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Purpose: To overcome the constraint of common multiple-baseline designs that only one case per stagger position is permitted., Methods: Three alternative strategies for assigning more than one case to each stagger position are examined., Results: The three recommended strategies achieve the objective while maintaining the study's internal and statistical-conclusion validities., Conclusions: ExPRT, a freely available Excel-based randomization-test package, can be used to assist in both the design and statistical analysis associated with each of the strategies.

Under the three-treatment three-period crossover design with simple carry-over effects, we derive the least-squares estimators for period effects, treatment effects and carry-over effects, as well as their covariance matrix in closed and explicit expressions. Using Monte Carlo simulation, we compare the test procedure adjusting carry-over with that ignoring carry-over with respect to Type I error and power. We further compare interval estimators adjusting carry-over with those ignoring carry-over with respect to the coverage probability and the average length. When the variation of responses within patients is small, the test procedure and interval estimators ignoring carry-over can lose accuracy in the presence of carry-over effects. When the variation of responses within patients is large, this loss of accuracy may become small or even minimal. We note that the loss of efficiency due to the adjustment of carry-over under the simple carry-over three-period crossover design is moderate, and is much less than that found for a two-period crossover design. We use the double-blind three-period crossover trial comparing formoterol solution aerosol and salbutamol suspension aerosol with a placebo for patients suffering from exercise-induced asthma on the forced expiratory volume in one second (FEV1) to illustrate the use of test procedures and interval estimators discussed here.