Why is ROC curve convex?

Why is ROC curve convex?

An ROC curve is said to be convex in this paper if, given two points A and B on the curve and a straight line s that passes between those points, there is no curve point between A and B that lies below s, for every pair of points on the curve.

Why ROC curve is concave?

For continuous distributions the slope of the ROC curve at any operating point is equal to the ratio of probability densities at that score. Consequently, the two leftmost segments of the ROC curve display a slight concavity.

Can ROC curve be concave?

If the ROC curve is concave then clearly the function R is concave as well, and so its derivative R (p) is nonincreasing in p ∈ (0,1). However, the slope R (p) equals the likelihood ratio LR(x) at a certain value x that decreases with p, which establishes the equivalence of (a) and (b).

Can ROC curve be a straight line?

A ROC curve is created by connecting all ROC points of a classifier in the ROC space. Two adjacent ROC points can be connected by a straight line, and the curve starts at (0.0, 0.0) and ends at (1.0, 1.0).

What is the ROC convex hull?

The convex hull of an ROC curve is a geometric construction that selects the points on the curve that are optimal under some class and cost distribution. It is analogous to the Pareto front in multiobjective optimization.

What do you mean by convex hull?

The Convex Hull is the line completely enclosing a set of points in a plane so that there are no concavities in the line. More formally, we can describe it as the smallest convex polygon which encloses a set of points such that each point in the set lies within the polygon or on its perimeter.

Is ROC curve monotonic?

By definition, ROC curve is monotone increasing from 0 to 1 and is invariant to any monotone transformation of test results. And it is often a curve with certain level of smoothness when test results from the diseased and non-diseased subjects follow continuous distributions.

What is area under the ROC curve?

The Area Under the ROC curve (AUC) is a measure of how well a parameter can distinguish between two diagnostic groups (diseased/normal). MedCalc creates a complete sensitivity/specificity report. The ROC curve is a fundamental tool for diagnostic test evaluation.

Why is a convex hull?

A few of the applications of the convex hull are: Collision avoidance: If the convex hull of a car avoids collision with obstacles then so does the car. Since the computation of paths that avoid collision is much easier with a convex car, then it is often used to plan paths.

What does the area under the ROC curve represent?

ROC curves are frequently used to show in a graphical way the connection/trade-off between clinical sensitivity and specificity for every possible cut-off for a test or a combination of tests. In addition the area under the ROC curve gives an idea about the benefit of using the test(s)…

How do you make an ROC curve?

To make an ROC curve you have to be familiar with the concepts of true positive, true negative, false positive and false negative. These concepts are used when you compare the results of a test with the clinical truth, which is established by the use of diagnostic procedures not involving the test in question.

What is the significance of an ROC curve in Clinical Biochemistry?

ROC curves are used in clinical biochemistry to choose the most appropriate cut-off for a test. The best cut-off has the highest true positive rate together with the lowest false positive rate. As the area under an ROC curve is a measure of the usefulness of a test in general,…

What is the use of a redroc curve?

ROC curves are frequently used to show in a graphical way the connection/trade-off between clinical sensitivity and specificity for every possible cut-off for a test or a combination of tests.