This section contains a description of some of the software routines used in preparing the Listeria risk assessment. These were developed by the agency to deal with recurring risk assessments problems
Data
In order to proceed, the routine must be supplied with data in the proper format. There are two ways to do that.
The first is to supply a data file that is in the correct format. The "File Open" button may be used to browse for the file name. The file is not actually opened unless the "Data Edit" or "Run" buttons are selected. Alternatively, the file name, including the path, may be entered into the text box to the right of the "File Open" button.
Alternatively, data may be entered using the "Data Editor," which is started with the "Data Edit" button. If a file name has already been entered the Data Editor will open this data file. If it has not, then the "Editor" begins with no entries.
Choosing Models The models used by the DoseFrequency curve-fitting routine have 1 to 3 components. The total number of models fit will be equal to the number of possible permutations of each of the three components selected
The mandatory component is the primary dose-response function listed in the "Models-to-be-Fit" box. At least one model must be selected for the program to proceed. However, any combination may be selected. The curve-fitting routine will attempt to fit all models selected. A description of the models currently supported is given below.
Models currently supported by the DF curve-fitting program and object: | ||
Model Name | Parameters | Equation for Frequency Given Dose |
Beta Poisson | alpha, beta | 1 - (1 + (dose / beta) alpha) |
Logistic | alpha, beta | ealpha + beta * ln(dose) / (1 + ealpha + beta * ln(dose) ) |
Exponential | slope | 1 - e -dose * slope |
Gompertz – Log | alpha, beta | 1 - e -e ^ (alpha + (beta * ln(dose))) |
Gompertz – Power | alpha, beta, power | 1 – e -e ^ (alpha + (beta * (dose ^ power))) |
Probit | alpha, beta | normal_cdf(alpha + beta * ln(dose)) |
Multihit | gamma, k | gamma_cdf(gamma * dose, k) |
Gamma Weibull | alpha, beta, gamma | 1 - (1 + (dosegamma/beta) – alpha) |
Ln = natural log. cdf = cumulative distribution function. ^ = raised to the power of |
Background Parameter
A parameter may be added to the model to accommodate other influences on the outcome of the causal event. There are three options:
The program will attempt to fit all options that are checked. For example, if all three boxes are checked, then the program will examine all three different options. At least one box must be checked.
If there are fewer than five data points, then a Background Parameter cannot be employed.
Threshold Parameter
If a threshold dose parameter is included in the model, and if the nominal dose is less than the threshold dose value, then the effective dose used to predict frequency is zero. If the nominal dose is greater than the threshold dose value, then the effective dose used to predict frequency is the nominal dose minus the threshold dose. The program attempts to fit all options that are checked. If both boxes are checked, then the program examines both options. At least one box must be checked. If there are fewer than five data points, then a "Threshold Parameter" cannot be employed.
Options
Selecting the "Options" button opens another dialog, which gives the user some additional choices regarding how the routine operates. These include choosing the goodness-of-fit measure, how the program weights models when creating a probability tree, and the initial estimates for each of the model parameters.
Bootstraps
In order to represent uncertainty arising from sampling error, dose measurement error, or the size of the exposed population in which illnesses are observed, multiple bootstraps may be performed. Sampling error, where the small sample of observed values is presumed to come from a much larger sample that is of interest, is represented by presuming a binomial distribution where the total set of values is infinitely large. The likelihood of a series of possible values for the actual frequency are computed by comparing the relative likelihood of generating the observed value. Dose and population size measurement error are sampled from distributions supplied with the data set. The total number of models fit equals the number of models selected times the number of bootstraps. While very large numbers are possible, the program has not been tested with more than 10,000 models.
Initial Parameter Estimates
The default initial parameter estimates that are used by the IMSL nonlinear regression program to produce an optimum fit may not work well for all data sets. The initial estimate for the primary functions can be changed in this dialog. Initial estimates for the threshold and background parameters cannot be changed at this time. Selecting "OK" results in retention of the new parameter estimate. Selecting "Cancel" will not.
