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Full-Text Articles in Mathematics
Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu
Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu
Department of Math & Statistics Faculty Publications
For diagnostic tests, we present an extension to the skill plot introduced by Briggs and Zaretski (Biometrics 2008; 64:250–261). The method is motivated by diagnostic measures for osteopetrosis in a study summarized by Hans et al. (The Lancet 1996; 348:511–514). Diagnostic test accuracy is typically defined using the area (or partial area) under the receiver operator characteristic (ROC) curve. If partial area is used, the resulting statistic can be highly subjective because the focus region of the ROC curve corresponds to a set of low false‐positive rates that are chosen by the experimenter. This paper introduces a more …
Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam
Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam
Department of Math & Statistics Faculty Publications
To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …