Concordance Probability for Insurance Pricing Models

The concordance probability, also called the C-index, is a popular measure to capture the discriminatory ability of a predictive model. In this article, the definition of this measure is adapted to the specific needs of the frequency and severity model, typically used during the technical pricing of a non-life insurance product. For the frequency model, the need of two different groups is tackled by defining three new types of the concordance probability. Secondly, these adapted definitions deal with the concept of exposure, which is the duration of a policy or insurance contract. Frequency data typically have a large sample size and therefore we present two fast and accurate estimation procedures for big data. Their good performance is illustrated on two real-life datasets. Upon these examples, we also estimate the concordance probability developed for severity models.

Performance of Self-Collected Saliva Testing Compared with Nasopharyngeal Swab Testing for the Detection of SARS-CoV-2

The aim of this study was to determine whether self-collected pure saliva (SCPS) is comparable to nasopharyngeal (NP) swabs in the quantitative detection of SARS-CoV-2 by RT-PCR in asymptomatic, mild patients with confirmed COVID-19. Thirty-one patients aged from 18 to 85 years were included between 9 June and 11 December 2020. A SCPS sample and a NP sample were taken for each patient. Quantitative PCR was performed to detect SARS-CoV-2 viral load. Results of SCPS vs NP samples testing were compared. Statistical analyses were performed. Viral load was significantly correlated (r = 0.72). The concordance probability was estimated at 73.3%. In symptomatic adults, SCPS performance was similar to that of NP swabs (Percent Agreement = 74.1%; p = 0.11). Thus, the salivary test based on pure oral saliva samples easily obtained by noninvasive techniques has a fair agreement with the nasopharyngeal one in asymptomatic, mild patients with a confirmed diagnosis of COVID-19.

Self-sampling versus health care professional-guided swab collection for SARS-CoV-2 testing

Purpose To evaluate the diagnostic reliability and practicability of self-collected oropharyngeal swab samples for the detection of SARS-CoV-2 infection as self-sampling could enable broader testing availability and reduce both personal protective equipment and potential exposure. Methods Hospitalized SARS-CoV-2-infected patients were asked to collect two oropharyngeal swabs (SC-OPS1/2), and an additional oropharyngeal swab was collected by a health care professional (HCP-OPS). SARS-CoV-2 PCR testing for samples from 58 participants was performed, with a 48-h delay in half of the self-collected samples (SC-OPS2). The sensitivity, probability of concordance, and interrater reliability were calculated. Univariate and multivariate analyses were performed to assess predictive factors. Practicability was evaluated through a questionnaire. Results The test sensitivity for HCP-OPS, SC-OPS1, and SC-OPS2 was 88%, 78%, and 77%, respectively. Combining both SC-OPS results increased the estimated sensitivity to 88%. The concordance probability between HCP-OPS and SC-OPS1 was 77.6% and 82.5% between SC-OPS1 and SC-OPS2, respectively. Of the participants, 69% affirmed performing future self-sampling at home, and 34% preferred self-sampling over HCP-guided testing. Participants with both positive HCP-OPS1 and SC-OPS1 indicating no challenges during self-sampling had more differences in viral load levels between HCP-OPS1 and SC-OPS1 than those who indicated challenges. Increasing disease duration and the presence of anti-SARS-CoV-2-IgG correlated with negative test results in self-collected samples of previously confirmed SARS-CoV-2 positive individuals. Conclusion Oropharyngeal self-sampling is an applicable testing approach for SARS-CoV-2 diagnostics. Self-sampling tends to be more effective in early versus late infection and symptom onset, and the collection of two distinct samples is recommended to maintain high test sensitivity.

Concordance probability as a meaningful contrast across disparate survival times

The performance of time-to-event models is frequently assessed in part by estimating the concordance probability, which evaluates the probabilistic pairwise ordering of the model-based risk scores and survival times. The standard definition of this probability conditions on any survival time pair ordering, irrespective of whether the times are meaningfully separated. Inclusion of survival times that would be deemed clinically similar attenuates the concordance and moves the estimate away from the contrast-of-interest: comparing the risk scores between individuals with disparate survival times. In this manuscript, we propose a concordance definition and corresponding method to estimate the probability conditional on survival times being separated by at least a minimum difference. The proposed estimate requires direct input from the analyst to identify a separable survival region and, in doing so, is analogous to the clinically defined subgroups used for binary outcome area under the curve estimates. The method is illustrated in two cancer examples: a prognostic score in clear cell renal cell carcinoma and two biomarkers in metastatic prostate cancer.

Redefining Stage I Endometrial Cancer: Incorporating Histology, a Binary Grading System, Myometrial Invasion, and Lymph Node Assessment

ObjectiveWe propose a new staging system for stage I endometrial cancer and compare its performance to the 1988 and 2009 International Federation of Gynecology and Obstetrics (FIGO) systems.MethodsWe analyzed patients with 1988 FIGO stage I endometrial cancer from January 1993 to August 2011. Low-grade carcinoma consisted of endometrioid grade 1 to grade 2 lesions. High-grade carcinoma consisted of endometrioid grade 3 or nonendometrioid carcinomas (serous, clear cell, and carcinosarcoma). The proposed system is as follows:IA. Low-grade carcinoma with less than half myometrial invasionIA1: Negative nodesIA2: No nodes removedIB. High-grade carcinoma with no myometrial invasionIB1: Negative nodesIB2: No nodes removedIC. Low-grade carcinoma with half or greater myometrial invasionIC1: Negative nodesIC2: No nodes removedID. High-grade carcinoma with any myometrial invasionID1: Negative nodesID2: No nodes removedResultsData from 1843 patients were analyzed. When patients were restaged with our proposed system, the 5-year overall survival significantly differed (P < 0.001): IA1, 96.7%; IA2, 92.2%; IB1, 92.2%; IB2, 76.4%; IC1, 83.9%; IC2, 78.6%; ID1, 81.1%; and ID2, 68.8%. The bootstrap-corrected concordance probability estimate for the proposed system was 0.627 (95% confidence interval, 0.590–0.664) and was superior to the concordance probability estimate of 0.530 (95% confidence interval, 0.516–0.544) for the 2009 FIGO system.ConclusionsBy incorporating histological subtype, grade, myometrial invasion, and whether lymph nodes were removed, our proposed system for stage I endometrial cancer has a superior predictive ability over the 2009 FIGO staging system and provides a novel binary grading system (low-grade including endometrioid grade 1–2 lesions; high-grade carcinoma consisting of endometrioid grade 3 carcinomas and nonendometrioid carcinomas).