Model Weighting
Even if bootstrapping is selected, the first bootstrap (the first set of models in the parameter file) always uses the original data.
Run
The routine begins by fitting curves when the "Run" button is selected. The "Parameter File" dialog appears when the routine is finished. A progress bar displays the percentage of the task that has been completed. However, unless bootstrapping is selected, the results are nearly instantaneous. Selecting the "Cancel" button causes the program to exit.
As the program fits the alternative models to the data set, it calculates a weight for each of the models that is used by the object to assign probabilities to each of the models. The weighting algorithm used by the program rewards models for goodness of fit, and penalizes for parameters. Moving the slider bar to the left increases the importance of producing a good fit, while moving it to the right emphasizes the use of fewer parameters.
When bootstraps are run, the weights are recalculated on a relative basis for each bootstrap, so that the total weight for each bootstrap is identical. This means if the routine is used soley to represent the uncertainty in the parameters for a given model (i. e., parameter uncertainty with no model uncertainty), then the model weighting algorithm has no effect.
ParamFit
ParamFit is a procedure for fitting a statistical distribution to a set of individual values for use in a subsequent Monte-Carlo simulation. It is similar in function to the routine included with Crystal Ball (Decisioneering) or BestFit, the add-on sold by Palisade as a companion to @Risk. The principle difference is that ParamFit is specifically intended for use in a population modeling exercise (e. g., public health). In this circumstance, the primary purpose of a distribution is to represent variability in the measured quantity among individuals in a population, rather than the uncertainty associated with the prediction of a single event. Under such circumstances, the uncertainty is associated with the distribution used to generalize the data and draw inferences about the population as a whole. The end product of ParamFit is an Excel function containing a list of plausible alternative models which may be used to draw an inference in a two-dimensional Monte-Carlo model. It was written in Excel Visual Basic for Applications and requires Excel 5.0 or later versions and the Toxfunct add-in.
Models
There are ten distributional models that may be employed for the purpose of describing the data and drawing inferences. Any models that are checked will be fit to the data. You may select only one model, all the models, or any subset. The following distributions are supported by ParamFit:
Model Weighting Criteria
The frequency of use of each model is allocated according to it relative model weight which is calculated as follows:
* = Multiplication symbol.
Pn = Number of Model Parameters. In general, this refers to the number of parameters which are adjusted to fit the curve. However, the minimum values for the beta, linear, and triangular models would fit equally well if they are not truncated at a minimum value; that is, two points describe a line which could be represented as a single parameter (a slope).
gof = Goodness-of-Fit. ParamFit uses a least residual squares for the predicted percentiles as an optimization criteria. The ratio of the sum of residual squares to the sum of total squares for the predicted percentile is used as a goodness-of-fit statistic. This criteria emphasizes fit in the middle of the distribution, so that outliers have less impact on the shape of the distribution, other methods such as the "likelihood ratio" rate residual deviations in predicted distribution values.
O = The Parameter penalty, an arbitrary constant named after William of Ockam. Increasing this number increases the penalty for using an extra parameter, which influences the extent to which models are penalized for using an extra parameter The maximum value is 10. Setting this value to 0 nulifies the parameter penalty.
H = The Association factor, an arbitrary constant named after David Hume. This value can be modified to increase or decrease the reward for providing a better fit. The minimum value is 0, in which case the models are weighted without regard to how well they fit the data. Increasing this value places greater emphasis on model fit.
The specific optimization criteria for the L. monocytogenes concentration were:
Where the parameters for the goodness of fit were Predicted and Observed are the cumulative percentiles for a given concentration of L. monocytogenes, n is the number of samples in the report, concentration is in cfu/g.
The model weight for the L. monocytogenes concentration = 1 / (pN * Gof 2).
Where pN is the number of adjustable parameters in the distribution being fitted.
