THREE CONCEPTS ABOUT THE RELATIONSHIPS OF VARIABLES IN RESEARCH

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THREE CONCEPTS ABOUT THE RELATIONSHIPS OF
VARIABLES IN RESEARCH

• CONFOUNDING
• MEDIATION
• EFFECT MODIFICATION, INTERACTION OR MODERATION

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THINKING ABOUT THE WAYS IN WHICH VARIABLES MAY BE
RELATED ILLUMINATES BIAS AND CONFOUNDING
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ILLUSTRATION OF CONFOUNDING

• Diabetes is associated with hypertension.
• Does diabetes cause hypertension?
• Does hypertension causes diabetes?
•  
• Or is it possible that diabetes and hypertension
  share a common antecedent?
•  

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• Thus while an exposure may cause a disease,
  another way in which exposure and disease may be
  related is if both variables are caused by FACTOR
  X. For hypertension and diabetes, Factor X might
  be obesity
•  
• X A (hypertension)
• (obesity)
• B (diabetes)
•  

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• If we had concluded that diabetes caused
  hypertension, whereas, in fact, they had no true
  causal relationship, we would say that
•  THE RELATIONSHIP BETWEEN HYPERTENSION AND
  DIABETES IS CONFOUNDED BY OBESITY. OBESITY WOULD
  BE TERMED A CONFOUNDING VARIABLE IN THIS
  RELATIONSHIP.
•  
• Another important truism
• CONFOUNDERS ARE TRUE CAUSES OF DISEASE, WHEREAS
  BIASES ARE ARTEFACTS

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MEDIATION AND CONFOUNDING

• Not every factor that is associated with both the
  exposure and the disease is a confounding
  variable. Such a factor could be a MEDIATING
  VARIABLE.
•  
• A mediator is also associated with both the
  independent and dependent variables, but is part
  of the causal chain between the independent and
  dependent variables.

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• FAILURE TO DISTINGUISH A CONFOUNDER FROM A
  MEDIATOR IS ONE OF THE COMMONEST ERRORS IN
  EPIDEMIOLOGY.  THESE TWO KINDS OF VARIABLES
  CANNOT BE DISTINGUISHED ON STATISTICAL GROUNDS.
  THEY CAN ONLY BE SEPARATED FROM EACH OTHER BASED
  ON AN UNDERSTANDING OF THE TOTAL DISEASE PROCESS.
•  To make this distinction clear, lets see how we
  set about to CONTROL FOR confounding in
  epidemiological research.

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APPROPRIATE CONTROL FOR CONFOUNDING

• HYPOTHESIS There is an association between an
  exposure (coffee drinking) and a disease
  (myocardial infarction), but we wonder whether
  cigarette smoking could be a confounder of this
  relationship.

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• STEP 1. IS THERE AN ASSOCIATION?
• Heavy coffee drinking is statistically associated
  with higher rates of myocardial infarction. Is
  coffee then a cause of myocardial infarction?
•  
• STEP 2. IDENTIFY POTENTIAL CONFOUNDERS
• Could cigarette smoking be a confounder?
•  
• STEP 3. IS THE POTENTIAL CONFOUNDER ASSOCIATED
  WITH THE EXPOSURE?
• Heavy coffee drinking is associated with higher
  rates of smoking. Smoking fulfills one criterion
  for potential confounding.

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• STEP 4. IS THE POTENTIAL CONFOUNDER ASSOCIATED
  WITH THE DISEASE OF INTEREST?
• Smoking is associated with higher rates of
  myocardial infarction. Smoking fulfills the
  second criterion for potential confounding.
•  
• STEP 5. WHAT HAPPENS WHEN WE CONTROL FOR
  CIGARETTE SMOKING?
• Adjustment for cigarette smoking eliminates the
  association of heavy coffee drinking and
  myocardial infarction. The association is
  explained by the fact that more coffee drinkers
  are also smokers

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CONCLUSION COFFEE DRINKING IS NOT A CAUSE OF
MYOCARDIAL INFARCTION
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INAPPROPRIATE CONTROL FOR CONFOUNDING

• HYPOTHESIS There is an association between an
  exposure (obesity) and a disease (myocardial
  infarction), but we wonder whether cholesterol
  level could be a confounder of this relationship.

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• STEP 1. IS THERE AN ASSOCIATION?  
• Obesity is statistically associated with higher
  rates of myocardial infarction. Is obesity then a
  cause of myocardial infarction?
•  
• STEP 2. IDENTIFY POTENTIAL CONFOUNDERS
• Could cholesterol level be a confounder?
•  
• STEP 3. IS THE POTENTIAL CONFOUNDER ASSOCIATED
  WITH THE EXPOSURE?
• Obesity and cholesterol level are associated.

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• STEP 4. IS THE POTENTIAL CONFOUNDER ASSOCIATED
  WITH THE DISEASE OF INTEREST?
• Cholesterol level is associated with higher rates
  of myocardial infarction.
• STEP 5. WHAT HAPPENS WHEN WE CONTROL FOR
  CHOLESTEROL LEVEL?
• Adjustment for cholesterol eliminates the
  association of obesity and myocardial infarction.

