Notes on testing equality and interval estimation in Poisson frequency data under a three-treatment three-period crossover trial

Testing treatment-by-period interaction in four-period crossover trials

Statistical analyses of crossover clinical trials have mainly focused on assessing the treatment effect, carryover effect, and period effect. When a treatment-by-period interaction is plausible, it is important to test such interaction first before making inferences on differences among individual treatments. Considerably less attention has been paid to the treatment-by-period interaction, which has historically been aliased with the carryover effect in two-period or three-period designs. In this article, from the data of a newly developed four-period crossover design, we propose a statistical method to compare the effects of two active drugs with respect to two response variables. We study estimation and hypothesis testing considering the treatment-by-period interaction. Constrained least squares is used to estimate the treatment effect, period effect, and treatment-by-period interaction. For hypothesis testing, we extend a general multivariate method for analyzing the crossover design with multiple responses. Results from simulation studies have shown that this method performs very well. We also illustrate how to apply our method to the real data problem.

Sample Size Determination for a 3-Treatment 3-Period Crossover Trial in Frequency Data

BACKGROUND

To reduce the number of patients needed or increase the power of hypothesis testing for the parallel groups design, the crossover design has been often employed when one is studying noncurable chronic diseases. This article focuses attention on sample size calculation for testing non-inferiority and equality in frequency data under a 3-treatment 3-period crossover trial.

METHOD

Under a multiplicative mixed effects model, this article provides asymptotic sample size calculation procedures for testing non-inferiority of an experimental treatment to a control treatment, as well as for simultaneously testing either of 2 treatments versus a placebo. To improve the performance of these asymptotic procedures in small-sample cases, this article further suggests a simple ad hoc adjustment.

RESULTS

On the basis of Monte Carlo simulation, we demonstrate that the asymptotic test procedures proposed here can perform well with respect to Type I error. We find that the asymptotic sample size calculation procedures can generally perform well with respect to power when the resulting sample size is moderate or large. We further find that using the simple ad hoc adjustment can improve the performance of the proposed sample size calculation procedures, which are derived from large-sample theory, in small-sample cases.