BIAS AND CONFOUNDING

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BIAS AND CONFOUNDING

• Nigel Paneth

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HYPOTHESIS FORMULATION AND ERRORS IN RESEARCH

• All analytic studies must begin with a clearly
  formulated hypothesis. The hypothesis must be
  quantitative and specific. It must predict a
  relationship of a specific size.

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• For example
•   Babies who are breast-fed have less illness
  than babies who are bottle-fed.
•  
• Which illnesses? How is feeding type defined?
  How large a difference in risk?
• A better example
•   Babies who are exclusively breast-fed for
  three months or more will have a reduction in the
  incidence of hospital admissions for
  gastroenteritis of at least 30 over the first
  year of life.

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• Only specific prediction allows one to draw
  legitimate conclusions from a study which tests a
  hypothesis. But even with the best formulated
  hypothesis, two types of errors can occur.
•  
• Type 1 - observing a difference when in truth
  there is none.
•  
• Type 2 - failing to observe a difference when
  there is one.

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• These errors are generally produced by one or
  more of the following
•  
• RANDOM ERROR
• RANDOM MISCLASSIFICATION
• BIAS
• CONFOUNDING

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RANDOM ERROR

• Deviation of results and inferences from the
  truth, occurring only as a result of the
  operation of chance. Can produce type 1 or type 2
  errors.

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RANDOM (OR NON-DIFFERENTIAL) MISCLASSIFICATION

• Random error applied to the measurement of an
  exposure or outcome. Errors in classification
  can only produce type 2 errors, except if applied
  to a confounder or to an exposure gradient.

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BIAS

• Systematic, non-random deviation of results and
  inferences from the truth, or processes leading
  to such deviation. Any trend in the collection,
  analysis, interpretation, publication or review
  of data that can lead to conclusions which are
  systematically different from the truth.
  (Dictionary of Epidemiology, 3rd ed.)
•  

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MORE ON BIAS

• Note that in bias, the focus is on an artifact
  of some part of the research process (assembling
  subjects, collecting data, analyzing data) that
  produces a spurious result. Bias can produce
  either a type 1 or a type 2 error, but we usually
  focus on type 1 errors due to bias.

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MORE ON BIAS

• Bias can be either conscious or unconscious. In
  epidemiology, the word bias does not imply, as in
  common usage, prejudice or deliberate deviation
  from the truth.

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CONFOUNDING

• A problem resulting from the fact that one
  feature of study subjects has not been separated
  from a second feature, and has thus been
  confounded with it, producing a spurious result.
  The spuriousness arises from the effect of the
  first feature being mistakenly attributed to the
  second feature. Confounding can produce either a
  type 1 or a type 2 error, but we usually focus on
  type 1 errors.

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THE DIFFERENCE BETWEEN BIAS AND CONFOUNDING

• Bias creates an association that is not true,
  but confounding describes an association that is
  true, but potentially misleading.

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EXAMPLES OF RANDOM ERROR, BIAS, MISCLASSIFICATION
AND CONFOUNDING IN THE SAME STUDY

• STUDY In a cohort study, babies of women who
  bottle feed and women who breast feed are
  compared, and it is found that the incidence of
  gastroenteritis, as recorded in medical records,
  is lower in the babies who are breast-fed.

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EXAMPLE OF RANDOM ERROR

• By chance, there are more episodes of
  gastroenteritis in the bottle-fed group in the
  study sample, producing a type 1 error. (When in
  truth breast feeding is not protective against
  gastroenteritis).
• Or, also by chance, no difference in risk was
  found, producing a type 2 error (When in truth
  breast feeding is protective against
  gastroenteritis).

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EXAMPLE OF RANDOM MISCLASSIFICATION

• Lack of good information on feeding history
  results in some breast-feeding mothers being
  randomly classified as bottle-feeding, and
  vice-versa. If this happens, the study finding
  underestimates the true RR, whichever feeding
  modality is associated with higher disease
  incidence, producing a type 2 error.

