Crossover trials are studies in which participants receive two or more treatments in a particular (usually random) order.
They are used to compare different treatments given at different times in random order to the same people. The treatment effect is estimated by comparing outcomes (e.g. coughing) in the time period during which one treatment was allocated, to outcomes in the time period during which the other treatment was allocated within the same individuals.
For example, to assess whether an inhaled drug could help patients with a persistent, dry cough, during one period of time (some weeks), chosen randomly, each participant in a crossover study would use an inhaler containing a drug; during another period of time the participant would use an identical-looking inhaler which did not contain the drug.
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