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CONCLUSION WE SHOULD NOT CONCLUDE THAT OBESITY
IS NOT A REAL CAUSE OF MYOCARDIAL INFARCTION,
BECAUSE CHOLESTEROL LEVEL MAY BE PART OF THE
PATHWAY FROM OBESITY TO MYOCARDIAL INFARCTION.
CONTROLLING FOR A PART OF THE CAUSAL PATHWAY IS
OVER-CONTROL.
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SUMMARY OF HOW A THIRD VARIABLE CAN RELATE TO TWO
OTHER VARIABLES(EXPOSURE AND DISEASE)

• A. IT CAN BE A CONFOUNDING VARIABLE
•  
• CONFOUNDER
•  
• EXPOSURE DISEASE

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• B. IT CAN BE A MEDIATING VARIABLE (SYNONYM
  INTERVENING VARIABLE)
•  
•  
• EXPOSURE MEDIATOR DISEASE
•  
•  
• AN EXPOSURE THAT PRECEDES A MEDIATOR IN A CAUSAL
  CHAIN IS CALLED AN ANTECEDENT VARIABLE.

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• Example
•  
• African-American babies are smaller than white
  babies. Smaller babies have higher mortality.
  Controlling for birth weight reduces or
  eliminates the differences between the ethnic
  groups in infant mortality. Does this mean that
  Ethnicity is not important in infant mortality?
  No, because birth weight is part of the causal
  pathway from ethnicity to infant mortality. It is
  a mediator.

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• C. IT CAN BE A MODERATOR VARIABLE (SYNONYMS
  INTERACTING OR EFFECT-MODIFYING VARIABLE)
•  
• MODERATOR
•  
• EXPOSURE DISEASE
•  
•  A moderator variable is one that moderates or
  modifies the way in which the exposure and the
  disease are related. When an exposure has
  different effects on disease at different values
  of a variable, that variable is called a
  modifier.

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• Examples
•  
• Aspirin protects against heart attacks, but
  only in men and not in women. We say then that
  gender moderates the relationship between aspirin
  and heart attacks, because the effect is
  different in the different sexes. We can also
  say that there is an interaction between sex and
  aspirin in the effect of aspirin on heart
  disease. 
• In individuals with high cholesterol levels,
  smoking produces a higher relative risk of heart
  disease than it does in individuals with low
  cholesterol levels. Smoking interacts with
  cholesterol in its effects on heart disease.

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AN EXAMPLE OF INTERACTION OR EFFECT MODIFICATION

• A study finds that there is no relationship,
  in infants lt 2,000g at birth, between multiple
  birth status (i.e. being a singleton or a twin)
  and the risk of mortality (Paneth et al, American
  J of Epidemiology, 1982116364-375).

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• ODDS RATIO FOR MORTALITY IN SINGLETONS (COMPARED
  TO TWINS)
•  
• UNADJUSTED 1.06
• ADJUSTED FOR BIRTHWEIGHT 1.02
•  
• However, this odds ratio conceals interesting
  information. It turns out that there is indeed a
  relationship between plurality and mortality, in
  the following way

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• BIRTHWEIGHT ODDS FOR MORTALITY
• IN SINGLETONS
• 501-750G 0.58
• 751-1000G 0.65
• 1001-1250G 0.91
• 1251-1500G 1.09
• 1501-1750G 2.45
• 1751-2000G 1.94

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• Clearly, under 1250g mortality is lower in
  singletons, above 1250g it is higher in
  singletons. These effects in opposite directions
  canceled each other out. This reversal of RRs
  is unusual - usually interaction accentuates a
  relative risk that is present at all values.
• The test for interaction is that the ODDS RATIO
  (or other measure of association) changes
  substantially according to different values of a
  third variable.

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HOW RANDOM MISCLASSIFICATION CAN SOMETIMES
PRODUCE A TYPE 1 ERROR

• 1. RANDOM MISCLASSIFICATION OF A CONFOUNDER
•  
• If a confounding variable is randomly
  misclassified, and then the exposure-disease
  relationship is stratified (or controlled) for
  this confounder, a spurious association can be
  produced. This usually requires that the
  confounding variable be very strongly related to
  the exposure.

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• Example Cigarette smoking and coffee drinking
  are associated. Since more coffee drinkers are
  smokers, more coffee drinkers recorded as
  non-smokers are really smokers than are
  non-coffee drinkers recorded as non-smokers. As
  a result, coffee drinkers can be found in some
  studies to have higher rates of lung cancer, even
  after smoking is controlled.

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• 2. RANDOM MISCLASSIFICATION ALONG AN EXPOSURE
  GRADIENT 
• If an exposure has a strong association with
  disease only above a certain threshold, random
  misclassification of that exposure is likely to
  produce a dose-response relationship. (Although
  this phenomenon surely occurs, I have never seen
  a clear demonstration of it in epidemiology.) 
• If cigarette smoking only produced lung cancer in
  two-pack a day smokers, the data would likely
  show some effect in one-pack a day smokers,
  because more of the two-pack a day smokers are
  likely to be misclassified as one-pack a day
  smokers than as non-smokers.

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CHECKLIST FOR BIAS AND CONFOUNDING

• Choice and framing of study question
• Choice of study population source
• Participation of study population
• Baseline assessments of participants
• Subsequent assessments of data from or about
  participants
• Exposure data
• Outcome data
• Analysis of data
• Publication of data
• Adapted from Bhopal, 2002, p. 73