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.

Optimal and/or Efficient Two treatment Crossover Designs for Five Carryover Models.

Crossover designs robust to changes in carryover models are useful in clinical trials where the nature of carryover effects is not known in advance. The designs have been characterized for being optimal and efficient under no carryover-, traditional-, and, self and mixed carryover- models, however, ignoring the number of subjects, which has significant impact on both optimality and administrative convenience. In this article, adding two more practical models, the traditional, and, self and mixed carryover models having carryover effect only for the new or test treatment, a 5M algorithm is presented. The 5M algorithm based computer code searches all possible two treatment crossover designs under the five carryover models and list those which are optimal and /or efficient to all the five carryover models. The resultant exhaustive list consists of optimal and/or efficient crossover designs in two, three, and four periods, having 4 to 20 subjects of which 24 designs are new optimal for one of the established carryover models, and 34 designs are optimal for newly added models.