Variability
Variability is real variation in the individual members of a population or system with which a decision- maker is concerned. It cannot be eliminated by improved measurement technique. It is information the decision-maker needs. It answers the question being asked. A distribution describing variability describes the frequency of occurrence.
The distinction between variability and uncertainty is in some circumstances contextual, and depends on the question which is being answered. Variability which is present in the experiment that is not also present in the real world circumstances with which the decision-maker is concerned is a source of uncertainty. Uncertainty reflects imperfections in our knowledge about what is real. It can be reduced by improved technique. Although, the decision-maker should want to know the extent of the uncertainty associated with a calculation, he/she would prefer not to have it. A distribution describing uncertainty describes the likelihood or expectation of occurrence. There is often very little basis for segregating true variability from experimental variability, where the former is expected to be reproduced in the problem at hand, while the latter is not. The extent of the variability is quite often itself a source of uncertainty.
Adaptation of a Monte-Carlo simulation process to provide for separate accounting of both variability and uncertainty requires modification of both the front and back ends of the procedure. The descriptive statistics used to describe the variance for each of the data sets must have separate distributions for each source. The output from the iteration collection procedure must have two dimensions: one for variability, and one for uncertainty.
The technique known as two-dimensional Monte-Carlo is simply a simulation of simulations, in which one simulation is nested inside the other. The two-dimensional collection routine proceeds by collecting the results of a specified number of uncertainty iterations, each of which consists of a specified number of population iterations. Each of the two-dimensional functions has one or more random elements which are identified as either uncertainty or variability terms. The random terms identified as arising as a result of variability are varied after each iteration, while those identified as uncertainty terms are reset only at the start of each uncertainty iteration (i. e., at the conclusion of an entire population simulation). This procedure is very calculation intensive.
Running a Monte-Carlo simulation where variability and uncertainty are distinguished allows model selection to be included as a source of uncertainty. In order to simulate model uncertainty, a probability tree may be used which distributes the use of two or more models as a source of uncertainty. Which model is used for a given uncertainty iteration (an entire population simulation) can vary randomly. The frequency of use may be varied by how well the model fits. This will ensure that the uncertainty contributed by model selection is reflected in the final analysis. Monte-Carlo is not a cure for not having data, nor does it require any more data than would otherwise be needed. It is simply a better way of a) retaining information regarding variability in an analysis, and b) retaining quantitative descriptions of the degree of uncertainty. If this is not done, the end result will appear less variable and more certain than it should.
Running MC2D
Before you run a two-dimensional Monte-Carlo simulation using MC2D, you must specify the number of iterations and identify the output cells. The number of iterations and the output cells are specified with the dialog opened by the MC2D\SETTINGS command. The size of the simulation is restricted by available memory. In order to conserve both memory and disk storage space, MC2D stores single precision numbers, which should be more than adequate for most purposes. A single-precision number requires 4 bytes of storage space. Consequently, the total size of the simulation may be calculated as follows:
The total number of iterations will be the product of the number of variability iterations and the number of uncertainty iterations. The number of iterations cannot be changed once a simulation has been started. If another simulation has been run or loaded, it will be discarded (after prompting for permission). This feature allows the Iteration command to be used to reset the simulation after one has been run.
Output Range
The cells from the worksheet model from which values are collected after each iteration are specified using the OUTPUT command on the MC2D menu. The number of output cells cannot exceed 10. The output cells cannot be changed once a simulation has been started. In addition, the simulation program will not keep track of the output cell position. If the insertion or deletion of cells results in a change in the output cell(s), the Output command must be executed again to change the reference.
Reduce
If this box is checked, the population distributions will be reduced to 101 values (the minimum, maximum, and the intervening 99 percentiles). This will reduce the amount of space required for storage and the amount of time required for all subsequent calculations. However, some precision will be lost. If you have enough memory to store the whole simulation, it is recommended that this option not be used.
