Optimal and/or efficient three treatment crossover designs for five carryover models

The additional benefits in the analysis of crossover designs with two active treatments and a placebo motivated us to study these kinds of designs. These designs have been studied through a computer search algorithm, called 5M balanced algorithm, in two to four periods for different number of units, which resulted in optimal and/or efficient crossover designs. The new two periods crossover designs having two active treatments and a placebo, enables the estimation of treatment contrasts, unlike the classic two treatments two periods crossover which fails to estimate the treatment contrasts under self and mixed carryover model. The crossover designs having three or four periods in two active treatments and a placebo, estimate treatment contrasts more efficiently under self and mixed carryover model than the usual two treatments crossover designs. An exhaustive list of optimal and/or efficient crossover designs has been provided for designs in two periods having 6-21 subjects, three periods having 3-20 subjects and four periods having 3-14 subjects. In this list, 35 new designs are optimal for one of the established carryover models and 26 new designs are optimal and/or efficient to all four plausible carryover models.