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EXAMPLE OF BIAS

• The medical records of bottle-fed babies only are
  less complete (perhaps bottle fed babies go to
  the doctor less) than those of breast fed babies,
  and thus record fewer episodes of
  gastro-enteritis in them only.
• This is called ias because the observation itself
  is in error.

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EXAMPLE OF CONFOUNDING

• The mothers of breast-fed babies are of higher
  social class, and the babies thus have better
  hygiene, less crowding and perhaps other factors
  that protect against gastroenteritis. Crowding
  and hygiene are truly protective against
  gastroenteritis, but we mistakenly attribute
  their effects to breast feeding. This is called
  confounding. because the observation is correct,
  but its explanation is wrong.

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PROTECTION AGAINST RANDOM ERROR AND RANDOM
MISCLASSIFICATION

• Random error can work to falsely produce an
  association (type 1 error) or falsely not produce
  an association (type 2 error).
• We protect ourselves against random
  misclassification producing a type 2 error by
  choosing the most precise and accurate measures
  of exposure and outcome.

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PROTECTION AGAINST TYPE 1 ERRORS

• We protect our study against random type 1
  errors by establishing that the result must be
  unlikely to have occurred by chance (e.g. p lt
  .05). P-values are established
  entirely to protect against type 1 errors due to
  chance, and do not guarantee protection against
  type 1 errors due to bias or confounding. This is
  the reason we say statistics demonstrate
  association but not causation.

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PROTECTION AGAINST TYPE 2 ERRORS

• We protect our study against random type 2
  errors by
• providing adequate sample size, and
• hypothesizing large differences.
• The larger the sample size, the easier it will
  be to detect a true difference, and the largest
  differences will be the easiest to detect.
  (Imagine how hard it would be to detect a 1
  increase in the risk of gastroenteritis with
  bottle-feeding).

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TWO WAYS TO INCREASE POWER

• The sample size needed to detect a significant
  difference is called the power of a study.
•  Choosing the most precise and accurate measures
  of exposure and outcome has the effect of
  increasing the power of our study, because of
  variances of the outcome measures, which enter
  into statistical testing, are decreased.
• Having an adequate sized sample of study subjects
•  

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KEY PRINCIPLE IN BIAS AND CONFOUNDING

• The factor that creates the bias, or the
  confounding variable, must be associated with
  both the independent and dependent variables
  (i.e. with the exposure and the disease).
  Association of the bias or confounder with just
  one of the two variables is not enough to produce
  a spurious result.

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• In the example just given
•  
• The BIAS, namely incomplete chart recording, has
  to be associated with feeding type (the
  independent variable) and also with recording of
  gastroenteritis (the dependent variable) to
  produce the false result.
•  
• The CONFOUNDING VARIABLE (or CONFOUNDER) better
  hygiene, has to be associated with feeding type
  and also with gastroenteritis to produce the
  spurious result.

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• Were the bias or the confounder associated with
  just the independent variable or just the
  dependent variable, they would not produce bias
  or confounding.
• This gives a useful rule
• If you can show that a potential confounder is
  NOT associated with either one of the two
  variables under study (exposure or outcome),
  confounding can be ruled out.

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GOOD STUDY DESIGN PROTECTS AGAINST ALL FORMS OF
ERROR
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SOME TYPES OF BIAS

• 1. SELECTION BIAS
•  
• Any aspect of the way subjects are assembled in
  the study that creates a systematic difference
  between the compared populations that is not due
  to the association under study.  

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• 2. INFORMATION BIAS
• Any aspect of the way information is collected
  in the study that creates a systematic difference
  between the compared populations that is not due
  to the association under study. (some call this
  measurement bias). The incomplete chart
  recording in the baby feeding example would be a
  form of information bias.
• Other examples -
• Diagnostic suspicion bias
• Recall bias
•  Sometimes biases apply to a population of
  studies, rather than to one study, as in
  publication bias (tendency to publish papers
  which show positive results).