Confounding and effect modification Preben Aavitsland
Mar 27, 2015
Confounding and effect modification
Preben Aavitsland
Can we believe the result?
Rice Salmonellosis
OR = 3.9
Systematic error
• Does not decrease with increasing sample size
• Selection bias
• Information bias
• Confounding
Confunding - 1
“Mixing of the effect of the exposure on disease with the effect of another factor that is associated with the exposure.”
Exposure Disease
Confounder
Confounding - 2
• Key term in epidemiology
• Most important explanation for associations
• Always look for confounding factors
Surgeon Post op inf.
Op theatre I
Criteria for a confounder
1 A confounder must be a cause of the disease (or a marker for a cause)2 A confounder must be associated with the exposure in the source population3 A confounder must not be affected by the exposure or the disease
Umbrella Less tub.
Class1
3
2
Downs’ syndrome by birth order
Find confounders
“Second, third and fourth child are more often affected by Downs’ syndrome.”
Many children Downs’
Maternal age
Downs’ syndrome by maternal age
Downs’ syndrome by birth order and maternal age groups
Find confounders
”The Norwegian comedian Marve Fleksnes once stated: I am probably allergic to leather because every time I go to bed with my shoes on, I wake up with a headache the next morning.”
Sleep shoes Headache
Alcohol
Find confounders
“A study has found that small hospitals have lower rates of nosocomial infections than the large university hospitals. The local politicians use this as an argument for the higher quality of local hospitals.”
Small hosp Few infections
Well patients
Controlling confounding
In the design
• Restriction of the study
• Matching
Before data collection!
In the analysis
• Restriction of the analysis
• Stratification
• Multivariable regression
After data collection!
RestrictionRestriction of the study or the analysis to a subgroup that is homogenous for the possible confounder.
Always possible, but reduces the size of the study.
Umbrella Less tub.
ClassLowerclass
Restriction
We study only mothers of a certain age
Many children Downs’
35 year old mothers
Matching
“Selection of controls to be identical to the cases with respect to distribution of one or more potential confounders.”
Many children Downs’
Maternal age
Disadvantages of matching
• Breaks the rule: Control group should be representative of source population– Therefore: Special ”matched” analysis needed
– More complicated analysis
• Cannot study whether matched factor has a causal effect
• More difficult to find controls
Why match?
• Random sample from source population may not be possible
• Quick and easy way to get controls– Matched on ”social factors”: Friend controls,
family controls, neighbourhood controls– Matched on time: Density case-control studies
• Can improve efficiency of study• Can control for confounding due to factors
that are difficult to measure
Should we match?
• Probably not, but may:
• If there are many possible confounders that you need to stratify for in analysis
Stratified analysis
• Calculate crude odds ratio with whole data set
• Divide data set in strata for the potential confounding variable and analyse these separately
• Calculate adjusted (ORmh) odds ratio• If adjusted OR differs (> 10-20%) from
crude OR, then confounding is present and adjusted OR should be reported
Procedure for analysis
• When two (or more) exposures seem to be associated with disease
1. Choose one exposure which will be of interest
2. Stratify by the other variable– Meaning. Making one two by two table for those with
and one for those without the other variable (for example, one table for men and one for women)
• Repeat the procedure, but change the variables
Example
• Salmonella after wedding dinner• Disease seems to be associated with both chicken and rice• But many had both chicken and rice
Exposure Cases Controls Odds ratio 95% ci
Rice 37 / 50 21 / 50 3,9 (1,7 - 9,2)
Chicken 40 / 50 20 / 50 6,0 (2,8 - 12,7)
Cake 32 / 50 27 / 50 1,5 (0,7 - 3,4)
Juice 16 / 50 20 / 50 0,7 (0,3 - 1,6
Confounding
Is rice a confounder for the chicken salmonellosis association?
Stratify: Make one 2x2 table for rice-eaters and one for non-rice-eaters (e.g. in Episheet)
Chicken Salmonellosis
Rice
No confounding
Because:
OR for chicken alone = ORmh for chicken ”controlled for rice”
Exposure Cases Controls Odds ratio 95% ci
Rice-eaters: Chicken 36 / 37 18 / 21 6,0 (0,6 - 62)
Non-rice-eaters: Chicken 4 / 13 2 / 29 6,0 (0,9 - 38)
Chicken "controlled for rice" 40 / 50 20 / 50 6,0 (1,4 - 26)
Confounding
Is chicken a confounder for the rice salmonellosis association?
Stratify: Make one 2x2 table for chicken-eaters and one for non-chicken-eaters (e.g. in Episheet)
Rice Salmonellosis
Chicken
Confounding
Because:
OR for rice alone = ORmh for rice ”controlled for chicken”
Exposure Cases Controls Odds ratio 95% ci
Chicken-eaters: rice 36 / 40 18 / 20 1,0 (0,17 - 1,0)
Non-chicken-eaters: rice 1 / 10 3 / 20 1,0 (0,09 - 11)
Rice "controlled for chicken" 37 / 50 21 / 50 1,0 (0,24 - 4,2)
Not 3,9
Conclusion
• Chicken is associated with salmonellosis• Rice is not associated with salmonellosis
– confounding by chicken because many chicken-eaters also had rice
– rice only appeared to be associated with salmonellosis
• Stratification was needed to find confounding
• Compare crude OR to adjusted OR (ORmh)• If > 10-20% difference confounding!
Multivariable regression
• Analyse the data in a statistical model that includes
both the presumed cause and possible
confounders
• Measure the odds ratio OR for each of the
exposures, independent from the others
• Logistic regression is the most common model in
epidemiology
• But explore the data first with stratification!
Controlling confounding
In the design
• Restriction of the study
• Matching
In the analysis
• Restriction of the analysis
• Stratification
• Multivariable methods
Effect modification
• Definition: The association between exposure and disease differ in strata of the population– Example: Tetracycline discolours teeth in
children, but not in adults
– Example: Measles vaccine protects in children > 15 months, but not in children < 15 months
• Rare occurence