Calculation of the Probability of Multiplicities in Two Cell-Occupancy Models: Implications for Spontaneous Reporting Sy
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Drug Informarion Journ~l.Vol. 33, pp. 1195-1203, 1999 Printed in h e USA. All rights reserved.
CALCULATION OF THE PROBABILITY OF MULTIPLICITIES IN TWO CELLOCCUPANCY MODELS: IMPLICATIONS FOR SPONTANEOUS REPORTING SYSTEMS JOHN A. CLARK,MD, MSPH Senior Director, Drug Safety and Pharmacoepidemiology, Bracco Diagnostics, Inc., Princeton, New Jersey
ROBERTH.
BERK,
PHD
Director, Office of Statistical Consulting, Department of Statistics, Rutgers University, Piscataway, New Jersey
STEPHEN L.
KLINCEWICZ,
DO, MPH, JD
Medical Director, Zeneca Pharmaceuticals, Wilmington, Delaware
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.) reportsfrom 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 A E 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 infrequency, and evidence for the presence of a localized increase in frequency. These calculations imply that underreporting imposes a limitation on most generalized increased frequency analyses by eflectively restricting testing to methods that compare the number of regions or reporters rather than the number of reports. Key Words: Adverse drug reaction; Pharmacovigilance; Increased frequency analysis; Pharmacoepidemiology; Multinomid models
INTRODUCTION IS WIDELY ACCEPTED THAT spontaneOuS adverse event reporting systems C a n provide useful signals, that is, potential problems deserving additional investigation
Reprint address: John A. Clark, MD, MSPH, Bracco Diagnostics, Inc., P.O. Box 5225, Princeton, NJ 085435225.
(1,2,3). One such signaling methodology which has been suggested, increased frequency analysis, involves serial comparisons of report totals for a specific drug-m pair adjusted for differences in drug use (4). several statistical procedures have been proposed to carry out such comparisons with the aim in each case being to detect a generalized increased frequency of reporting Of an imprmt AE. It is understood that the results of such analyses must be in-
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John A. Clark, Robert H.Berk, and Stephen L. Klincewicz
terpreted in the context of potential reporting biases (4,5,6). The United States Food and Drug Administration (FDA) recently issued a final rule that eliminated the postmarketing requirement for expedited forwarding of incr
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