ABSTRACT: Compositional data are vectors of non-negative real numbers with the property that their values sum to a constant. The analysis of these data is focused on the relative information carried by each part of the composition, which is why they are usually presented as proportions. Compositional data have been commonly analyzed using multivariate data analysis. However, this approach can lead to paradoxes and misinterpretation of the results. In this seminar, we will present an introduction of the special adjustments to common statistical tools needed for compositional data analysis. Additionally, the study of follow-up images of patients in the early stages of non-small cell lung cancer (NSCLC) receiving radiation therapy will be shown as an application of longitudinal compositional data analysis.