Confounding in studies

Confounding

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 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.

Cohort Study (hypothetical)

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.

Gender	Cases	Total	Attack Rate	RR
Boys	819	1000	82%	4.52
Girls	181	1000	18%	ref

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.

Stratified	Gender	Cases	Total	Attack Rate	RR
Unvaccinated	Boys	814	950	86%	1.00
	Girls	86	100	86%	ref
Vaccinated	Boys	5	50	10%	0.95
	Girls	95	900	11%	ref

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.

Case-control study

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	Cases	Controls	Odds Ratio
<0.1	2939	16835	ref
0.10-0.19	11369	60859	0.93

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	Cases	Controls	OR	95%CI
<50yrs	<0.1	840	9222	ref
	0.10-0.19	2833	29282	0.94	0.87	1.02
≥50yrs	<0.1	2083	7613	ref
	0.10-0.19	8536	31577	1.01	0.96	1.07

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

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 , .

	Cases Cured	Total cases	Percentage cured	RR
Treatment A	273	350	78%	ref
Treatment B	289	350	83%	1.06

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.

		Cases Cured	Total cases	Percentage cured	RR
Small stones	Treatment A	81	87	93%	1.07
	Treatment B	234	270	87%	ref
Large stones	Treatment A	192	263	73%	1.06
	Treatment B	55	80	69%	ref

For both smaller and larger kidney stones; Treatment A resulted in the higher proportion of patients cured.

Two facts are evident:

1. Those with small stones tend to be given Treatment B preferentially, while those with large stones are provided with Treatment A. So there are dominating proportions - the patients are not evenly distributed between treatment groups regardless of the confounding variable (size of stones). There is an association between the size of the stone and the treatment option offered.
2. The confounding variable has a large effect on the outcome: those with large stones, even if given the better treatment (A), will see less success than those with small stones. There is an association between the size of stone and the proportion of success.

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.