Background:
You are working as Medical Lab Assistant for Locums Inc., a firm of biomedical science, you have been
asked to investigate the wisdom and efficacy of ‘screening’ programmes for various potentially fatal diseases. At first sight the issues seem clear cut: if there is a test which can tell you whether or not you have a disease at an early stage, so that if you have, you can be given treatment, surely that is a good thing?
That would certainly be true if such tests were infallible, but unfortunately that is rarely the case: they can
wrongly return negative results for a person who actually has the disease, and sometimes also register as
positive someone who does not have it. Suppose, for example, that historic data suggests one person in
200,000 suffers from Gauss’s Disease, and that a new test has just been developed that can detect this
unpleasant complaint before any symptoms appear. However, early results indicate that the test returns a
false positive in 2 per cent of cases, and also that it gives a false negative in 5 per cent of cases.
a.) What are the definitions of false positive and false negative in the medical test? [15%]
b.) What are the definitions of true positive and true negative in the medical test? [15%]
c.) If you have just been tested for Gauss’s Disease and given a positive result, what is the chance that you
actually have the disease for the random sample of 4,000,000? [30%]
d.) What is the implication of your answer to c.) for the introduction of widespread screening for the
disease?
[20%]
e.) What assumptions are being made in your approach to this problem, and to what extent do you think
they are realistic. [20%]
Sample Solution