10-1 Concept and Definition
Simpson's Paradox is illustrated by a hat shopping
Confounding – a bias that may occur when there is failure to account for other variables, like age, gender, or smoking status, in assessing E→D relationships.
Example: Relationship between TCX and Lung Cancer
More smokers among those exposed to TCX than those unexposed to TCX?
“Stratify” on smoking history.
In this example, we are controlling for smoking history.
A study finds that alcohol consumption is associated with lung cancer, crude OR = 3.5. Using the data below, determine whether smoking could be confounding this relationship.
1. What is the OR among smokers? . . . ???
2. What is the OR among non-smokers? . . ???
3. Does the OR change when we control for smoking status? ???
4. Is there evidence from this data that smoking is a confounder of the relationship between alcohol consumption and lung cancer? ???
Confounding assessed by comparing crude estimate of effect (e.g., ) where no variables are controlled, with adjusted estimate of effect (e.g., ), where one or more variables are controlled.
From TCX->Lung cancer example:
= ? Must be between two stratum-specific estimates 1.0 & 1.3
Note: We will discuss how to calculate an adjusted value later.
How do we decide if there is confounding?
The data-based criterion for confounding:
Crude estimate is meaningfully different from adjusted estimate
How different must these two estimates be to conclude there is confounding?
The investigator must decide whether or not there is an “important” difference.
No statistical test for confounding
Common approach - prior to looking at data, determine change of crude compared to adjusted estimate, typically 10 per cent.
Example: crude risk ratio = 4, a 10% change; if adjusted risk ratio were below 3.6 or above 4.4 we would say that confounding has occurred.
10-2 Adjusted Estimates
Example: TCX and Lung Cancer. What is a “crude” estimate?
How to derive “adjusted” estimate? Combine stratum specific estimates to obtain a single summary measure; a weighted average of the stratum specific estimates.
Assuming equal weights:
What weights should we use? Based on sample size in each stratum? Other factors? More discussion on this later.
One more example of weighting; assumes 10 times the weight for stratum 1:
· In addition to data-based criterion, 3 a priori criteria.
· Considered at study design stage to identify variables for possible control in the analysis.
1. A confounder must be a risk factor for the health outcome.
· Example – relation between toxic chemical exposure and lung cancer
· Based on the literature, may need to control for age and smoking status, known risk factors for lung cancer.
· The goal is to determine whether exposure to the chemical contributes over and above the effects of age and smoking on lung cancer.
2. A confounder cannot be an intervening variable between the exposure and the disease.
Example: Control for HDL?
3. A confounder must be associated with the exposure in the source population being studied.
Example: Case control study on genetic type BRCA1 and breast cancer; can age confound the association? Assume no association in source population between gene type and age; but a case-control study finds an association. This would be an example where criterion 3 is NOT met.
10-3 A priori Criteria/Study Designs
Case-control study to assess relationship of alcohol consumption & oral ca.
10-4 Confounding, Interaction, and Effect Modification
Consider results from case-control study to assess relation between alcohol consumption and bladder cancer. Data stratified on race (3 categories).
Note stratum-specific odds ratios.
Confounding? Precision-based OR = 2.16; little evidence of confounding
Confounding and interaction are different concepts.
· A variable modifies the exposure-disease relationship.
· A statistical test can be applied to determine the presence/absence of interaction (e.g., Breslow-Day test)
· A statistical test is not used for assessing confounding