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. 2011 Apr;8(4):509–516. doi: 10.1089/fpd.2010.0714

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.

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