Analysis of surveillance data with poisson regression: A case study

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Abstract
One way to examine the ability of a statistical technique to detect changes in surveillance data is to analyse data sets with known changes and observe how accurately these changes can be detected. The elimination of restrictions on legal abortions should have reduced mortality associated with abortions, particularly mortality associated with illegal abortions. The sensitivity of Poisson regression to detect changes in abortion associated mortality from 1962 to 1984 was assessed for the entire United States of America and for specific states. Although it is clear that this change occurred using data from the entire United States, only the largest of the individual state data sets examined (370 events over 23 years) consistently demonstrated the expected pattern. Inconsistent patterns were found in data sets from two states with between one-fourth and one-half this number of events. The legal change was not detected at all in three states with a small number of events (1 event per year or less). From this case study, a minimum of two or three events per year seems to be necessary before Poisson regression can detect outliers. Comparisons of the four tests used suggest that tests based on model deviance are superior to tests based on comparison of observed and expected number of events.