Crossover Design

The crossover design (also referred to as a replicated Latin square design) refers to a longitudinal study in which participants receive a sequence of treatments that varies based on the group to which the individual is assigned. The groups may be randomly assigned in the case of an experiment or allocated based on some other criteria (e.g., geographic location, classroom) in the case of a nonexperimental study. In its simplest form, the crossover design involves two periods by two treatments. Figure 1 depicts a basic 2 × 2 crossover design with two treatment sequences: AB and BA. As depicted in the diagram, all participants undergo a pretest at the commencement of the study. Then, in the first period of the study, one group of participants receives Treatment A while the other receives Treatment B. At the completion of the first treatment period, participants are administered a posttest. Groups then “crossover,” in the second period, so that individuals who started with Treatment A commence Treatment B and those who began with Treatment B undergo Treatment A. Another posttest is conducted after the second period.

Figure 1 Basic crossover design

More complex variations of the crossover design can include more than two treatments or groups or could involve the use of a treatment in more than one period. The number of waves (or treatment periods) can vary considerably based on the nature of the research question and the length of each treatment. Depending on the design selected, researchers can apply a variety of statistical analyses to determine the impact of period, sequence, carryover, and treatment effects. Designs vary to the extent that they are balanced (i.e., whether or not each treatment is preceded by every other treatment the same number of times) and uniform (i.e., whether each period allocates each treatment to the same number of subjects or whether each subject receives every treatment the same number of times). An example of a balanced uniform crossover design (4 periods × 4 groups) would produce four treatment sequences: ABBA, BAAB, AABB, and BBAA.

Crossover designs have been employed in a wide variety of settings ranging from educational to epidemiological research. The crossover design is primarily used to allow researchers to compare the efficacy or impact of multiple treatments or a combination of treatments and control or placebo conditions. Crossover designs are most appropriate for interventions that are considered temporary, so that multiple treatment options can be tested. Depending on the nature of the treatments, there may be a washout interval between periods to allow the effects of one treatment to wear off before undergoing the next treatment. Clinical trials in medical or pharmaceutical research frequently employ crossover designs to assess the efficacy of different types of medications on a disease or condition. In the social sciences, crossover designs can be used to examine a wide variety of research questions such as the impact of different clinical rotation sequences on examination performance or the effectiveness of different [Page 438]psychotherapy approaches on depression. The remainder of this entry discusses the strengths and limitations of the crossover design.

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