Optimization of functional diagnostic test: the effect of kernel method as an estimator of ROC curve

Technical development over the last few decades has resulted in the emergence of complex data, in many cases functional data (FD). This type of data can emerge in many medical studies which are geared towards detecting diseases, predicting their course or evaluating the response to a therapy, to name a few. Thus, it is very useful to have statistical methods enabling us to evaluate diagnostic tests based on functional biomarkers. In fact, a diagnostic test that uses functional variables as biomarkers has been developed recently. Their authors proposed a functional version of ROC analysis, resulting in an empirical estimate of the functional ROC curve. In order to improve this methodology, the present paper proposes a procedure to obtain a smooth version of non-parametric estimator of the ROC curve. In addition, a comprehensive simulation study lets to investigate the discriminatory and predictive abilities of the resulting functional diagnostic test. Two examples with real medical data illustrate the approach developed: one deals with gene expression levels for tumoural/normal samples of prostate cancer; the other dataset is about white matter structures in the brain in multiple sclerosis patients.