U. S. Food and Drug Administration
Center for Food Safety and Applied Nutrition
January 2001


Draft Risk Assessment on the Public Health Impact of
Vibrio parahaemolyticus in Raw Molluscan Shellfish

Table of Contents

V. Hazard Characterization/Dose-Response

Hazard characterization describes the adverse effects on the host of a particular substance, organism, or other entity. It may be a quantitative and/or qualitative evaluation of the nature of these adverse effects. Dose-response, which is quantitative, is the relationship of the levels of V. parahaemolyticus ingested with the frequency and magnitude of illness. Human dose-response relationships for V. parahaemolyticus can be derived directly from human clinical feeding trials and epidemiological (outbreak) investigations, if sufficient data exist. To date, little information in terms of estimated exposure doses has been obtained from outbreak investigations. For V. parahaemolyticus, dose-response data is available directly from several human clinical feeding trials. However, these studies were performed prior to 1974 with uncharacterized strains, antacid administration and with no information on the immune status of the volunteers in terms of preexposure to V. parahaemolyticus. Even partial immunity to V. parahaemolyticus could raise the observable infectious dose compared to what may occur in the general population. In addition, in outbreak settings, lower doses of V. parahaemolyticus may cause illness if the organism is mixed with food that can buffer the gastric acidity thereby lowering the infectious dose. It is unlikely that any additional human feeding studies with V. parahaemolyticus will be undertaken due to the observed cardiotoxicity of TDH in animal models (60, 119). In the absence of additional data for V. parahaemolyticus, an alternative for dose-response modeling is to select an appropriate surrogate bacteria for which additional dose-response data is either available or can be generated. Additional information considered essential would include greater low dose exposure data (including biomarkers) and the role of the food matrix on dose-response relationships. Information on non-O1 V. cholerae is provided as a possible surrogate organism.

Since limited human clinical information was available, it was assumed that all V. parahaemolyticus clinical isolates are equally virulent (105) and that the primary virulence factor is TDH (105). This may be modified as new data become available that identify new virulence determinants. In particular, recent data from British Columbia (77) may suggest an association of urease positive strains with clinical isolates, which may or may not be TDH positive.

Animal models using V. parahaemolyticus or a surrogate organism can be used as surrogates to provide a basis for extrapolating dose-response estimates for humans. Animal models can also be used to assess the virulence potential of different strains and serotypes, susceptibility of the sensitive subpopulation (i.e., immune compromised), and to study the role of specific virulence determinants. Several V. parahaemolyticus animal models have shown the virulence potential of TDH negative strains (59,84). However, it remains to be determined whether the virulence potential indicated for TDH- strains also applies to humans. The effect of food matrices and other environmental factors on virulence and the dose-response relationship can be evaluated more readily in animal models.

Human Clinical Feeding Studies

Feeding trials with V. parahaemolyticus

In the study by Takikawa et al. (125), a Kanagawa-positive strain (production of TDH, as observed on a blood agar plate) caused diarrhea in 1 of 2 individuals fed a dose of approximately 106 cells. Diarrhea occurred in 2 of 2 individuals fed approximately 107 cells (125). Ingested doses were estimated assuming that V. parahaemolyticus cultures can reach maximum growth densities of approximately 1010 cells per milliliter.

Three Kanagawa negative strains (no production of TDH as observed on a blood agar plate) isolated from cases of gastroenteritis were fed to groups of four volunteers each. No illness was observed in any of the groups at doses as high as 2 x 1010 cells. A Kanagawa positive strain also isolated from a gastroenteritis case produced no symptoms at a low dose of 200 viable cells. Abdominal discomfort occurred in 1 of 4 volunteers at a dose of 2 x 105 viable cells, and 2 of 4 volunteers experienced abdominal discomfort and diarrhea at 3 x 107 viable cells. All volunteers received antacid tablets prior to challenge with cultures suspended in gelatin (116).

Feeding tests carried out with 15 Kanagawa negative strains isolated from fish produced no illnesses when doses as high as 109 viable cells were used (115).

