Determining sample size for cross-over designs with multiple groups

In clinical research, determining sample size plays an important role. A cross-over design (CD) is widely used to compare multiple groups in order to verify the statistical significance of mean difference among multiple groups, because it has an advantage of removing any factors caused by subject variability. When multi-omics data such as metabolomics data is analysed, we often adopt CD to identify biomarkers that have group effects. While some methods exist for determining the sample size when comparing two groups, no available method allows comparison of more than two treatment groups. In this research, we propose a novel method for determining the sample size of CD with multiple treatment groups. We first propose a method for testing single biomarkers and then a method for a large number of biomarkers while controlling the false discovery rate or the family wise error rate.