# Crossover Experiment

A Crossover Experiment is a repeated measures experiment with two experiment groups where the groups swap treatments at some time period.

**AKA:**Crossover Study**Context:**- It can range from (typically) being a Randomized Crossover Experiment to being a Non-Randomized Crossover Experiment.
- It can be analyzed by a Crossover Experiment Analysis Task.
- It can require a Washout Period, to account for treatment delay/treatment carry-over where the treatment in one period affects outcome in later periods

**Example(s):**- in a trial in which each subject received three treatments A, B and C, in one of the six sequences: ABC, ACB, BAC, BCA, CAB and CBA, we have [math]t[/math]=3, [math]p[/math]=3 and [math]s[/math]=6.
- a Continuous Outcome Cluster Randomized 2x2 Crossover Experiment, such as eEPC Lift Evaluation 2x2 Crossover Experiment.

**Counter-Example(s):****See:**Observational Study, Factorial Experiment.

## References

### 2013

- http://en.wikipedia.org/wiki/Randomized_controlled_trial#By_study_design
- Crossover – over time, each participant receives (or does not receive) an intervention in a random sequence.
^{[1]}^{[2]}…… An analysis of the 616 RCTs indexed in PubMed during December 2006 found that 78% were parallel-group trials, 16% were crossover, 2% were split-body, 2% were cluster, and 2% were factorial.

^{[3]}

- Crossover – over time, each participant receives (or does not receive) an intervention in a random sequence.

- ↑ Jones, Byron; Kenward, Michael G. (2003).
*Design and Analysis of Cross-Over Trials*(Second ed.). London: Chapman and Hall. - ↑ Vonesh, Edward F.; Chinchilli, Vernon G. (1997). "Crossover Experiments".
*Linear and Nonlinear Models for the Analysis of Repeated Measurements*. London: Chapman and Hall. pp. 111–202. - ↑ Cite error: Invalid
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- http://en.wikipedia.org/wiki/Repeated_measures_design#Crossover_studies
- A popular repeated-measures design is the crossover study. A
**crossover study**is a longitudinal study in which subjects receive a sequence of different treatments (or exposures). While crossover studies can be observational studies, many important crossover studies are controlled experiments, which are discussed in this article. Crossover designs are common for experiments in many scientific disciplines, for example psychology, education, pharmaceutical science, and health-care, especially medicine.Randomized, controlled, crossover experiments are especially important in health-care. In a randomized clinical trial, the subjects are randomly assigned treatments. When the randomized clinical trial is a repeated measures design, the subjects are randomly assigned to a

**sequence**of treatments. A crossover clinical trial is a repeated-measures design in which each patient is randomly assigned to a sequence of treatments, including at least two**crosses over**from one treatment to another.

- A popular repeated-measures design is the crossover study. A

- http://en.wikipedia.org/wiki/Crossover_study
- A
**crossover study**, also referred to as a**crossover trial**, is a longitudinal study in which subjects receive a sequence of different treatments (or exposures). While crossover studies can be observational studies, many important crossover studies are controlled experiments, which are discussed in this article. Crossover designs are common for experiments in many scientific disciplines, for example psychology, education, pharmaceutical science, and medicine.Randomized, controlled, crossover experiments are especially important in health care. In a randomized clinical trial, the subjects are randomly assigned to different arms of the study which receive different treatments. When the randomized clinical trial is a repeated measures design, the same measures are collected multiple times for each subject. A crossover clinical trial is a repeated measures design in which each patient is randomly assigned to a sequence of treatments, including at least two treatments (of which one "treatment" may be a standard treatment or a placebo).

Nearly all crossover designs have "balance", which means that all subjects should receive the same number of treatments and that all subjects participate for the same number of periods. In most crossover trials, in fact, each subject receives all treatments.

Statisticians suggest that designs have four periods, a design which allows studies to be truncated to three periods while still enjoying greater efficiency than the two-period design.

^{[1]}^{[2]}However, the two-period design is often taught in non-statistical textbooks, partly because of its simplicity.

- A

### 2003

- (Jones & Kenward, 2003) ⇒ Byron Jones, and Michael G Kenward. (2003). “Design and Analysis of Cross over Trials." CRC Press. ISBN:0412606402
- QUOTE: This book is concerned with a particular sort of comparative trial known as the cross-over trial in which subjects receive different sequences of treatments. …
For a cross-over trial we will denote by [math]t[/math], [math]p[/math] and [math]s[/math], respectively, the number of treatments, periods and sequences. So for example, in a trial in which each subject received three treatments A, B and C, in one of the six sequences: ABC, ACB, BAC, BCA, CAB and CBA, we have [math]t[/math]=3, [math]p[/math]=3 and [math]s[/math]=6. In general, we denote by [math]y_{ijk}[/math] the response observed on the [math]k[/math]

^{th}subject in period [math]j[/math] of sequence group [math]i[/math]. It is assumed that [math]n_i[/math] subjects are in sequence group [math]i[/math].

- QUOTE: This book is concerned with a particular sort of comparative trial known as the cross-over trial in which subjects receive different sequences of treatments. …