Parallel-Group vs Crossover Design

These are the two basic ways of arranging a comparison. In a parallel-group design each participant is randomised to one arm and stays there, so the contrast is between different people and carries all their variability with it. In a crossover design each participant receives every treatment in a randomised sequence separated by a washout, so the contrast is within a person and the between-person variation drops out of the error term entirely.

Crossover is the standard for pharmacokinetic and bioequivalence work, where a two-period two-sequence design with a few dozen healthy subjects is enough, and for short mechanistic endpoints such as gastric emptying or energy intake at a test meal. Parallel design is compulsory when the effect does not reverse in a practical washout: weight loss and cardiovascular outcomes cannot be crossed over, and a compound with a half-life near a week needs roughly five weeks of washout before the second period begins.

The reason to want a crossover is precision per participant: it can answer with twenty to forty subjects a question a parallel design would need hundreds for. The price is carryover, in which the first treatment is still acting during the second period, and period effects, in which the disease or the participant changes with time. A dropout also costs far more, because it removes a whole matched comparison rather than one observation from one arm.

The error to watch is treating any randomised crossover as strong evidence of clinical benefit. The design is efficient, but crossovers are typically small, short and built around a proxy measurement, so a crossover showing reduced food intake at one buffet meal supports a mechanism and not a treatment claim. The other recurring problem is a crossover analysed as though it were parallel, pooling the periods and discarding the pairing that justified the sample size.