StatTools : Curve Fitting for Receiver Operator Characteristics (ROCs) Explained

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Receiver Operator Characteristics (ROC) Explained Page
Curve Fitting for Receiver Operator Characteristics (ROCs) Program Page

Introduction Example References
This page supports the program from the Curve Fitting for Receiver Operator Characteristics (ROCs) Program Page . The algorithm is derived from publications listed in the references panel

The Need for Curve Fitting the Receiver Operator Characteristic (ROC) Curve

The underlying assumptions of the ROC curve is that the Outcome is binary, but the Test is a continuous variable. In establishing the ROC from a set of reference data, it is assumed that the sample size provided is large enough, and the granularity of the values in the data set is fine enough, to produce a reproducible curve.

The reference data set unfortunately often failed these assumptions. A major problem is that test measurements are often rounded to clinically meaningful intervals, so that the granularity of the data is coarse, and changes occurred in a series of steps rather than in a smooth curve.

Furthermore, with rounding of values, often there are multiple cases with the same test value, and to include or exclude values at the cut off makes a large difference to the subsequent use. Also the changes to the False Positive Rate (FPR) is not always accompanied by any change to the True Positive Rate (TPR)

An example of this is shown in the plot to the left. If the cut off for decision making is 155 (the black line), data points can be clearly separated into above or below that value. However, if the cut off value is set at 154, there are 3 data points in the Outcome Positive group and 2 in the Outcome Negative group that have this exact value. Whether these are considered above the cut off, below the cut off, or excluded from consideration, will have a large impact on subsequent results produced.

The resulting ROC plot would be as the black line in the plot to the right.

Curve fitting would result in a ROC curve that has the closest fit with the data, yet allows a continuous interpretation along the whole range of the Test values, as shown in the red line in the plot to the right.