What circumstances lead to correlated observations?

The multivariable methods that we have discussed thus far assume that each observation (subject) is independent (i.e., the outcomes of different subjects are not correlated). However, it has become increasingly common to study data where the observations are correlated with one another, often referred to as clustered observations or clusters.

As you can see from Table 11.1, a variety of circumstances leads to correlated observations. One common circumstance leading to correlated observations is longitudinal studies, where subjects are observed repeatedly (e.g., baseline and every six months thereafter). Because it is the same subject being observed multiple times, the responses are correlated (i.e., the same subject is more likely to have a similar response each time he or she is observed than a different subject would).

Also, when the same subject receives different treatments, as occurs in a crossover study, responses will be correlated because the same person is more likely to respond to different circumstances in a similar way than different individuals receiving different treatments. And the responses of different body parts of the same person (e.g., the right and left eye of Mr. A) will be correlated because the body parts of the same person are more likely to respond similarly than body parts belonging to different persons (e.g., the right eye of Mr. A and the left eye of Mr. B).