Autosave
If this box is checked, the simulation will be automatically saved at the end of intervals corresponding to the number of uncertainty iterations specified in the dialog.
Running the Simulation
The simulation may be started or resumed by selecting the RUN command on the MC2D menu. Memory for new simulations is allocated at this point. You may be notified if there is insufficient storage space for the simulation. The simulation will continue until it is either paused or the specified number of iterations have been completed. Simulation progress is displayed in the message bar along the bottom of the Excel window.
Saving a Simulation
Whether or not it has been completed, the current simulation may be saved using the SAVE command on the MC2D menu. The "mc2" extension is suggested as an identifier for MC2D data files. Both a header describing the simulation and the total number of iterations are stored in these files. If the model worksheet has not yet been saved, you will be prompted to do so. You must close MC2D ("EXIT") to recover the memory used by the simulation.
Loading a Simulation
A previously saved simulation may be loaded using the LOAD command on the MC2D menu. If the simulation has not been completed, MC2D will attempt to restore the simulation by opening or activating the model worksheet. The simulation may then be restarted by selecting RUN. If MC2D cannot locate the worksheet (it may have been renamed or moved), you may activate it yourself and proceed with the simulation.
Appendix 7. Table 1. Total Number of Samples and Percent Contaminated with Listeria monocytogenes by Food Category and Date of Study Used in this Risk Assessment. | ||||
Food Category | 1993 and earlier study samples |
Post-1993 study samples | ||
Total | % Positive | Total | % Positive | |
SEAFOOD | ||||
Smoked Seafood | 2,433 | 12.1 | 1,189 | 21.5 |
Raw Seafood | 2,545 | 5.9 | 11,066a | 7.4 |
Preserved Fish | 811 | 7.2 | 503 | 15.1 |
Cooked RTE Crustaceans | 178 | 10.1 | 3,461 | 2.5 |
PRODUCE | ||||
Vegetables | 2,302 | 7.5 | 1,089a | 8.4 |
Fruits | 340 | 7.4 | 185a | 16.8 |
DAIRY | ||||
Soft Mold-Ripened and Blue-Veined Cheese | 1,334 | 6.6 | 429 | 3.0 |
Goat, Sheep, and Feta Cheese | 752 | 7.7 | 79 | 0 |
Fresh Soft Cheeseb | 148b | 12.8b | 49b | 30.6c |
Heat-Treated Natural Cheeses and Processed Cheese | 577 | 0.7c | 89c | 4.5 |
Aged Cheese | 3,163 | 2.1 | 203a | 0 |
Pasteurized Fluid Milk | 3,146 | 1.0 | 6367 | 0.1 |
Unpasteurized Fluid Milk | 9,962 | 4.3 | 3,064 | 4.6 |
Ice Cream and Frozen Dairy Products | 1,536 | 2.0 | 22,794 | 0.6 |
Miscellaneous Dairy Products | 756 | 1.5 | 587 | 0.7 |
MEAT | ||||
Frankfurters | 150 | 27.3 | 1,788 | 5.9 |
Dry/Semi-Dry Fermented Sausages | 1,706 | 5.9 | 821 | 12.8 |
Deli meatsc | 240 | 10.0 | 10,805 | 2.7c |
Pâté and Meat Spreads | 769 | 19.9 | 4,260 | 3.1 |