Although never published, a personal communication is cited (71) that reports it took 6 to 8 hours incubation for a V. parahaemolyticus hemolytic variant to cause disease while an non hemolytic variant required approximately 18 hours to cause disease after challenge. The infecting dose was stated to be approximately 106 organisms. No information is provided about the strain and it is unknown if the strain was truly a TDH- strain since no genetic analysis of the strain was performed.

Feeding trials with non-O1 V. cholerae

One of three strains of non-O1 V. cholerae fed to healthy volunteers caused no diarrhea in 2 volunteers fed 105 cells, 2 of 3 fed 106, 1 of 2 fed 107 and 3 of 3 fed 109. Two other strains produced no disease at doses as high as 109 cells (98).

V. cholerae O139 Bengal fed to volunteers caused diarrhea in 2 of 4 fed 104 cells and in 7 of 9 fed 106 cells (97).

Animal Models

For possible inclusion in future modeling, animal dose-response data and several factors influencing the infectious dose of V. parahaemolyticus, using animal studies are described in this section.

Animal models for V. parahaemolyticus

Suckling rabbits infected orally with a Kanagawa-positive strain at doses of 109 to 1010 had positive blood cultures in 9 of 36 tested, positive spleen cultures in 11 of 21 tested and positive liver cultures in 14 of 21 tested (20). Similar doses of a Kanagawa negative crab isolate were negative for bacteremia, liver or spleen invasion in all 12 animals challenged (20).

Combined results of seven experiments in which mice were challenged intraperitoneally with 1 of 7 strains (four TDH+ strains and three TDH- negative strains) resulted in 0 deaths with a dose of 105 cells; 4% deaths with a dose of 106; 61% deaths with a dose of 107, and 90% deaths with a dose of 108 cells (59).

Combined results of two experiments in which mice were challenged orally with 1 of 2 TDH+ strains resulted in 38% deaths with a dose of 107 cells, 57% deaths with a dose of 108 and 80% deaths with a dose of 109 cells (59). There were no significant differences in mortality between the TDH+ and TDH- strains at any of the doses.

In rabbit ileal loop studies the effective dose required to produce ileal loop dilation in 50% of rabbits for three Kanagawa positive strains ranged from 2.6 x 105 to 7.7 x 106 cells. It was estimated that the initiation of positive loops occurred with doses from 102 to 105 cells (134).

Animal models for other Vibrio spp.

Severity of disease increased and time until death decreased in rabbits when a non-O1 V. cholerae strain shown to cause diarrhea in volunteers, was administered in increasing doses of 103, 104 and 109 cells using the removable intestinal tie adult rabbit diarrhea (RITARD) model (114).

Fluid accumulation, diarrhea, and mortality of strains of non-O1 and O1 V. cholerae and V. fluvialis was studied in orogastrically challenged suckling mice. The 50% lethal dose values ranged from 107 to 109 CFU. The effective oral dose producing stained feces was about 1 log lower than the LD50 dose for each strain (106).

Factors Influencing the Infectious Dose of V. parahaemolyticus

Modeling of the Public Health Module

Figure V-1. See text for analysis.
Figure V-1. Schematic depiction of the Public Health Module of the V. parahaemolyticus (Vp) risk assessment model.

The Public Health Module predicts distributions of illness based on the distribution of serving size (oysters per serving and weight of oysters), the predicted levels of pathogenic V. parahaemolyticus at time of consumption and an estimated relationship between the probability of illness and ingested number of organisms per serving (Fig. V-1). For the purpose of modeling, only Kanagawa-positive V. parahaemolyticus strains have been considered as being pathogenic. In most studies, greater that 90% of the V. parahaemolyticus strains isolated from the stools of symptomatic cases are found to be Kanagawa-positive (34, 145). In contrast, less than 1% of strains isolated from the environment are found to be Kanagawa-positive. To date no other virulence determinant has been correlated with clinical disease. The predicted density of pathogenic V. parahaemolyticus at time of consumption is determined in the Post Harvest Module under assumptions of current industry practice and possible mitigations. Distributions of number of organisms ingested are obtained by multiplying the estimated densities of pathogenic V. parahaemolyticus by serving size.

