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Let's ROC, Part 3

Welcome to the third installment in a series of articles that will examine ROC Curves

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Welcome to the third installment in a series of articles that will discuss the application of Receiver Operator Characteristic statistics (ROC)* and ROC Curves, as well as other statistics, including Odds Ratios, Likelihood Ratios, Relative Risks and other statistics and graphics that are used to study outcomes. As an example of a practical application of ROC statistics in medicine imagine that a physician orders certain tests when there are certain symptoms and signs of illness.  These test results need to be evaluated by the physician, not only for their analytical value, but for their ability to aid in ruling in or ruling out diagnoses, thus raising the possibility of another diagnosis.   The ROC statistics and graphs provide the information on how well the test (or tests) aid in ruling in or ruling out a certain disease.

We begin with a bit of review and a few definitions that are necessary when discussing ROC Curves.

·         "TN" - "true" negative -- the patient does not have the disease [according to the physician - the patient is labeled negative] and the laboratory test# value is below the cut-off. [You will see that we put true in quotes.  That is because in an ROC study it is possible that either the lab or the physician or both made an error in ruling in or ruling out the disease(s) being sought.]

·         "FN" - "false" negative -- the patient does have the disease [according to the physician - the patient is labeled positive], but the laboratory test value is below the cut-off (IF the cut-off is set to detect abnormal patients whose test 'should be' below the cut-off.)

·         "FP" - "false" positive  -- the patient does not have the disease [according to the physician - the patient is labeled negative], but the laboratory test value is above the cut-off. (IF the cut-off is set to detect abnormal patients whose test 'should be' higher than the cut-off.)

·          "TP" - "true" positive  -- the patient does have the disease [according to the physician - the patient is labeled positive], and the laboratory test value is above [OR below] the cut off.

*The ROC was first developed by electrical engineers and radar engineers during World War II.  In radar the cathode ray tube was the receiver and would search the British skies for German planes.  If the receiver was tuned too high, it found not only planes but birds; when set too low is could miss planes.  Thus the receiver and its operator had certain characteristic.

The ROC is also known as a relative operating characteristic curve, because it is a comparison of two operating characteristics (A "true" Positive Response and A "false" Positive Response) as the criterion changes.


Let's ROC, Part 3

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Shouldn't Negative Predictive Value (NPV) is the proportion (or the chances) of the negative test results that come from patients who, according to the clinician, are free of the disease be:
NPV = TN/(TN+"FP")

Jodie KearyApril 01, 2014




     

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