Case-control study 3:Bias and confounding

and analysis

Preben Aavitsland

Contents

• Monday 1– Design: Case-control study as a smarter cohort study– The odds ratio

• Tuesday 2– Choosing cases and controls– Power calculation

• Wednesday– Case-control studies in outbreaks

• Thursday 3– Bias and confounding– Matching– Analysis

Summary of the case-control study

• Study causal effects of exposures (risk factors, preventive factors) on disease

• Define cases• Find source population• Select controls that are representative of source

population• Ask cases and controls the same questions

about exposures• Compare exposure ratios between cases and

controls, OR = a/b / c/d

Calculating the odds ratio (OR)

• Cross product ratio: ad / bc = a/b / c/d

Exposed Unexposed

Cases a b

Controls c d

Dog No dog

TBE-cases 24 16 OR = ad/bc = 4,5

Controls 20 60

Can we believe the result?

Having a dog TBE

OR = RR = 4.5

What can be wrong in the study?

Random error

Results in low precision of the epidemiological measure measure is not precise, but true

1 Imprecise measuring

2 Too small groups

Systematic errors(= bias)

Results in low validity of the epidemiological measure measure is not true

1 Selection bias

2 Information bias

3 Confounding

Random errors

Systematic errors

Errors in epidemiological studiesError

Study size

Systematic error (bias)

Random error (chance)

Random error

• Low precision because of– Imprecise measuring

– Too small groups

• Decreases with increasing group size

• Can be quantified by confidence interval

Estimation

• When we measure OR, we estimate a point estimate– Will never know the true value

• Confidence interval indicates precision or amount of random error– Wide interval low precision

– Narrow interval high precision

• OR = 4.5 (2.0 – 10)

OR and confidence interval

• Shows magnitude of the causal effect

• Shows direction of the effect– OR > 1 increases risk (risk factor)

– OR > 1 decreases risk (preventive factor)

• Shows the precision around the point estimate

• Condition: no systematic errors

• Forget about p-values! No advantages.

Larger study narrower interval

Dog No dog

TBE-cases 24 16 OR= 4.5 (2.0 - 10)

Controls 20 60

Dog No dog

TBE-cases 240 160 OR= 4.5 (3.5 - 5.8)

Controls 200 600

Use Episheet

Systematic error

• Does not decrease with increasing sample size

• Selection bias

• Information bias

• Confounding

Selection bias

• Error because the associationexposure disease

is different for participants and non-participants in the study

• Errors in the– procedures to select participants

– factors that influence participation

Examples of selection bias

• Self-selection bias

• Healthy worker effect

• Non-response

• Refusal

• Loss to follow-up

Can we believe the result?

Having a dog TBEOR = IRR = 4.5

Cases were interviewed in the hospital. Controls were interviewed by phone to their home in the evening. But then, many dog-owners would be walking their dog…

Dog No dog

TBE-cases a b

Controls c dOR=ad / bc

Preventing selection bias

• Same selection criteria

• High response-rate

• High rate of follow-up

Information bias

• Error because the measurement of exposure or disease

is different between the comparison groups.

• Errors in the– procedures to measure exposure

– procedures to diagnose disease

Examples of information bias

• Diagnostic bias

• Recall bias

• Researcher influence

Can we believe the result?

Having a dog TBEOR = IRR = 4.5

Cases were so eager to find an explanation for their disease that they included their neighbours’ dog when they were asked whether they had a dog…

Dog No dog

TBE-cases a b

Controls c dOR=ad / bc

Misclassification

Dog No dog

TBE-cases 20 20 OR = ad/bc = 3,0

Controls 20 60

Dog No dog

TBE-cases 24 16 OR = ad/bc = 4,5

Controls 20 60

Dog No dog

TBE-cases 24 16 OR = ad/bc = 2,8

Controls 28 52

True

Differential

Non-differential

Non-differential misclassification

• Same degree of misclassification in both cases and controls

• OR will be underestimated– True value is higher

• If no causal effect found, ask:– Could it be due to non-differential

misclassification?

Preventing information bias

• Clear definitions

• Good measuring methods

• Blinding

• Standardised procedures

• Quality control

Confunding - 1

“Mixing of the effect of the exposure on disease with the effect of another factor that is associated with the exposure.”

Eksposure 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

In the analysis

• Restriction of the analysis

• Stratification

• Multivariable regression

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

Stratification

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

Controlling confounding

In the design

• Restriction of the study

• Matching

In the analysis

• Restriction of the analysis

• Stratification

• Multivariable methods

What can be wrong in the study?

Random error

Results in low precision of the epidemiological measure measure is not precise, but true

1 Imprecise measuring

2 Too small groups

Systematic errors(= bias)

Results in low validity of the epidemiological measure measure is not true

1 Selection bias

2 Information bias

3 Confounding