15.1 - Overview of the Crossover Designs
15.1 - Overview of the Crossover DesignsThe order of treatment administration in a crossover experiment is called a sequence and the time of a treatment administration is called a period. Typically, the treatments are designated with capital letters, such as A, B, etc.
The sequences should be determined a priori and the experimental units are randomized to sequences. The most popular crossover design is the 2-sequence, 2-period, 2-treatment crossover design, with sequences AB and BA, sometimes called the 2 × 2 crossover design.
In this particular design, experimental units that are randomized to the AB sequence receive treatment A in the first period and treatment B in the second period, whereas experimental units that are randomized to the BA sequence receive treatment B in the first period and treatment A in the second period.
We express this particular design as AB|BA or diagram it as:
Period 1 | Period 2 | |
Sequence AB | A | B |
Sequence BA | B | A |
Examples of 3-period, 2-treatment crossover designs are:
Period 1 | Period 2 | Period 3 | |
Sequence ABB | A | B | B |
Sequence BAA | B | A | A |
and
Period 1 | Period 2 | Period 3 | |
Sequence AAB | A | A | B |
Sequence ABA | A | B | A |
Sequence BAA | B | A | A |
Examples of 3-period, 3-treatment crossover designs are
Period 1 | Period 2 | Period 3 | |
Sequence ABC | A | B | C |
Sequence BCA | B | C | A |
Sequence CAB | C | A | B |
and
Period 1 | Period 2 | Period 3 | |
Sequence ABC | A | B | C |
Sequence BCA | B | C | A |
Sequence CAB | C | A | B |
Sequence ACB | A | C | B |
Sequence BAC | B | A | C |
Sequence CBA | C | B | A |
Some designs even incorporate non-crossover sequences such as Balaam's design:
Period 1 | Period 2 | |
Sequence AB | A | B |
Sequence BA | B | A |
Sequence AA | A | A |
Sequence BB | B | B |
Balaam’s design is unusual, with elements of both parallel and crossover design. There are advantages and disadvantages to all of these designs; we will discuss some and the implications for statistical analysis as we continue through this lesson.