variables (problematic if there are sparse data in some strata or too many variables to adjust for)
- each calculation requires a rearrangement of tables
- limited to categorical confounders
How to Identify a Confounder
- Prior knowledge
- Change-In-Estimate strategy
Collapsibility-based confounding:
–when the estimate for adjusted effect measure does not equal the estimate for crude effect measure (which is obtained when covariate is ignored/collapsed)
Identifying a Confounder: Prior Knowledge
Prior knowledge of a causal relationship from previous empirical studies, biologic plausibility, or theories/models
existing DAG’s
Identifying a Confounder: Change in Estimate Strategy
A crude effect estimate is compared to the adjusted effect estimate.
- Stratify effect estimates by variable
- If the difference after adjustment is >= 10%, then the variable in question is a confounder
* provided stratum specific measures are homogenous
Magnitude of confounding = (crude - adjusted / adjusted)
Methods of Controlling for Confounding
- Design and conduct of a study (randomization, matching)
- Analytic methods of adjustment
(DAG’s)
Controlling for Confounding:
Design and Conduct of a Study
- Randomization (experiments):
- -controls for all confounders, including those that are unmeasured or unrecognized.
- -since there is no guarantee that randomization has eliminated all bias, especially with small sample bias, other options are used to control for confounding. - Restricting the eligibility of subjects according to values of potential confounders (in any type of study).
- -commonly used in observational studies to control for known confounders.
Matching
Method used to control for confounders in observational studies
- Restrict eligibility of unexposed subjects by making them similar/comparable to exposed subjects with respect to matching variables (confounders)
Matching in Cohort Studies
- -Unexposed subjects are matched to exposed subjects
- -used to prevent confounding due to the matching factors
- -if there is no source of bias other than confounding by the matching factors, statistical adjustment (modeling) for these factors may be unnecessary to remove bias
Matching in Case-Control Studies
Matching is more common in case-control studies, because there is more likely to be a relative shortage of cases than there is to be a shortage of controls
Controls are matched to the cases
- -used to increase statistical efficiency when a subsequent procedure (stratification) is used to adjust for confounding but introduces bias
- -statistical adjustment/modeling for the matching factors may be necessary to remove bias even if they were not originally confounders
Types of Matching:
Individual matching
Frequency matching
Individual Matching
- –One or more unexposed subjects are selected separately for each exposed subject
- —such that each set of unexposed subjects is made similar to the corresponding exposed group on one or more matching variables
