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.

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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