THREE CONCEPTS ABOUT THE RELATIONSHIPS OF

VARIABLES IN RESEARCH

• CONFOUNDING

• MEDIATION

• EFFECT MODIFICATION, INTERACTION OR MODERATION

THINKING ABOUT THE WAYS IN WHICH VARIABLES MAY BE

RELATED ILLUMINATES BIAS

AND CONFOUNDING

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?

 

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) 

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

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.

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.

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.

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.

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

CONCLUSION: COFFEE DRINKING IS NOT A CAUSE OF MYOCARDIAL INFARCTION

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.

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.

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.

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.

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

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.

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.

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.

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.

AN EXAMPLE OF INTERACTION OR EFFECT

MODIFICATION

A study finds that there is no relationship, in infants < 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, 1982;116:364-375).

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:

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

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 RR’s 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.

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.

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.

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.

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