Crossover Design

Crossover Design

The crossover design is a repetitive measurement design. In this design, each experimental unit (patient) receives a different treatment during different time periods, i.e., the patient spans from one treatment to another during the trial. On the contrary, patients in a parallel design will get treatment at random and maintain the treatment throughout the trial.

The reason for considering the crossover design when planning a clinical trial is that it can produce a more effective treatment comparison than a parallel design, i.e., fewer patients may be required to achieve the same level of statistical power or precision in a crossover design compared to a parallel design. This seems reasonable because each patient acts as his/her own matching control. They will receive both treatment A and B, then resulting a comparison. Crossover design is very popular in medicine, agriculture, manufacturing, education and many other disciplines.

However, the main disadvantage of crossover design is the carryover effect, which is defined as the effect of treatment in the previous time period on the response to the current time period. In other words, if the patient receives treatment A during the first period and treatment B during the second period, the measurement performed during the second period may be the result of the direct effect of treatment B administered during the second period, and/or the carryover or residual effect of treatment A administered during the first period. These carryover effects will produce statistical bias. That’s why we have washout period to diminish the impact of carryover effects. Instead of immediately stopping and then starting the new treatment, patients will experience a period of time to wash out the drug from their body system. The length of washout period depends on the half-life of the drug within the patients (Figure 1).

Half-life of the drug within the patients
Figure 1. Half-life of the drug within the patients.

In general, the crossover design is suitable for chronic diseases such as diabetes, asthma and chronic non-cancer pain. This is because the patient's disease status usually does not change much during the study period and the treatment only controls the symptoms, but does not cure these diseases. In other words, patients with chronic conditions can provide a consistent study population for different treatments by acting as their own controls. Thus, the crossover design may not be suitable for acute infections which may have a significantly change at the end of the first treatment period. It also does not apply to diseases that are expected to have many dropouts or deaths, such as cancer.

Here is an example of the 2 × 2 crossover design in Table 1 which includes nuisance effects for sequence, period, and first-order carryover.

Table 1. Expected values of responses of an AB|BA crossover design.

Expected values of responses of an AB|BA crossover design.

µA and µB: population means for the direct effects of treatments A and B, respectively; ν: a sequence effect; p: a period effect; λA and λB: carryover effects of treatments A and B, respectively.

An estimator of µA (or µB): the average over all cells

the average over all cells

The expectations of these estimators:

expectations of these estimators

  • From (1) the direct treatment effects and the treatment difference are not aliased with sequence or period effects, but are aliased with the carryover effects.
  • The treatment difference is not aliased with carryover effects when the carryover effects are equal, i.e., λA = λB.
  • The results in (1) are due to the fact that the AB|BA crossover design is uniform and balanced w.r.t. first-order carryover effects.

At CD BioSciences, we can help you with not only the crossover design but also the appropriate choice of statistical strategy. If you have any questions, please feel free to contact us.

1. Tao, W., et al. (2016) ‘Crossover design and its application in late‐phase diabetes studies’, Journal of Diabetes, 8(5), 610-618.

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