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.

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 [1].  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 [2;3].

 

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.  

References

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[6967], 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.  

 

See also the following EPIET Lectures:

The Third Factor