How do I analyze 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.

By far the most common circumstance leading to correlated outcomes 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).

However, as you can see from Table 12.1, there are disparate sets of circumstances that may lead to correlated observations.

Although the study designs listed in Table 12.1 seem disparate, what they all have in common is that observations are clustered. In the case of a longitudinal study, the cluster is the subject (subjects are observed multiple times). When subjects receive different treatments or have different body parts observed, the cluster is also the subject. In the case of subjects who have been randomized or recruited, based on an established group (e.g., families, doctors' practices), the cluster is the established group. In a matched design, the cluster is the matched case and control.