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A confounding variable is one which is associated with both the exposure and the disease. It confounds the measured association (RR or OR). A variable is NOT a confounder if it lies on the causal pathway between the exposure and disease.
Confounding should always be addressed in studies investigating causality. Because the confounding variable is not evenly distributed between exposed and unexposed (in a cohort study) or between cases and controls (case-control study), and it is also a risk factor for the disease, the measured association is distorted or biased. The bias could be negative (an underestimate) or positive (an overestimate) or could even reverse the apparent direction of effect.
A cohort study was conducted during the investigation of an outbreak of a vaccine-preventable disease among 2000 children. Teachers had noticed that boys were more likely to be ill than girls.
One of the study objectives was to compare the risk of disease between boys and girls.
The following table illustrates the crude results. The risk of illness is 82% among boys compared to 18% among girls (risk ratio = 4.52). We would then suggest that risk of illness among boys was 4.5 times higher than among girls.
Given vaccination is likely to be a confounding variable affecting whether a person becomes ill with a vaccine preventable disease or not; the study population was divided in two strata, the vaccinated, and unvaccinated.
In the above example the distribution of vaccinations differs between boys and girls, therefore vaccination is associated with gender (5% of boys are vaccinated compared to 90% of the girls). In addition vaccination is associated to (a protective factor for) occurrence of disease. The risk of illness is 86% among unvaccinated and 10.5% among vaccinated. However, if we only consider the unvaccinated group, there is no longer a difference in occurrence of disease between boys and girls. Likewise, among the vaccinated group, the difference in disease occurrence between the genders is negligible;
The apparent association between gender and disease was confounded by vaccination status. Stratification according to the confounding variable showed that the association between gender and disease was absent.
A large case-control study was conducted in Sweden, to determine whether occupational magnetic fields were associated with female breast cancer . 20,400 cases of breast cancer were identified from the cancer registry, and 116,227 controls were selected randomly from the population register of all women between 1976 and 199 gainfully employed in Stockholm or Gotland County in Sweden. Exposure assessment was based on information about occupation obtained from the Swedish census, by linking a new job-exposure matrix to the occupation type.
Amount of exposure
This suggests that there is no association between levels of magnetic field exposure and development of cancer. But if a person is exposed to a greater amount of magnetic field over a longer time, then surely that would have an effect?
Age at diagnosis
Amount of Exposure
Showing that the same proportion of cases developed breast cancer regardless of exposure levels and age at diagnosis - i.e. when controlled for age, being exposed to a higher level of magnetic field has no effect on developing breast cancer. Therefore, in this example, age is not a confounder of the relationship between magnetic field exposure and breast cancer.
Simpsons Paradox refers to the reversal of the direction of an association when data from several groups are combined to form a single group.
Here is the crude result from the comparison of two treatment types (A and B) on kidney stones [2;3].
This analysis shows that Treatment B ought to be the preferred option.
If the size of the kidney stones is a confounding variable for the effect of the treatment; the analysis must be stratified.
For both smaller and larger kidney stones; Treatment A resulted in the higher proportion of patients cured.
Two facts are evident:
The apparent association between treatment type and outcome is confounded by the uneven distribution treatment between the two groups and by the fact that the percentage cured differs between the two groups.
The existence of two kidney stone sizes with unequal proportion of treatments and of success confounds the measured effect.
1. Forssen UM, Rutqvist LE, Ahlbom A, Feychting M. Occupational Magnetic Fields and Female Breast Cancer: A Case-Control Study using Swedish Population Registers and New Exposure Data. Am J Epidemiol 2005 Feb 1;161(3):250-9.
2. S.A.Julious, M.A.Mullee. Confounding and Simpson's paradox. BMJ 309, 1480. 3-12-1994.
3. C.R.Charig, D.R.Webb, S.R.Payne, J.E.A.Wickham. Comparison of treatment of renal calculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy. BMJ 292, 879-881. 29-3-1986.
The Third Factor
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Arnold Bosman posted on 7/5/2011 8:38:58 AM:
It may be good to include that Bradford Hill himself presented this as viewpoints, rather than criteria. In his own writing, he made explicit that none of these viewpoints can be considered irrevocable evidence of causality, nor can they be seen as a sine qua non.
To present them as "criteria" may enhance the misnterpretation that they should be seen as evidence for causality.
The book "history of epidemiological methods and concepts" includes some very insightful and educational quotes from Bradford Hill on these viewpoints. I will try later this week to include them in this chapter (as soon as I get behind a desktop computer, since this is written from my iPad)
Vladimir Prikazsky replied on 1/18/2017 12:03:24 PM:
More to read about Hill's criteria - viewpoints:
Association or causation: Evaluating links between “environment and disease” http://www.who.int/bulletin/volumes/83/10/792.pdf
Applying the Bradford Hill criteria in the 21st century: how data integration has changed causal inference in molecular epidemiology https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4589117/
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