A two-period crossover design for the comparison of two active treatments and placebo

This paper discusses a two-period crossover design for the comparison of two active treatments (A and B) and placebo (P) for relief of recurrent symptoms of a chronic health disorder. It is based on blocks of ten patients for which the treatment sequences A:B and B:A are each assigned to three patients and the sequences A:P, P:A, B:P, and P:B are each assigned to one patient; thus, treatment periods have a 2:2:1 allocation for A, B, and P. The principal model for analysis of this design involves additive subject effects, period effects, and treatment effects. Analysis of within-patient differences provides an estimate of the comparison between active treatments with variance (2vw/7r) and an estimate of the comparison between an active treatment and placebo with variance (4vw/7r); here vw is the within-patient variance and r is the number of blocks of ten patients. Analyses which address carryover effects and treatment effects adjusted for carryover effects are also described. An example using simulated data on relief of recurrent gastrointestinal pain illustrates the methodology.