ABSTRACT
Experimental designs that generate correlated measurements of an outcome are widely used in biomedical, social, and behavioral studies. We usually classify such experimental designs into two types: clustered or longitudinal. In a clustered trial, randomization is performed at the level of some aggregate, such as schools, clinics, or communities. It is often adopted due to necessity where the intervention under test is delivered on a group basis, for example, a radio campaign against smoking in a socially and economically disadvantaged community. It can also be employed for administrative convenience. For example, to examine the effectiveness of a new hypertension control strategy taking advantage of electronic medical records (EMR) versus the traditional strategy, randomization is performed on caring physicians, by whom the patients are clustered. The reason is that operationally it is difficult for a physician to simultaneously practice different treatment strategies. As for a longitudinal trial, randomization is performed at the individual level. However, over the study period the outcome variable is measured multiple times from the same individuals, hence giving rise to the issue of within-subject correlation. A key difference between these two types of design is that under the clustered design the measurements within a randomization unit (cluster) are usually considered exchangeable. Thus the compound symmetric correlation structure has been frequently employed. Under the longitudinal design, however, the measurements within a unit (individual) are distinguished by their time stamps due to the potential temporal trend. Thus an autoregressive-type of correlation is more frequently used which assumes the correlation to decay by the temporal distance between measurements. In practice researchers are also likely to encounter correlated outcomes with a hierarchical structure, which is even more complicated. For example, patients can be clustered by physicians, while physicians can be clustered by clinics. In this case the correlation structure contains multiple levels of nested clustering. This topic is further explored in Chapter 6. Another example is that patients are clustered by physicians, but each patient contributes a longitudinal series of outcome measurements. In such cases we encounter a hybrid type of correlation structure.
