Case-control study 3: Bias and confounding and analysis

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Case-control study 3Bias and confoundingand
analysis

• Preben Aavitsland

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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

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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

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Calculating the odds ratio (OR)

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

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Can we believe the result?
Having a dog
TBE
OR RR 4.5
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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
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Random errors
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Systematic errors
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Errors in epidemiological studies
Error
Random error (chance)
Systematic error (bias)
Study size
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Random error

• Low precision because of
• Imprecise measuring
• Too small groups
• Decreases with increasing group size
• Can be quantified by confidence interval

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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)

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OR and confidence interval

• Shows magnitude of the causal effect
• Shows direction of the effect
• OR gt 1 ? increases risk (risk factor)
• OR gt 1 ? decreases risk (preventive factor)
• Shows the precision around the point estimate
• Condition no systematic errors
• Forget about p-values! No advantages.

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Larger study ? narrower interval
Use Episheet
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Systematic error

• Does not decrease with increasing sample size
• Selection bias
• Information bias
• Confounding

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Selection bias

• Error because the association exposure ?
  diseaseis different for participants and
  non-participants in the study
• Errors in the
• procedures to select participants
• factors that influence participation

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Examples of selection bias

• Self-selection bias
• Healthy worker effect
• Non-response
• Refusal
• Loss to follow-up

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Can we believe the result?
Having a dog
TBE
OR IRR 4.5
ORad / bc
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
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Preventing selection bias

• Same selection criteria
• High response-rate
• High rate of follow-up

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Information bias

• Error because the measurement of exposure or
  diseaseis different between the comparison
  groups.
• Errors in the
• procedures to measure exposure
• procedures to diagnose disease

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Examples of information bias

• Diagnostic bias
• Recall bias
• Researcher influence

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Can we believe the result?
Having a dog
TBE
OR IRR 4.5
ORad / bc
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
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Misclassification
True
Differential
Non-differential
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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?

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Preventing information bias

• Clear definitions
• Good measuring methods
• Blinding
• Standardised procedures
• Quality control

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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
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Confounding - 2

• Key term in epidemiology
• Most important explanation for associations
• Always look for confounding factors

Surgeon
Post op inf.
Op theatre I
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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
Class
3
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Downs syndrome by birth order
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Find confounders
Second, third and fourth child are more often
affected by Downs syndrome.
Many children
Downs
Maternal age
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Downs syndrome by maternal age
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Downs syndrome by birth order and maternal age
groups
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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
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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
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Controlling confounding

• In the design
• Restriction of the study
• Matching

• In the analysis
• Restriction of the analysis
• Stratification
• Multivariable regression

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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
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Restriction
We study only mothers of a certain age
Many children
Downs
35 year old mothers
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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
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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

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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

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Should we match?

• Probably not, but may
• If there are many possible confounders that you
  need to stratify for in analysis

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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 (gt 10-20) from crude OR,
  then confounding is present and adjusted OR
  should be reported

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Stratification
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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

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Controlling confounding

• In the design
• Restriction of the study
• Matching

• In the analysis
• Restriction of the analysis
• Stratification
• Multivariable methods

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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