Two stage pattern clustering analysis in cross-over experimental design

In interventional studies, biomarkers such as metabolites, are usually measured across serial time points. And when the interest lies in comparing expression levels between different experimental conditions, summary measures such as area under curve (AUC), have been widely used. Although the summary measure based approaches have been successful in identifying novel biomarkers, they do not reveal anything about time-dependent changing patterns of biomarkers which can demonstrate the reactivity of biomarkers to various physiological conditions. To account for such patterns, all measurements across time points need to be used, and clustering analysis with the measurements can group together biomarkers having similar changing patterns. Some such popularly used clustering methods include hierarchical- and K-means clustering. While these may provide some well-clustered results, their patterns are quite dependent on input data sets, making it difficult to obtain consistent patterns across different interventional studies. In addition, it is problematic for these methods to discriminate biomarkers with weakly active patterns that need to be grouped as static, compared to those having strongly active patterns, when their patterns are highly similar. To address these issues, we propose a new clustering method for improving identification of changing patterns. Our approach is based on a two-stage process: the first is elimination of stable markers using Euclidean distances, while the second stage assigns the remaining biomarkers to predefined patterns using 1-correlation distance measure. By simulation studies, we showed that our proposed method had superior classification performances, compared to other unsupervised clustering methods. We expect that this approach can complement the existing summary measure based approaches.