# Associations

## Associations

Two variables are associated, statistically dependent, if one of the variables says something about the other, and this can range from nothing to everything. Correlated variables are always dependent, but dependent variables are not necessarily correlated because correlation refers to linear relationships. It is, for example, easy to show that the two mathematically coupled variables X and Y, where Y = X² and completely dependent, are not correlated when x = -3, -2, -1, 0, 1, 2, 3.

Many authors use the word association when describing relationships between risk factors and disease or between treatments and recovery. The reason for this may be that they wish to avoid being accused of interpreting observed correlations in terms of cause and effect. It is well known that this is a controversial subject.

However, in order to study risk factor and treatment effects, the statistical analysis needs to be based on assumptions regarding cause and effect, i.e. in terms of a statistical model Y = f(X), that the studied outcome, Y, is an effect of exposure to a factor X. Moreover, if Y = f(X, Z) where Z is a biasing factor, the effect estimate must be adjusted for the influence of Z, and this requires further cause-effect relations. Otherwise attempts to reduce confounding bias may induce adjustment bias. This would happen when a mediator or collider is included in the statistical model instead of a confounder (mediators, colliders and confounders being defined by different cause-effect relationships).

The word association is often used as a camouflage for avoiding discussing considerations regarding technical issues about used effect estimates (RR, HR, OR, IR, SMR, etc.) and for avoiding presentation and motivation of assumptions underlying the confounding adjustment.

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