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

Abstract

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.

Keywords:

• Diagnostic test
• functional biomarkers
• kernel smoothing
• ROC curve

Disclosure statement

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Notes

1 If this assumption is not verified on the entire domain of curves, a subset of such domain, where the overlap of groups is less, could be selected and then carry out the diagnostic test on it. You could also choose to apply some transformation to the original functional data, for instance the first derivative, before running the diagnostic test. Without loss of generality, it can be assumed that curves of one group (for example, affected subjects) tend to take higher values than the curves of the other group (for example, non-affected subjects). Such a condition is easy to validate by means of some homogeneity test for the studied biomarker, for example, by using the Functional ANOVA ideas (see [32] or infinite-dimensional Wilcoxon–Mann–Whitney type test in [12]).

Additional information

Funding

This research was supported by MICINN, Spain grant PID2020-113578RB-I00 and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14 and Centro de Investigación del Sistema Universitario de Galicia ED431G 2019/01), all of them through the ERDF.