Transcript 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.

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)
Exposed
Unexposed
Cases
a
b
Controls
c
d
• Cross product ratio: ad / bc = a/b / c/d
Dog
No dog
TBE-cases
24
16
Controls
20
60
OR = ad/bc =
4,5
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 studies
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
Controls
20
60
Dog
No dog
TBE-cases
240
160
Controls
200
600
OR= 4.5 (2.0 - 10)
OR= 4.5 (3.5 - 5.8)
Use Episheet
Systematic error
• Does not decrease with increasing sample
size
• Selection bias
• Information bias
• Confounding
Selection bias
• Error because the association
exposure  disease
is different for participants and nonparticipants 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
TBE
OR = IRR = 4.5
Dog
No dog
TBE-cases
a
b
Controls
c
d
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…
OR=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
TBE
OR = IRR = 4.5
Dog
No dog
TBE-cases
a
b
Controls
c
d
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…
OR=ad / bc
Misclassification
True
Dog
No dog
TBE-cases
20
20
Controls
20
60
Dog
No dog
TBE-cases
24
16
Controls
20
60
Dog
No dog
TBE-cases
24
16
Controls
28
52
Differential
Nondifferential
OR = ad/bc =
3,0
OR = ad/bc =
4,5
OR = ad/bc =
2,8
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 population
3 A confounder must not be affected by the exposure or the
disease
Umbrella
Less tub.
2
1
3
Class
Downs’
by birth
Cases ofsyndrome
Down syndroms
byorder
birth order
Cases per 100 000
live births
180
160
140
120
100
80
60
40
20
0
1
2
3
Birth order
4
5
Find confounders
“Second, third and fourth child are more often
affected by Downs’ syndrome.”
Downs’
Many children
Maternal
age
Downs’ syndrome by maternal age
Cases of Down Syndrom by age groups
Cases per
100000 live
births
1000
900
800
700
600
500
400
300
200
100
0
< 20
20-24
25-29
30-34
Age groups
35-39
40+
Downs’ syndrome by birth order and
maternal age groups
Cases per
100000
1000
900
800
700
600
500
400
300
200
100
0
1
2
3
Birth order
4
5
<2
0
25
-29
35
-39
up
o
gr
e
Ag
s
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
Restriction
Restriction 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.
Lower
Class
class
Restriction
We study only mothers of a certain age
Downs’
Many children
35 year old
mothers
Matching
“Selection of controls to be identical to the
cases with respect to distribution of one or
more potential confounders.”
Downs’
Many children
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
Cases per
100000
1000
900
800
700
600
500
400
300
200
100
0
1
2
3
Birth order
4
5
<2
0
25
-29
35
-39
up
o
gr
e
Ag
s
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