Exploring the Use of Functional Data for Binary Classifications: The Case of Tissue Doppler Imaging in Cardiotoxicity Related-Therapy Cardiac Dysfunction Detection

Functional data are nowadays routinely collected and stored in a wide variety of fields. Their adequate use and analysis are a challenge for the scientific community. Mathematically, each function can be understood as a sequence of infinite related numbers. Therefore, for statisticians, functional data can be read as a collection of a strongly correlated infinite-dimensional variable. Most existing statistical procedures have been adapted to functional data scenarios. In this manuscript, we are interested in understanding the use of functions for constructing adequate ROC curves and, therefore, for carrying out binary classifications. In particular, we consider the problem of studying the real capacity of functions derived from tissue doppler imaging (TDI) for identifying cardiac dysfunction related to cardiotoxicity therapy (CRTCD) in breast cancer women with high levels of the protein human epidermal growth factor receptor 2 (HER2). With this goal, we use public and freely available data that has been already used for illustrating the use of functional data in the binary classification problem with very different take-home messages. This variability in the conclusions made us question the reproducibility of the results. Here, we explore five different functional approaches, and we think about the clinical use of the provided solutions and their potential overfitting. The main aim of this manuscript is identifying whether published results are excessively optimistic or if they adequately capture the actual capacity of TDI for accurately diagnostic CRTCD.