Confounding, interactions, methods for assessment of effect modification; Strategies to allow/adjust for confounding in design and analysis

While the results of an epidemiological study may reflect the true effect of an exposure on the development of the outcome under investigation, it should always be considered that the findings may in fact be due to an alternative explanation.¹

Such alternative explanations may be due to the effects of chance (random error), bias or confounding which may produce spurious results, leading us to conclude the existence of a valid statistical association when one does not exist or alternatively the absence of an association when one is truly present.¹

Observational studies are particularly susceptible to the effects of chance, bias and confounding and all three need to be considered at both the design and analysis stage of an epidemiological study, so their potential effects can be minimised.

Confounding, interaction and effect modification

Confounding provides an alternative explanation for an association between an exposure (X) and an outcome. It occurs when an observed association is in fact distorted because the exposure is also correlated with another risk factor (Y). This risk factor Y is also associated with the outcome, but independently of the exposure under investigation, X. As a consequence, the estimated association is not that same as the true effect of exposure X on the outcome.

An unequal distribution of the additional risk factor, Y, between the study groups will result in confounding. The observed association may be due totally or in part to the effects of differences between the study groups other than the exposure under investigation.¹

A potential confounder is any factor that might have an effect on the risk of disease under study. This may include factors with a direct causal link the disease, as well as factors that are proxy measures for other unknown causes, such as age and socioeconomic status.²

In order for a variable to be considered as a confounder:

1. The variable must be independently associated with the outcome (i.e. be a risk factor).
2. The variable must be also associated with the exposure under study in the source population.
3. It should not lie on the causal pathway between exposure and disease.

Examples of confounding

A study found alcohol consumption to be associated with the risk of Coronary Heart Disease. However, smoking may have confounded the association between alcohol and CHD.

Smoking is a risk factor in its own right for CHD, so is independently associated with the outcome, and smoking is also associated with alcohol consumption because smokers tend to drink more than non-smokers.

Controlling for the potential confounding effect of smoking may in fact show no association between alcohol consumption and CHD.

Effects of confounding

Confounding factors, if not controlled for, cause bias in the estimate of the impact of the exposure being studied. The effects of confounding may result in:

• An observed difference between study populations when no real difference exists.
• An observed difference between study populations when a true association does exist.
• An underestimate of an effect.
• An overestimate of an effect.

Controlling for confounding

Confounding can be dealt with either at the study design stage, or at the analysis stage providing sufficient relevant data have been collected. A number of methods can be applied to control for potential confounding factors and the aim of all of them is to make the groups as similar as possible with respect to the confounder.

Potential confounding factors may be identified at the design stage based on previous studies or because the factor may be considered as biologically plausible.

Controlling for confounding at the design stage

• Randomisation (random allocation)

This is the ideal method of controlling for confounding because all potential confounding variables, both known and unknown, should be equally distributed in the study groups. It involves the random allocation (e.g. using a table of random numbers) of individuals to study groups. However, this method can only be used in experimental clinical trials.

• Restriction

Restriction limits participation in the study to individuals who are similar in relation to the confounder. For example if participation in a study is restricted to non-smokers only, any potential confounding effect of smoking will be eliminated. However, a disadvantage of restriction is that it may be difficult to generalize the results of the study to the wider population if the study group is homogenous.¹

• Matching

Matching involves selecting controls so that the distribution of potential confounders (e.g. age or smoking) is as similar as possible to that amongst the cases. In practice this is only utilised in case-control studies, but it can be done in two ways:

1. Pair matching - selecting for each case one or more controls with similar characteristics (e.g. same age and smoking habits)
2. Frequency matching - ensuring that as a group the cases have similar characteristics to the controls

Detecting the presence of confounding

The presence or magnitude of confounding in epidemiological studies is evaluated by observing the degree of discrepancy between the crude and adjusted estimates.¹ One method to assess for the presence of confounding is to calculate the crude relative risk (without controlling for confounding) and compare this measure with the relative risk adjusted for the potential confounder. If the relative risk has changed and there is little variation between the stratum specific rate ratios, then there is evidence of confounding

It is inappropriate to use statistical tests to assess the presence of confounding, but the following methods may be used to minimise its effect

Controlling for confounding during analysis

• Stratification

Stratification allows the association between exposure and outcome to be examined within different strata of the confounding variable, for example by age or sex. The strength of the association is initially measured separately within each stratum of the confounding variable.

Assuming the stratum specific rates are relatively uniform, they may then be pooled to give a summary estimate of the relative risk adjusted or controlled for the potential confounder. One drawback of this method is that the more the original sample is stratified, the smaller each stratum will become, and the power to detect associations is reduced. Standardisation is an example of stratification.

• Multivariate analysis

As the number of confounders that can be controlled for simultaneously is limited, particularly as this may lead to small numbers in some strata, statistical modelling (e.g. logistic regression) is commonly used to control for more that one confounder at the same time.

Residual confounding

It is only possible to control for confounders in the analysis if data on confounders were accurately collected. Residual confounding occurs when a confounder has not been adequately adjusted for in the analysis. An example would be socioeconomic status, because it influences multiple health outcomes but is difficult to measure accurately.3

Random misclassification of a confounder can result in either an over- or under- estimate of the true effect of the exposure under investigation.

Interaction (effect modification)

Interaction occurs when the direction or magnitude of an association between two variables differs due to the effect of a third variable. It may reflect a cumulative effect of multiple risk factors which are not acting independently and produce a greater or lesser effect than the sum of the effects of each factor acting on its own.

References

1. Hennekens CH, Buring JE. Epidemiology in Medicine, Lippincott Williams & Wilkins, 1987.
2. Bailey L, Vardulaki K, Langham J, Chandramohan D. Introduction to Epidemiology. Open University Press, 2005.
3. http://www.edmundjessop.org.uk/fulltext.doc - Accessed 11/01/09

© Helen Barratt, Maria Kirwan 2009