On post-hoc assessments of disease-cluster alarm rates
We consider a method of evaluating whether a suspected disease cluster alarm rate (i.e., an observed group specific disease incidence rate that comes to the attention of a health official because of its large size) is greater than that expected on the basis of appropriate prevailing or historical rates. This method differs from methods used in the past based on adjustment of the signal detection level including one proposed recently based on what we refer to as universe enlargement. The method proposed here takes into consideration the concept of "visibility", i.e., the fact that cluster alarm rates are not representative of the underlying distribution of the group specific incidence rates about which an inference is to be made, since rates not perceived to be high would be unlikely to become cluster alarm rates. Using various visibility models, we incorporate this concept into the computations of observed versus expected number of events used in assessing whether or not a particular cluster alarm rate is significantly higher than what would be expected on the basis of endemic rates. We show tables that display the effects of visibility on the statistics commonly used to assess cluster alarm rates, and compare our method with methods based on universe enlargement and other adjustments of the signal detection level.