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A Precalculus Unit on Area under Curves

The Two-Year College Mathematics Journal, 1975
The purpose of the "Computer Corner" is to provide readers an opportunity to share mathematically-related problems which can be demonstrated or solved using a computer. The computer programs accompanying the problem should be short and as simple as possible.
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Quantifying the SSEP — the area under the curve

1994
The use of neurophysiological evoked potentials for intraoperative monitoring of the spinal cord is rapidly increasing. There are a multitude of different techniques in use, each with claimed or proven advantages, and it is likely that a combination of complementary methods will eventually provide the most accurate and reliable surveillance of the cord
R. O’Brien, K. Gordiev, B. A. Taylor
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The Area under an ROC Curve with Limited Information

Medical Decision Making, 2003
The area under the receiver operating characteristic (ROC) curve of a diagnostic test can be used as a summary measure for its discriminative ability. If only a single point of an ROC curve is available, then the entire form of the ROC curve is unknown and the area under it cannot be calculated.
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The partial area under the summary ROC curve

Statistics in Medicine, 2005
The area under the curve (AUC) is commonly used as a summary measure of the receiver operating characteristic (ROC) curve. It indicates the overall performance of a diagnostic test in terms of its accuracy at various diagnostic thresholds used to discriminate cases and non-cases of disease.
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A′r : An estimate of area under isosensitivity curves

Behavior Research Methods, Instruments & Computers, 1996
A′ was identified by Pollack and Norman (1964, p. 126) as “the average of the areas subtended by the upper, and by the lower, bounds” of the isosensitivity curve. That estimate of the area under the isosensitivity curve is used when only one point on the curve is available, as with yes/no data.
Colette Good, Wayne Donaldson
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Optimum numerical integration methods for estimation of area-under-the-curve (AUC) and area-under-the-moment-curve (AUMC)

Journal of Pharmacokinetics and Biopharmaceutics, 1992
Eleven numerical methods for estimation of AUC (including 4 new methods) and 22 methods for AUMC (including 8 new methods) were tested on large simulated noisy datasets representing bolus, oral and infusion concentration-time profiles. Some methods were unacceptable because their mean error was large; these included a commonly recommended form of the ...
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Analog integration of the area under a thermal dilution curve

Biomedical Engineering, 1985
The problem of computing the area under the thermodilution curve to determine the cardiac output by the thermodilution method is discussed. The circuit of an analog integrator is developed that outputs continuously a current area value. Recommendations for the choice of main integrator elements and methods of computing the cardiac output with the ...
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Discrimination Index, the Area Under the ROC Curve

2002
The accuracy of fit of a mathematical predictive model is the degree to which the predicted values coincide with the observed outcome. When the outcome variable is dichotomous and predictions are stated as probabilities that an event will occur, models can be checked for good discrimination and calibration.
Byung-Ho Nam, Ralph B. D'Agostino
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