Table 2.
Estimation of the Annual Number of Domestically Acquired Sporadic Cases of Salmonellosis
| Notation | Description | Estimation |
|---|---|---|
| Cases per Salmonella serotype | ||
| I | Subscript for Salmonella serotype associated with a reported case of salmonellosis | |
| Y | Subscript for study year: 1998–2003 | |
| sssyi | Observed cases of i reported to national surveillance system in year y | NSSS Data |
| kti | Observed cases of i that were known to be unrelated to an outbreak (sporadic) but were international travel-related (also includes cases that were classified as both outbreak- and international travel-related) | FoodNet Data |
| ksi | Observed cases of i that were known to be sporadic and not travel-related (domestically acquired) | FoodNet Data |
| αuti | Probability that a case of i that is known to be unrelated to an outbreak but is missing travel information is international travel-related | Beta(kti + 1; ksi + 1) |
| bi | Observed cases of i that were sporadic but had no information regarding travel | FoodNet Data |
| λti | Estimated expected number of international travel-related cases of i among those cases known to be unrelated to outbreaks but missing travel information | bi x αuti |
| xi | Expected number of international travel-related cases of i among those cases known to be unrelated to outbreaks but missing travel information | Poisson(λti)) x I[xi < bi] |
| ntspi | Estimated number of sporadic cases of i with no known travel history that were domestically acquired | bi - xi |
| koi | Observed cases of serotype i that were known to be domestically acquired and outbreak-related | FoodNet Data |
| αobi | Probability that a case of serotype i that was known to be domestically acquired but had no outbreak history was outbreak-related | Beta(koi + 1; ksi + 1) |
| ai | Observed cases of serotype i that were known to be domestically acquired but had an unknown outbreak history | FoodNet Data |
| λobi | Estimated expected number of cases of serotype i that were outbreak-related among those cases that were domestically acquired but lacked outbreak information | ai x αobi |
| oi | Expected number of outbreak-related cases of i among those cases known to be domestically acquired but lacking outbreak information | Poisson(λobi) x I[oi < ai] |
| nospi | Estimated number of cases of i that were sporadic among those known to be domestically acquired but had an unknown outbreak history | ai - oi |
| αspoi αdobi αtrspoi | Probability that a randomly selected FoodNet case of i was domestically acquired, sporadic (αspoi), domestically acquired, outbreak-related (αdobi) and international travel-related, sporadic cases (αtrspoi). All three estimated probabilities sum to 1. | Dirichlet(ksi + 1, koi + 1, kti + 1) |
| Ui | Observed number of FoodNet cases of i designated as unknown for both international travel and outbreak. | FoodNet Data |
| si | Estimated number of domestically acquired, sporadic cases of i that were designated as unknown for both international travel and outbreak in FoodNet Data (estimated numbers of domestically acquired, outbreak-related and international travel-related, sporadic cases were also calculated) | Multinomial (Ui, αspoi, αdobi, αtrspoi) |
| Sporadic | Total estimated number of domestically acquired, sporadic cases of i reported by FoodNet sites | ksi + ntspi + nospi + si |
| αfnspoi | Proportion of FoodNet cases of i that were domestically acquired, sporadic after allocating all cases with partial and completely unknown data (estimated proportions were also calculated for domestically acquired, outbreak-related [αfnoutyi] and international travel-related, sporadic categories [αfntravyi]) | Gamma(Sporadic; 1) Σ Gamma(Sporadic; 1) |
| ssspoyi | Estimated number of sporadic cases of i in year y reported to Salmonella Surveillance System (estimated case numbers were also calculated for outbreak [ssoutyi] and travel-related cases [sstravyi]) | pfnspoi x sssyi |
Adapted from Hald et al. (2004).
NSSS, National Salmonella Surveillance System.