Human clinical trials with Kanagawa-positive V. parahaemolyticus strains conducted prior to 1974 were evaluated for the purpose of determining a dose-response relation for converting distributions of ingested doses into distributions of risk per serving (2, 116, 125). However, in consideration of oyster consumption statistics and predicted levels of pathogenic V. parahaemolyticus at time of consumption, the dose-response (e.g. ID50) in the human feeding trials was found to overpredict the CDC estimates of annual number of illnesses by a factor of 10. This strongly suggests that the dose-response under conditions of normal population exposure is different than under the conditions of the feeding trials. Possible reasons for the difference include food matrix or immunological effects of preexposure to the organism including antibodies/vaccines to the organism (88). Consequently, a plausible dose-response was obtained by shifting the dose-response by a factor of 10, estimated from the feeding trials so as to be generally consistent with CDC estimates of illness. The predicted number of illnesses associated with oysters from each region and season were derived based on the projected number of raw oyster-servings. The probable number of illnesses associated with the oysters landed from each region was determined rather than the number of illness within each geographic region. Obviously, the number of illnesses occurring within a given region and season is due to oysters originating from various regions of the country.

An estimate of the distribution of risk per serving due to oysters originating from various locations would be obtained as a weighted average of the distributions of risk associated with oysters harvested from each region. However, a reliable estimate of the extent of interregional transport, which would be necessary to estimate the appropriate weights, was not identified.

Distribution of dose of pathogenic V. parahaemolyticus per serving

The distribution of the dose of pathogenic V. parahaemolyticus ingested per serving was estimated based on distributions of (a) the number of oysters consumed; (b) the weight of oysters consumed; and (c) the density of pathogenic V. parahaemolyticus per g output from the Post Harvest Module. The distribution of densities of pathogenic V. parahaemolyticus obtained in the Post Harvest Module is projected to represent the variation of average density over collections of oysters being consumed on any given occasion. This is appropriate in so far as total V. parahaemolyticus densities measured in the DePaola et al. (38) study were average densities over composites of twelve oysters and this is a typical serving size per serving. Implicitly, a collection of oysters being consumed on any given occasion is assumed to have originated from the same region.

Figure V-2. See text for analysis.
Figure V-2. Observed frequency of number of oysters consumed per serving (University of Florida consumption survey) (36).

The distribution of the number of oysters consumed per serving is shown in Figure V-2. The most typical serving sizes were 6, 12 and 24 oysters. This frequency distribution is based on a 1994 Florida consumer survey conducted by the Florida Agricultural Market Research Center (University of Florida) (36). To obtain the estimate of the distribution of meat weight per serving, estimated distributions of meat weight for servings of a given size were combined with the distribution of serving size.

Based on review of available data, the distribution of the meat weight corresponding to a serving of n oysters was adequately approximated as a normal distribution with mean and variance of n*mu and n*sigma2, respectively, where mu and sigma2 are the mean and variance of meat weight per single oyster. The distribution was truncated to eliminate values below 15*n and above 35*n grams on the assumption that it was unlikely that individual oysters would have meat weight outside of the range of 15 to 35 grams. An estimate of the mean and standard deviation of meat weight of individual Gulf oysters is 26 and 7.3 grams respectively (37). When combined with the distribution of serving size, the resulting distribution of meat weight per serving was considered typical of all regions.

Although, oysters harvested in the Pacific Northwest are somewhat larger than Gulf oysters the meat weight per serving is unlikely to vary substantially across different regions of the country. The distribution of number of oysters per serving is based on a survey of Florida consumers who would have been consuming predominately Gulf oysters. Therefore it is appropriate to combine this distribution with the distribution of meat weight of Gulf oysters.

The distribution of the number of pathogenic V. parahaemolyticus ingested per serving was determined by multiplying the distribution of the densities of pathogenic V. parahaemolyticus per gram oyster meat (the average density projected for composites of oysters) and the distribution of meat weight per serving, as determined above.

