## Info

Figure 21.1. Probability P of receiving at least three case-reports according to several theoretical values of RR and under-reporting coefficient U (see text).

population, the expected number of fortuitous, i.e. non-causal, associations is: 0.0961 x 7 = 0.67. According to the Poisson formula (cumulative probabilities), there is only 48% chance that one case or more really occurs by chance in this population. Considering a probable under-reporting, it becomes highly improbable that one or more of such a non-causal association will be reported. For example, if U = 4 (25% of cases which have occurred were reported), m = 0.67/4 = 0.17. The probability of receiving one report or more under these conditions is 16%. This probability falls to 0.07% for three reports or more, which allows us to exclude the possibility of a non-causal association (Begaud et al., 1994). This simulation explains the well recognized value of SR for signal generation (Fletcher, 1991; Tubert-Bitter et al., 1992): for rare events, only causal associations (characterized by a RR far greater than one) have a good chance of being reported, even if the reporting approaches 100%. This is illustrated by Figure 21.1 which plots, for different theoretical values of underreporting and RR, the probability of receiving three reports or more when the expected number of fortuitous associations is, as above, 0.67.

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