As previously mentioned, the actual number a of cases that have occurred during the surveillance period t could theoretically be estimated by a = k • U, where k is the number of reports during the surveillance period and U is the under-reporting coefficient varying from one (exhaustive reporting) to infinite (i.e. the reporting rate is null).
Unfortunately, it is extremely difficult and/or hazardous to estimate the magnitude of this under reporting, even if in most cases it can be thought to be huge, even for serious cases (Alvarez-Requejo et al, 1998; Eland et al, 1999).
For example, in 1998 a nation-wide prospective study conducted in a representative sample of French public hospitals estimated that 128 768 patients (95% CI: 100 916-156 620) were admitted that year in these hospitals because of an ADR (Pouyanne et al., 2000). This study did not consider other aspects of seriousness such as death, nor admissions to private hospitals. Nevertheless, the obtained figure (128 768) was far larger than the number of serious reactions (about 15 000) reported during the same period to the French pharmacovigilance system still considered as particularly efficient.
The capture-recapture approach, when applicable, could appear appealing to estimate the total number of cases of a given effect that have occurred in the surveyed population (Jeeger et al., 1996). This approach derives the size of the source-population from the number of individuals both "captured" by two independent samplings from this population (a more accurate estimate would be obtained by a greater number of samplings, e.g. three or four). To apply this method to pharmacovigilance consists in considering two or more independent sources of reports in the same territory. For instance, if kj and k2 reports have been collected, respectively, during the same period, through two independent sources, e.g. the regional pharmacovigilance centres network and the concerned manufacturer and if c was the number of duplicates (i.e. cases identified by both sources 1 and 2), then the total number of cases would be ki • k2
If kj and k2 were large enough (e.g. >15), the normal approximation can be used to calculate the 1 — a confidence interval (CI) for a:
Example: During a one-year surveillance period, 127 cases were reported to the first system and 42 to the second; 12 duplicates were identified. The estimate for the total number of cases is
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