Calculation of the Probability of Multiplicities in Two Cell-Occupancy Models: Implications for Spontaneous Reporting Systems

Using Maxwell-Boltzmann and Bose-Einstein models, we derive formulae for the exact probability that an adverse event (AE) report series will present with additional (ie, second, third, etc.) reports from a single geographical reporting region, under the assumption that each region has an equal probability of report generation. These formulae are used to calculate critical values for the number of regions beyond which the probability of additional same-region reporting falls below a predefined level. The results using either model suggest that for widely distributed drugs, the presence of even a single additional same-region AE report is extremely unlikely and provides reasonable evidence for differential reporting rates between regions with multiple versus single reports. Multiple same-region reports, therefore, provide evidence against the validity of report-based tests for a generalized increase in frequency, and evidence for the presence of a localized increase in frequency. These calculations imply th...