COMBINATION FOODS | ||||
Deli Salads | 800 | 8.1 | 2,318 | 10.5 |
a Includes data from Heinitz (1999) that spans years 1990 to 1998. b Modeling includes soft ripened cheese made from unpasteurized fluid milk data used as surrogate. c Includes one study that used a < 20 cfu/g detection limit. This value was considered to approximate the presence/absence detection limit of 0.04 cfu/g. |
Appendix 8. Table 1: Growth Rate of Listeria monocytogenes in Food Categories Considered for this Risk Assessment Growth Product | |||||
Food Category Reference | Food | Literature Values | EGRc at 5 °C (log10 cfu/day) |
Maximum population (log10 cfu/g) |
|
Temperature | Growth Ratea,b | ||||
SEAFOOD | |||||
Smoked Seafood | Duffes et al., 1999 | cold-smoked salmon | 4 °C 8 °C 4 °C 8 °C |
2.1 logs in 28 days 5.4 logs in 21 days 2.0 logs in 21 days 4.6 logs in 14 days |
0.107 0.116 0.136 0.149 |
5 8.1 5 8 |
Jemmi and Keusch, 1992 | hot-smoked trout | 4 °C 8 to 10 °C |
0.5 logs in 20 days 6.5 logs in 20 days |
0.035 0.120 |
— 8 |
Hudson and Mott, 1993b | cold-smoked salmon | 5 °C 10 °C |
4 logs in 650 hours 4-4.5 logs in 125 hours |
0.148 0.249 |
8 – 8.5 8 – 8.5 |
Szabo and Cahill, 1999 | Smoked salmon | 4 °C 10 °C |
3.9 logs in 28 days 2.7-4.3 logs in 9 days |
0.198 0.119 |
6.3 7.6 |
Dillon and Patel, 1993 | cold-smoked cod | 4 °C | 2.8 logs in 21 days | 0.190 | > 5 |
Guyer and Jemmi, 1991 | Smoked salmon (26 to 30 °C) |
4 °C 10 °C |
1.0-1.5 logs in 10 days 3-3.5 logs in 10 days |
0.177 0.099 |
— 6.8 - 7.5 |
Pelroy et al., 1994b | cold-smoked salmon | 5 °C 5 °C 10 °C 10 °C |
2.5-5 logs in 40 days 2 logs in 40 days 4.5 to 7 logs in 10 days 5 logs in 11 days |
0.092 0.050 0.249 0.139 |
— — 6 - 8 7 to 8 |
Pelroy et al., 1994a | cold-smoked salmon | 5 °C 10 °C |
4 logs in 50 days 4.5 logs in 15 days |
0.080 0.092 |
> 5 6.5 |
Peterson et al., 1993 | cold-smoked salmon | 5 °C 5 °C 10 °C 10 °C 10 °C |
3 logs in 20 days 2.5 logs in 20 days 4 logs in 7 days 3.7 logs in 7 days 6 logs in 20 days |
0.150 0.125 0.175 0.162 0.092 |
4 to 6 4 6 to 8 7 to 8 7 |
Nilsson et al., 1997 | cold-smoked salmon | 5 °C | 5 logs in 9 days | 0.556 | 8 |
Raw Seafood | |||||
Fernandes et al., 1998 | fresh trout catfish |
4 °C 4 °C |
1 logs in 15 days 2 logs in 15 days |
0.100 0.185 |
6 7 |
Lovett et al., 1990 | raw shrimp, crab, surimi and whitefish | 7 °C | GT in 12 hours | 0.342 | 8 |
Kaysner et al., 1990 | raw oysters | 4 °C | No growth in 21 days | 0.000 | — |
Leung et al., 1992 | catfish | 4 °C | 1-1.5 logs in 12 days | 0.133 | — |
Shineman and Harrison, 1994 | raw shrimp and fin fish | ice chest | No growth (Decrease 1 log in 21 days) |
— | (Not used in risk assessment model) |
Harrison et al., 1991 | raw shrimp and fin fish | ice chest | No growth (Decrease 0.5 log in 14 days) |
