AbstractsMathematics

We derive a sample size calculation formula for a three-treatment three-period crossover design with continuous outcomes and with restriction on treatment sequences that lower dose must be administered prior to higher dose of a drug. The three-period crossover is defined by these three sequences, D??? [arrow right]D??? [arrow right]D??? , D???[arrow right]D??? [arrow right] D??? and D??? [arrow right]D??? [arrow right]D??? , where D??? , D??? and D??? are referred to as placebo, the low dose and the high dose, respectively. Appropriate contrast coefficients are derived for model 1 without carry-over effect, and for model 2 with carry-over effect as well. Based on these coefficients, the unbiased contrast variances are estimated and a sample size formula is derived in terms of hypothesis testing with normal distribution of assumption. Parameters introduced for sample size calculation include contrast coefficients, the number of contrasts, the desired differences of treatment effects, and common within-subject variance. Using the developed formula, we calculate the minimum sample size required for determining the differences between treatment effects for models with or without carry-over. Further, Monte Carlo simulations are carried out to evaluate the performance of this formula. The results show that the formula can work well to achieve desired power for model 1 and model 2. Finally, the formula is demonstrated in an example of comparing Tacrine at the low dose (40mg/day) and the high dose (80mg/day) with a zero dose (placebo).