Number of raw oyster servings

The number of raw oyster servings associated with oysters harvested from different regions and seasons was estimated based on National Marine Fisheries Service (NMFS) landings data. The total monthly oyster landings reported by NMFS were averaged over the period 1990 to 1998, then grouped by season and region (Table V-1). Oyster landings are reported by NMFS as pounds of oyster meat weight. Industry figures suggest that 50% of the harvest is consumed raw with little variation across different seasons. Therefore, the projected number of illnesses which may occur have been based on the assumption that 50% of the harvest is consumed raw. The actual fraction of the landings consumed raw in any particular year may vary somewhat with a range of 40% to 60% being reasonable. However, total landings also vary from year-to-year in a manner that is not predictable due to the influence of other factors (e.g. closures due to water quality, effect of parasites). Oyster landings have been generally increasing over the past 5 years but it is uncertain to what extent this trend will continue in the future.

Table V-1. National Marine Fisheries Service (NMFS) average yearly oyster landings 1990-1998

Location Average Number of Pounds of Oyster Meats Harvested
Winter
(Jan-March)
Spring
(April-June)
Summer
(July-Sept)
Fall
(Oct-Dec)
Total
Atlantic Northeast 2,112,000 714,000 676,000 3,710,000 7,212,000
Mid-Atlantic 946,000 125,000 66,000 1,492,000 2,629,000
Gulf Coast
Louisiana
Other States
Gulf Total
2,751,000
2,096,000
4,848,000
2,630,000
1,393,000
4,023,000
2,854,000
847,000
3,701,000
2,769,000
2,358,000
5,127,000
11,004,000
6,694,000
17,699,000
Pacific Northwest 2,402,000 1,682,000 1,379,000 3,181,000 8,644,000
Total 10,308,000 6,544,000 5,822,000 13,509,000 36,183,000
Source of data: http://www.nmfs.noaa.gov/

The number of raw servings associated with oysters from each harvest region and season were estimated as:

Li * f
W * S

where Li are the regional and seasonal total landings expressed in units of meat weight (grams), f is the percentage of oysters consumed raw, W is the average meat weight per oyster (grams), and S is the average number of oysters per serving (14.7 based the 1994 FL consumer survey) (36).

Dose-Response

Generally, the most appropriate data upon which to estimate the dose-response relationship of a bacterial pathogen would be the outcome of feeding trials with human subjects. Although subjects selected for feeding trials tend to be healthier than the general population, the magnitude of the uncertainty when extrapolating from such data is generally less than that associated with the extrapolation of dose-response determined from animal studies. In particular, animal data were not utilized in our initial modeling efforts because the endpoint was death rather than illness. Measures of the severity of illness used in animal studies often do not correspond with definitions of human illness on which reporting statistics are based.

For pathogenic V. parahaemolyticus, as identified by the Kanagawa test, several human clinical feeding trials were conducted prior to 1974. Epidemiological investigations of V. parahaemolyticus provide additional information on plausible dose-response of gastroenteritis but are somewhat limited due to the lack of data concerning ingested doses of pathogenic strains associated with reported cases of illness (e.g. epidemiological traceback studies). Epidemiological case series data do provide valuable information which can be used to estimate the likelihood of illness progressing to more severe outcomes (i.e., septicemia, death) for both immune compromised and otherwise healthy populations. Estimates pertaining to the severity of illness based on epidemiological data are presented in the next section.

The dose-response relationship for illness (gastroenteritis or septicemia) was estimated based on the 1974 study of Sanyal and Sen (116) augmented by data from studies by Takikawa (125) and Aiso (2). Overall, 5 of the 16 subjects who received higher ingested doses of Kanagawa positive strains developed symptoms of gastroenteritis in these studies. No severe outcomes were observed. Dose-response, using all the doses from the three studies, was characterized by fitting several dose-response models chosen to span the range of extremes of model extrapolated risks at projected levels of population exposure.

The selected models were the Beta-Poisson, Gompertz, and Probit (Log-normal). The Gompertz and the Probit are generalized linear models. For these two models, the linear predictor was chosen to be a linear function of log10 ingested dose. The mathematical form of these dose-response models is shown in Table V-2.

