Sensitivity and specificity of case definitions may vary according to the purpose of the case identification. For a severe disease with epidemic potential like SARS or Ebola Haemorrhagic fever, epidemiologists will choose to use first a very sensitive case definition to cast a wide net: they want to avoid missing cases that can further spread the disease. A very sensitive case definition will ensure that all true cases will be caught, yet it will also include individuals that do not have the disease.
Alternatively for research purpose investigators will often want to use case definition with high specificity, e.g. to study risk factors for transmission. The same goes for the investigation of a food borne outbreak in which the case definition should be specific if one wants to increase the probability to rightly identify a food vehicle and risk factors for the outbreak.
The table below shows the relation between sensitivity and specificity:
Sensitivity = [ a / (a+c) ]
Specificity = [ d / (b+d) ]
In other words, the sensitivity of a case definition is the proportion among all individuals with the disease in the study sample that are identified by the case definition. The table also suggests that if we change a case definition to include more individuals of 'all diseased', it will automatically start to include also more individuals of 'non-diseased'. So the cost of increased sensitivity will (usually) be decreased specificity. Note that this usage of the concepts sensitivity and specificity are exactly the same as are explained in the chapter on 'Validity and accuracy'; in that sense, the case definition may be seen as 'a test' to determine the classification of an individual to the 'case' category or the 'non case' category.
Just be aware that increasing specificity and losing sensitivity of a case definition in a case control design may increase your ability to find a difference between cases and controls. However, in a cohort study the opposite may happen, as misclassification of cases will bias the result towards the null hypothesis.