Confidence intervals around Bayes Cost in multi-state diagnostic settings to estimate optimal performance

A fiducial-based confidence interval for the linear combination of multinomial probabilities

Across a broad set of applications, system outcomes may be summarized as probabilities in confusion or contingency tables. In settings with more than two outcomes (e.g., stages of cancer), these outcomes represent multinomial experiments. Measures to summarize system performance have been presented as linear combinations of the resulting multinomial probabilities. Statistical inference on the linear combination of multinomial probabilities has been focused on large-sample and parametric settings and not small-sample settings. Such inference is valuable, however, especially in settings such as those resulting from pilot or low-cost studies. To address this gap, we leverage the fiducial approach to derive confidence intervals around the linear combination of multinomial parameters with desirable frequentist properties. One of the original arguments against the fiducial approach was its inability to extend to multiparameter settings. Therefore, the great novelty of this work is both the derived interval and the logical framework for applying the fiducial approach in multiparameter settings. Through simulation, we demonstrate that the proposed method maintains a minimum coverage of1 - α $1 - \alpha$ , unlike the bootstrap and large-sample methods, at comparable interval lengths. Finally, we illustrate its use in a medical problem of selecting classifiers for diagnosing chronic allograph nephropathy in postkidney transplant patients.

On optimal biomarker cutoffs accounting for misclassification costs in diagnostic trilemmas with applications to pancreatic cancer

Pancreatic ductal adenocarcinoma (PDAC) is the most deadly cancer and currently there is strong clinical interest in novel biomarkers that contribute to its early detection. Assessing appropriately the accuracy of such biomarkers is a crucial issue and often one needs to take into account that many assays include biospecimens of individuals coming from three groups: healthy, chronic pancreatitis, and PDAC. The ROC surface is an appropriate tool for assessing the overall accuracy of a marker employed under such trichotomous settings. A decision/classification rule is often based on the so-called Youden index and its three-dimensional generalization. However, both the clinical and the statistical literature have not paid the necessary attention to the underlying false classification (FC) rates that are of equal or even greater importance. In this article we provide a framework to make inferences around all classification rates as well as comparisons. We explore the trinormal model, flexible models based on power transformations, and robust non-parametric alternatives. We provide a full framework for the construction of confidence intervals, regions, and spaces for joint inferences or for clinically meaningful points of interest. We further discuss the implications of costs related to different FCs. We evaluate our approaches through extensive simulations and illustrate them using data from a recent PDAC study conducted at the MD Anderson Cancer Center.

A comprehensive and comparative review of optimal cut-points selection methods for diseases with multiple ordinal stages

Cut-points selection is a key topic in the field of diagnostic studies. For binary classification, there exist several well-developed methods, some of which have been extended to three-class settings and beyond. This paper focuses on optimal cut-points selection methods for diseases with multiple ordinal stages. The purpose of this paper is two-fold: 1) to propose three new cut-points selection methods; and 2) to present a comprehensive simulation study to assess and compare the performance of all the available methods. Two real data sets, one from ovarian cancer and the other from pancreatic cancer, are analyzed.

A new diagnostic accuracy measure and cut-point selection criterion

Most diagnostic accuracy measures and criteria for selecting optimal cut-points are only applicable to diseases with binary or three stages. Currently, there exist two diagnostic measures for diseases with general k stages: the hypervolume under the manifold and the generalized Youden index. While hypervolume under the manifold cannot be used for cut-points selection, generalized Youden index is only defined upon correct classification rates. This paper proposes a new measure named maximum absolute determinant for diseases with k stages ([Formula: see text]). This comprehensive new measure utilizes all the available classification information and serves as a cut-points selection criterion as well. Both the geometric and probabilistic interpretations for the new measure are examined. Power and simulation studies are carried out to investigate its performance as a measure of diagnostic accuracy as well as cut-points selection criterion. A real data set from Alzheimer's Disease Neuroimaging Initiative is analyzed using the proposed maximum absolute determinant.