Cumulative/dynamic ROC curve estimation under interval censorship

Abstract

The Receiver Operating Characteristic (ROC) curve is a graphical tool commonly used to assess the discriminatory ability of continuous markers in binary classification problems. Different extensions of the ROC curve have been proposed in the prognosis context, where the characteristics in study are time-dependent events. Perhaps the most direct generalization is the so-called cumulative/dynamic (C/D) ROC curve. The main particularity when dealing with the C/D ROC curve estimation is the presence of incomplete information. Several approximation methods addressing this censoring problem have been suggested in the statistical literature, most of them focused on the right-censored case. Interval censorship arises naturally from those studies where subjects undergo periodical follow-ups. They may miss a scheduled appointment and the exact event times are only known to fall in a certain range. A new approach for estimating the C/D ROC curve under the particular scheme of interval censorship is presented in this work. Its finite-sample behavior is studied via Monte Carlo simulations on two different scenarios. Results suggest that the proposed approximation is better than the existing one in terms of absolute error. Its direct application is illustrated in the real-world data set which motivated this research. The uniform strong consistency and a suitable R function for its practical implementation are provided as appendices.

Time‐dependent ROC curve estimation for interval‐censored data

“…The results show that the proposed empirical time-dependent ROC curve estimators have better overall finite sample performance than the WU method. When we compare the method of Díaz-Coto et al (2020) and our empirical estimator, we can see that they perform very similarly in most cases, with a slight advantage to our method. But when we incorporate smoothing, our method exhibits clearly better results.…”

“…In this section, we present and discuss the main findings of our simulation study. We will start by comparing our method with the one of as implemented in the R package intcensROC (Lin et al, 2018) and the method proposed by Díaz-Coto et al (2020). For the latter, the calculation was done using the R-function intCDroc as provided by the authors.…”

“…(2020) and Díaz‐Coto et al. (2020), hereafter referred to by WU and Diaz, respectively. The next section presents the data‐generating process, and the results will follow after.…”

“…Moreover, the authors (without declaring it) assumed that, whatever the time horizon 𝑡 is, the event status 𝐼(𝑇 ≤ 𝑡) is unknown for all subjects under study, which naturally induce loss of information. Closely related papers to this one are the work of Wu and Cook (2020), who considered the evaluation of a parametric prediction model using a validation sample of individuals subject to the case 𝐾 interval censoring, and the work of Díaz-Coto et al (2020) who proposed an imputation method based on the semiparametric proportional hazards model to estimate the AUC from a sample of individuals all subject to interval-censoring.…”

“…Closely related papers to this one are the work of Wu and Cook (2020), who considered the evaluation of a parametric prediction model using a validation sample of individuals subject to the case $$K$$ interval censoring, and the work of Díaz‐Coto et al. (2020) who proposed an imputation method based on the semiparametric proportional hazards model to estimate the AUC from a sample of individuals all subject to interval‐censoring.…”