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Crossover Design
There are many different types of experimental designs for different study scenarios. Crossover design is a special design in which each experimental unit receives a sequence of experimental treatments. In practice, it is not necessary that all permutations of all treatments be used. Researchers also call it switchover design, compared with a parallel group design, in which some experimental units only get a specific treatment and other experimental units get another treatment. In fact, the crossover design is a specific type of repeated measures experimental design. In the traditional repeated measures experiment, the experimental units, which are applied to one treatment (or one treatment combination) throughout the whole experiment, are measured more than one time, resulting in correlations between the measurements. The difference between crossover design and traditional repeated measures design is that in crossover design, the treatment applied to an experimental unit for a specific time continues until the experimental unit receives all treatments. Some experimental units may be given the same treatment in two or more successive periods, according to the needs of the research.
The following example illustrates the display of the crossover design. Researchers altered the diet ingredients of 18 steers in order to study the digestibility of feedstuffs in beef cattle. There were three treatments, or feed mixes, each with a different mix of alfalfa, straw, and so on. A three-period treatment was used, with 3 beef steers assigned to each of the six treatment sequences. Each diet in each sequence was fed for 30 days. There was a 21-day washout between each treatment period of the study. Assume that the dependent variable is the neutral detergent fiber digestion coefficient calculated for each steer. For this case, there are three treatment periods and 3! = 6 different sequences. The basic layout may be displayed as in Table 1.
Basic Conceptions, Advantages, and Disadvantages
Crossover designs were first used in agriculture research in 1950s and are widely used in other scientific fields with human beings and animals. The feature that measurements are obtained on different treatments from each experimental unit distinguishes the crossover design from other experimental designs.
| Table 1 Six-Order Sequence Crossover Table | ||||
|---|---|---|---|---|
| Sequence | Units | Period 1 | Period 2 | Period 3 |
| 1 | 1,2,3 | A | B | C |
| 2 | 4,5,6 | B | C | A |
| 3 | 7,8,9 | C | A | B |
| 4 | 10,11,12 | A | C | B |
| 5 | 13,14,15 | B | A | C |
| 6 | 16,17,18 | C | B | A |
This feature entails several advantages and disadvantages. One advantage is reduced costs and resources when money and the number of experimental units available for the study are limited. The main advantage of crossover design is that the treatments are compared within subjects. The crossover design is able to remove the subject effect from the comparison. That is, the crossover design removes any component from the treatment comparisons that is related to the differences between the subjects. In clinical trials, it is common that the variability of measurements obtained from different subjects is much greater than the variability of repeated measurement obtained from the same subjects.
A disadvantage of crossover design is that it may bring a carryover effect, that is, the effect of a treatment given in one period may influence the effect of the treatment in the following period(s). Typically the subjects (experimental units) are given sufficient time to “wash out” the effect of the treatments between two periods in crossover designs and return to their original state. It is important in a crossover study that the underlying condition does not change over time and that the effects of one treatment disappear before the next is applied. In practice, even if sufficient washout time is administered after two successive treatment periods, the subjects’ physiological states may have been changed and may be unable to return to the original state, which may affect the effects of the treatment in the succeeding period. Thus, the carryover effect cannot be ignored in crossover designs. In spite of its advantages, the crossover design should not be used in clinical trials in which a treatment cures a disease and no underlying condition remains for the next treatment period. Crossover designs are typically used for persistent conditions that are unlikely to change over the course of the study. The carryover effect can cause problems with data analysis and interpretation of results in a crossover design. The carryover prevents the investigators from determining whether the significant effect is truly due to a direct treatment effect or whether it is a residual effect of other treatments. In multiple regressions, the carryover effect often leads to multicollinearity, which leads to erroneous interpretation. If the crossover design is used and a carryover effect exists, a design should be used in which the carryover effect will not be confounded with the period and treatment effects. The carryover effect makes the design less efficient and more time-consuming.
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