Table V-2. Dose-response models of the relationship between
probability of illness and number of V. parahaemolyticus organisms ingested.

Dose-response model Risk of illness as a function of dose a
Beta-Poisson Pr (ill | d) = 1 - (1 + d/beta) raised to -alpha

Probit

Pr (ill | d) = capital phi (alpha + beta * log_10 (d))
Gompertz Pr (ill | d) = 1 - exp [-exp [alpha + beta * log_10 (d)]]

aalpha and beta are the location and shape (steepness) parameters, respectively, for the Probit and Gompertz models;
alpha and beta are the shape (steepness) and location parameters, respectively, for the Beta-Poisson;
capital phi denotes the cumulative distribution function of a standard normal random variable

The maximum likelihood estimates (MLE) of the Beta-Poisson, Gompertz and Probit dose-response models are shown in Figure V-3. For example, at a dose of 100 (2 log10) V. parahaemolyticus organisms, the Beta-Poisson model predicts a risk of approximately 7 cases of illness per 10,000 challenges at that dose. Best estimates of the risk of illness at ingested doses of less than 103 organisms vary by more than 10-fold across this set of plausible models. However, based on the estimates of exposure developed in the Harvest and Post Harvest Modules, the mean (average) exposure to pathogenic V. parahaemolyticus exceeds 100,000 cells per serving for the Gulf Coast summer harvest. At this level of exposure the differences between the dose-response models is not substantial. The average dose associated with the Gulf Coast summer harvest is less than 2 log10 below that of ID50 estimates for the human feeding trial studies based on any of the three models considered.

Figure V-3. See text for analysis.
Figure V-3. Maximum likelihood estimates (MLE) of the Beta-Poisson, Gompertz, and Probit dose-response curves based on pooled data from human feeding studies of V. parahaem olyticus (Vp).

Consideration of the predicted density of pathogenic V. parahaemolyticus, the number of raw oyster servings for the Gulf Coast summer harvest and the likely number of illnesses occurring (CDC personal communication) (80), strongly suggests that the predicted risks per serving based on dose-response curves shown in Figure V-3 are not plausible. Consequently, direct extrapolation of the dose-response under conditions of exposure in the feeding trials is not supported by the epidemiological data. The human feeding trials were conducted under conditions of concurrent antacid administration. For V. cholerae, the ID50 observed in feeding trials is known to be substantially lower when V. cholerae is ingested with antacid versus no antacid (88). The same effect is likely to be the case with V. parahaemolyticus. It is also possible that food matrix or immunological effects of preexposure to the organism, including antibodies/vaccines, contribute to the apparent difference in dose-response obtained under experimental versus natural conditions (88). Antibodies to V. cholerae increased the ID50 (88). Likewise, prior consumption of oysters containing non pathogenic V. parahaemolyticus, may also contribute to a higher ID50. It has also been reported, for example, that in rats, high milk fat intake results in higher concentrations of gastric bactericidal lipids, which protect against Listeria infection (123). Furthermore, gastrin, the most potent stimulant of gastric acid secretion is released after eating a protein-rich meal, like oysters (8). The increased production of gastric acid would provide greater protection against infection, thus increasing the infectious dose.

The relevant epidemiological data is summarized by estimates of annual incidence of Vibrio illness developed by Mead et al. (94) as part of a comprehensive evaluation of the national burden of infectious food-related illness in the United States. Mead et al. (94) have estimated an average annual burden of 7,880 Vibrio illnesses excluding those due to V. vulnificus, and that 65% percent of this total incidence is estimated to be food-related. This estimate was based on frequency of reported cases obtained by passive surveillance from 1988 through 1996 and frequency of reported cases through FoodNet in 1996 as extrapolated to the 1997 population. This total illness caused by non-vulnificus Vibrio spp. is based on an estimate of 20 to 1 underreporting and underdiagnosing of illness (80, 94).

