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1.2 Choose a medical condition and suggest a clinical test which would have:
(a) High sensitivity but low specificity,
(b) Low sensitivity but high specificity.
Solution. (a) the sensitivity is defined as the number of true positives divided by
the sum of the true positives and the false negatives, whereas the specificity is the
number of true negatives divided by the sum of the true negatives and false
positives. So a high sensitivity but low specificity suggests a diagnosis with a very
low number of false negatives but significant number of false positives, i.e. a
diagnosis which doesn’t often miss the disease but often suggests that there is a
disease present whereas in fact there isn’t. An example might be mammography
in which small lesions are very well visualized, but often subsequent biopsies
result in the lesions being found not to be malignant.
(b) A low sensitivity but high specificity implies a relatively high number of false
negatives and low number of false positives, i.e. a diagnosis that often misses the
disease but almost never gives a false impression that the disease is present when
it isn’t. An example might be cognitive and behavioural tests in the early
progression of neurodegenerative diseases such as Alzheimers. Signs are often
missed, but very poor test results are very certain indicators of brain disfunction.
1.3. What does an ROC curve that lies below the random line suggest? Could this be
diagnostically useful?
Solution. This suggests that the criteria that are being used to provide a clinical
assessment are being used to support a hypothesis that is directly opposite to the
truth. For example, cardiac disease is being diagnosed due to a low heart rate,
whereas in fact the low heart rate occurs due to the patients being more fit and
therefore these patients have a lower level of cardiac disease. Since the ROC
curve is not random, there is useful information in the analysis, but the
interpretation needs to be reversed with respect to the original hypothesis in order
to take advantage of this information.
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