Statistical discrimination in the presence of selection effects

Hilliam, R. M. (2005). Statistical discrimination in the presence of selection effects. Statistics in Medicine, 24(8) pp. 1219–1232.



Discrimination between diseases is a complex task. Cases may present contradictory information and
diseases can present with unusual or atypical symptoms. In many diagnostic problems the recorded
diagnosis is either a true diagnosis, based on hard evidence, or a working diagnosis, not necessarily
equivalent to the true underlying disease with an associated level of uncertainty. This problem is often
confounded since the type of diagnosis given may be subjected to selection effects. Much medical data
is categorical in nature, hence existing techniques for identifying selection e�ects are inappropriate. This
paper provides a method of obtaining a single parameter modelling, the probability of giving a true
diagnosis dependent on the nature of the true disease, thereby offering a simple measure for the presence
of selection effects. When the size of the data is limited identi�ability problems exist with calculating
this parameter, however this paper shows how a sensitivity analysis based on the profile likelihood can
be used to identify the presence of selection e�ects even in this difficult situation.

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