The reported cases of illness attributable to V. parahaemolyticus in recent years is a component of the data on which total incidence of non-vulnificus Vibrio illness is based on the information reported by Mead et al. (94). Specific yearly estimates of total illness attributed to V. parahaemolyticus for 1996, 1997 and 1998 are 4128, 15088 and 8567, respectively (94), based upon active FoodNet data surveillance. Assuming that 65% of these illnesses are food-related, CDC estimates that the total number of foodborne V. parahaemolyticus cases in the United States for 1996, 1997 and 1998 was approximately 2700, 9800, and 5600, respectively.

Given these estimates of annual illness rate it was determined that at least a 10-fold increase of the ID50 estimated with respect to the feeding trials was necessary to infer a dose-response consistent with the epidemiology. It is possible that the true ID50 for the general population is even greater than implied by this adjustment but this uncertainty was not evaluated in the present risk assessment.

The uncertainty with regard to which model is most appropriate for risk extrapolation is often referred to as a structural uncertainty. An additional source of uncertainty in dose-response is referred to as parameter or statistical uncertainty. This uncertainty derives from the estimation of the parameters of a given model based on a small sample of observations. Parameter uncertainty is present even if there is no structural uncertainty.

Figure V-4. See text for analysis.
Figure V-4. Uncertainty distribution of infectious dose of V. parahaemolyticus corresponding to 10-3 risk for Beta-Poisson, Gompertz, and Probit dose-response models.

Parameter uncertainty in the extrapolated risk for the Beta-Poisson, Gompertz and Probit models was evaluated by nonparametric bootstrapping (i.e., replication) of feeding trial outcomes. Using this procedure, for each possible bootstrap, the models were refit to obtain a distribution of parameter estimates corresponding to the possible (unrealized) outcomes of the human feeding trials. The series of parameter estimates obtained are weighted by the probability of the corresponding bootstrap outcomes. For each model, the distribution of parameter estimates obtained defines the uncertainty of predictions or extrapolations conditional on the structure of the model (i.e., in the absence of structural uncertainty). For example, the parameter uncertainty associated with the model predicted infectious dose level corresponding to a risk of 10-3 is shown in Figure V-4 (as estimated by 1,000 bootstrap samples) for each of the three models considered. As can be seen, the uncertainty distribution of this particular benchmark dose has somewhat the same spread (or range) for both the Gompertz and the Probit. However, since the distribution for the Gompertz places much more weight on the extremes of the range, the uncertainty of the estimate is much greater for the Gompertz than for the Probit model. The uncertainty is somewhat less for the Beta-Poisson. The means of all three of these distributions are comparable to the predictions of the MLEs for these models, as shown in Figure V-4.

Parameter uncertainty was evaluated in the risk assessment by simulating the uncertainty of the estimate of risk associated with any dose consumed. For each of the models considered, the risk of illness at a specific dose was considered to have a distribution determined by the bootstrap distribution of parameter estimates. Given a risk of illness on an eating occasion/serving, whether or not illness occurs was then modeled as a Bernoulli random trial with the corresponding risk of illness as parameter. Structural uncertainty was evaluated by conducting multiple simulations using the different structural forms for the dose-response extrapolation.

Severity of Illness

The output of the Public Health model is the probability distribution for the number of illnesses expected to occur from consumption of oysters from different sources (seasons/regions). These predictions assume that the probability of infection at any given ingested dose is the same for all consumers. Clearly, most infections go unreported. In the Gulf Coast states where V. parahaemolyticus infections are more actively identified, individuals who are immune compromised or have liver disease are notably over represented in the case series of culture-confirmed illness. There are two possible explanations for this observation. It is possible that there exists a sensitive subpopulation that is more susceptible to infection at any given dose. However, it is more likely that there exists a sensitive subpopulation which, given the occurrence of infection, is more likely to progress to severe outcomes requiring the attendance of a physician. That is to say, the overrepresentation of immunocompromised individuals in culture-confirmed case series is likely to be a reporting phenomenon driven by the severity of illness.

For the purpose of the risk assessment, we have assumed that there is no sensitive subpopulation with respect to the occurrence of an infection leading to gastroenteritis or septicemia. However, given the occurrence of illness, we assume that it is more likely that the infection leads to severe outcome (e.g. septicemia or death) among individuals with an underlying condition. The best available information to quantify this differential likelihood of severe outcome is the CDC database of culture-confirmed V. parahaemolyticus cases in the Gulf Coast states.

