Obviously, it appears that an “ideal” crossover design is uniform and strongly balanced.
There are situations, however, where it may be reasonable to assume that some of the nuisance parameters are null, so that resorting to a uniform and strongly balanced design is not necessary (although it provides a safety net if the assumptions do not hold).
For example, some researchers argue that sequence effects should be null or negligible because they represent randomization effects. Another example occurs in bioequivalence trials where some researchers argue that carryover effects should be null. This is because blood concentration levels of the drug or active ingredient are monitored and any residual drug administered from an earlier period would be detected.
The message to be emphasized is that every proposed crossover trial should be examined to determine which, if any, nuisance effects may play a role. Once this determination is made, then an appropriate crossover design should be employed that avoids aliasing of those nuisance effects with treatment effects. This is a decision that the researchers should be prepared to address.
For example, an investigator wants to conduct a two-period crossover design, but is concerned that he will have unequal carryover effects so he is reluctant to invoke the 2 × 2 crossover design. If the investigator is not as concerned about sequence effects, then Balaam’s design in [Design 8] may be appropriate. Balaam’s design is uniform within periods but not within sequences, and it is strongly balanced. Therefore, Balaam’s design will not be adversely affected in the presence of unequal carryover effects.
Some researchers consider randomization in a crossover design to be a minor issue because a patient eventually undergoes all of the treatments (this is true in most crossover designs). Obviously, randomization is very important if the crossover design is not uniform within sequences because the underlying assumption is that the sequence effect is negligible. Randomization is important in crossover trials even if the design is uniform within sequences because biases could result from investigators assigning patients to treatment sequences.
At a minimum, it always is recommended to invoke a design that is uniform within periods because period effects are common. Period effects can be due to:
- increased patient comfort in later periods with trial processes;
- increased patient knowledge in later periods;
- improvement in skill and technique of those researchers taking the measurements.
The following is a listing of various crossover designs with some, all, or none of the properties.
| Uniform within Sequences | Uniform within Periods | Balanced | Strongly Balanced | Examples |
|---|---|---|---|---|
| no | no | no | no | AAB|ABB, ABCC|BCAA |
| yes | no | no | no | ABB|BAB, ABC|CBA |
| no | yes | no | no | ABCC|BCAA|CABB |
| no | no | yes | no | ABAA|BAAB |
| no | no | yes | yes | AABBA|BAABB |
| yes | yes | no | no | ABC|BCA|CAB |
| yes | no | yes | no | AABA|ABAA |
| no | yes | yes | no | ABA|BAB |
| yes | no | yes | yes | AABBA|ABBAA |
| no | yes | yes | yes | ABB|BAA, AB|BA|AA|BB |
| yes | yes | yes | no | AB|BA |
| yes | yes | yes | yes | ABBA|BAAB|AABB|BBAA |
It would be a good idea to go through each of these designs and diagram out what these would look like, the degree to which they are uniform and/or balanced. Make sure you see how these principles come into play!