Receiver operating-characteristic (ROC) curve is a popular graphical method frequently used in order to study the diagnostic capacity of continuous (bio)markers. When the considered outcome is a time-dependent variable, the direct generalization is known as cumulative/dynamic ROC curve. For a fixed point of time, t, one subject is allocated into the positive group if the event happens before t and into the negative group if the event is not happened at t. The presence of censored subject, which can not be directly assigned into a group, is the main handicap of this approach. The proposed cumulative/dynamic ROC curve estimator assigns a probability to belong to the negative (positive) group to the subjects censored previously to t. The performance of the resulting estimator is studied from Monte Carlo simulations. Some real-world applications are reported. Results suggest that the new estimators provide a good approximation to the real cumulative/dynamic ROC curve.

The use of the area under the receiver-operating characteristic, ROC, curve (AUC) as an index of diagnostic accuracy is overwhelming in fields such as biomedical science and machine learning. It seems that a larger AUC value has become synonymous with a better performance. The functional transformation of the marker values has been proposed in the specialized literature as a procedure for increasing the AUC and therefore the diagnostic accuracy. However, the classification process is based on some regions (classification subsets) which support the decision made; one subject is classified as positive if its marker is within this region and classified as negative otherwise. In this paper we study the capacity of improving the classification performance of univariate biomarkers via functional transformations and the impact of this transformation on the final classification regions based on a real-world dataset. Particularly, we consider the problem of determining the gender of a subject based on the Mode frequency of his/her voice. The shape of the cumulative distribution function of this characteristic in both the male and the female groups makes the resulting classification problem useful for illustrating the differences between having useful diagnostic rules and obtaining an optimal AUC value. Our point is that improving the AUC by means of a functional transformation can produce classification regions with no practical interpretability. We propose to improve the classification accuracy by making the selection of the classification subsets more flexible while preserving their interpretability. Besides, we provide different graphical approximations which allow us a better understanding of the classification problem.

Objective: Antifibrotics can improve the outcome of patients with idiopathic pulmonary fibrosis (IPF) and other fibrosing interstitial lung diseases (F-ILDs), but predictive biomarkers at diagnosis are needed to guide the use of immunomodulating and antifibrotic therapies. Methods: Flow cytometry quantification of lymphocytes and neutrophils in bronchoalveolar lavage (BAL) of 145 IPFs, 561 non-IPF-ILDs (125 F-ILDs), and 112 BAL controls were retrospectively correlated with the incidence of fibrosis and third-quartile overall survival (Q3–OS). Results: The incidence of IPF was directly proportional (9.6%, 22.2%, and 42.6%, p < 0.001) to BAL neutrophil counts (15%), but inversely proportional (34.1%, 18.6%, and 8.8%, p < 0.001) to BAL lymphocyte counts (20%). Elevated neutrophils (>5%) with low lymphocytes (<7%) were associated with an increasingly higher incidence of IPF (10.0–56.3%, p < 0.001) in patients aged 40 to 80, compared to the rest of patients (13.0–17.1%). Lymphocytes >20% compared to lymphocytes 15% (59.7% vs. 20.7%, p < 0.001) from IPF. In contrast, the incidence of F-ILD was not clearly related to BAL lymphocyte/neutrophil counts. Although, IPF and F-ILD showed a shorter Q3–OS (1.8 ± 0.3 and 4.6 ± 0.8 years; p < 0.001) than non-fibrotic-ILDs (11.1 ± 1.3 years), lymphocyte and neutrophil counts were associated with a longer and shorter Q3–OS of non-fibrotic-ILDs (p < 0.03) and F-ILDs (p < 0.04), respectively, but not with a Q3–OS of IPF patients (p < 0.708). Corticosteroids in patients with fibrosis showed a shorter Q3–OS than other immunomodulators (2.4 ± 0.3 vs. 4.0 ± 1.8 years, p = 0.011). Conclusions: Accurate counting of BAL lymphocytes and neutrophils by flow cytometry in ILD patients at diagnosis could help guide immunomodulatory and antifibrotic therapies.