Estimates of the conditional probabilities of septicemia and death following infection leading to illness in healthy and immune-compromised individuals can be estimated by using Bayes theorem(46) and the frequency of underlying conditions among identified culture-confirmed V. parahaemolyticus cases. Specifically, the calculation uses Bayes theorem in the form:

Pr(outcome | condition) = Pr(condition | outcome) * Pr(outcome)
Pr(condition)

where, for example, Pr(outcome|condition) denotes the probability or frequency of an outcome among a population of individuals grouped by health status (condition). All factors on the right hand side of the equation are identifiable from the epidemiological data.

The frequency of underlying conditions was identified among 107 oyster-related culture-confirmed V. parahaemolyticus cases (sporadic- and outbreak-related) occurring during 1997 and 1998 in the Gulf Coast States (6). The statistics of the case series were:

Of cases with available information:

Substituting the appropriate observed frequencies into the above equation provides estimates of the probabilities of progression to more severe outcomes conditional on culture-confirmed illness. For example, the probability of septicemia occurring following culture-confirmed illness among individuals with underlying chronic conditions is estimated as follows:

Pr(septicemia | sensitive) = Pr(sensitive | septicemia) * Pr(septicemia)
Pr(sensitive)
= 3/4 * 5/107
23/79
= 0.12

The probability of septicemia occurring after culture-confirmed illness in healthy individuals is estimated in a similar fashion. Overall, the estimated conditional probabilities of severe outcomes based on the CDC data are:

Pr(septicemia | sensitive & culture confirmed) = 0.12
Pr(septicemia | nonsensitive & culture confirmed) = 0.0165
Pr(septicemia | culture confirmed) = 0.047
Pr(death | septicemia) = 0.2

These estimated frequencies pertain to the population of culture-confirmed illnesses that may occur in any given year. Certain assumptions are necessary to estimate the frequency of severe outcomes occurring among the population of all V. parahaemolyticus illness, regardless as to whether it is culture-confirmed or not.

Clearly, there is a selection bias towards more severe outcomes in the culture-confirmed case series. It is unlikely that a significant fraction of cases of septicemia would go undiagnosed. Overall, considering the less severe outcomes, it is estimated that 1 in 20 cases (5%) of V. parahaemolyticus illness are reported or diagnosed in the Gulf Coast states (CDC, personal communication) (6). Thus we would estimate approximately 2140 illness occurring over a time period during which 5 septicemia cases were identified. Assuming that all septicemia are culture confirmed, the Bayes calculation for the probability of progression to septicemia among sensitive individuals who have become ill is:

Pr(septicemia | sensitive & ill) = 3/4 * 5/2140
23/79
= 0.006

If only 50% of septicemia are reported and culture-confirmed, the corresponding estimate is 0.012. For healthy individuals, the estimated rates of septicemia following illness are 0.0008 and 0.0016, assuming complete and 50% underreporting, respectively.

Given estimates of conditional probabilities, the frequency of septicemia can be simulated in the model based on the relative frequency of consumption of raw oysters by sensitive and healthy individuals. Approximately 7% of the general population have an underlying condition predisposing to V. vulnificus infection (82). The same set of conditions would likely predispose to more severe V. parahaemolyticus illness. If sensitive individuals consume raw oysters at the same frequency as the general population then the overall risk of septicemia occurring is the weighted average of the conditional probabilities of septicemia for sensitive and healthy individuals.

Pr(septicemia | ill) = 0.07 * Pr(septicemia | ill, sensitive) + 0.93 * Pr(septicemia | ill, healthy)

The distribution of the probable number of septicemia which may occur in a given year is therefore a binomial with size parameter equal to total number of illnesses and the probability parameter equal to the overall risk of septicemia following illness. Implicitly, this probability of septicemia (and the probability of other severe outcomes) has been assumed to be independent of the dose leading to infection and illness.



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