— | (Not used in risk assessment model) |
Preserved Fish | No growth | ||||
Cooked Ready-to-Eat Crustaceans | |||||
Rawles et al., 1995 | pasteurized crab | 5 °C | GT in 21.8 hours | 0.343 | > 8 (7 logs increase) |
Farber, 1991b | cooked lobster, shrimp,crab and smoked fish | 4 °C | 2-3 logs in 7 days | 0.508 | — |
Buchanan and Klawitter, 1992 | pasteurized crabmeat | 5 °C | 3 logs in 10 days | 0.300 | 6 |
PRODUCE | |||||
Vegetables | |||||
Steinbrugge et al., 1988 | lettuce, whole, ready to serve lettuce, whole, ready to serve, sealed lettuce, whole, ready to serve, open |
5 °C 12 °C 25 °C 25 °C |
0.00 to 0.3 logs in 7 days 0.00 to 2.03 logs in 7 days 0.00 to 0.31 logs in 7 days 0.00 to 0.35 logs in 7 days |
0.043 0.004 0.002 0.002 |
6.49 6.85 5.85 6.08 |
Beuchat and Brackett, 1990b | lettuce, shredded lettuce, shredded lettuce, whole |
5 °C 10 °C 10 °C |
0.00 to 0.1 logs in 15 days 1.5-2.0 logs in 3 days 1.0 logs in 15 days |
0.007 0.204 — |
5.0-5.5 6.5-7.0 7.0-7.5 |
Carlin and Nguyen, 1994 | lettuce, butterhead | 10 °C | 1.5 logs in 7 days | 0.065 | 6 |
Carlin and Nguyen, 1994 | lettuce, lamb's | 10 °C | 1.0 logs decrease in 7 days | -0.044 | — |
Carlin et al., 1996 | endive, broad leaved | 10 °C | 1.0 logs in 7 days | 0.044 | 5.5 |
Carlin and Nguyen, 1994 | endive, broad leaved | 10 °C | 1.5 logs in 7 days | 0.065 | 5 |
Carlin and Nguyen, 1994 | endive, curly-leaved | 10 °C | 0.5 logs in 7 days | 0.022 | 5 |
Beuchat and Brackett, 1991 | tomatoes | 10 °C 21 °C |
no growth (death in chopped tomatoes) Growth |
0.00 | — (Not used in risk assessment model) |
Beuchat and Brackett, 1990a | carrots, whole and shredded | 5 °C 15 °C |
no growth up to 7 days no growth up to 7 days |
0.00 0.00 |
spoil @ 7 days spoil @ < 7 days |
Beuchat et al., 1986 | cabbage, raw, shreds | 5 °C | 4 logs in 10 days | 0.400 | 8 |
Berrang et al., 1989 | asparagus | 4 °C 15 °C |
0.5-1.0 logs in 14-21 days 2.0 logs in 2 days |
0.059 0.146 |
5.8, spoils 14-21 days 7.5, spoils 4-6 days |
Berrang et al., 1989 | broccoli | 4 °C 15 °C |
0.25-0.5 logs in 14-21 days 3.0 logs in 4 days |
0.059 0.109 |
4.0, spoils 14-21 days 8.5, spoils 6-10 |
Berrang et al., 1989 | cauliflower | 4 °C 15 °C |
≤ 0.25 logs in 14-21 days 3.0 logs in 4 days |
0.020 0.109 |
3.5, spoils 14-21 days 6.5, spoils 6-8 days |
Sizmur and Walker, 1988 | salads, mixed, prepacked including fruits/nuts | 4 °C | 0.30 logs in 4 days | 0.106 | — |
Fruits | |||||
Parish and Higgins, 1989 | orange, serum (juice) | 4 °C | pH 5.0, 1.0 logs in 35 days | 0.041 | 7.5 |
DAIRY PRODUCTS | |||||
Soft, Mold Ripened and Blue-Veined Cheeses | |||||
Ryser and Marth, 1987b | Camembert | 6 °C ripening | 4 logs in 45 days | 0.066 | 6 to 8 3 to 5 on surface |
Farber et al., 1987 | Camembert | 4 °C | Indefinite Survival | 0.000 | 4 to 5 |
Back et al., 1993 | Camembert | 3 °C 6 °C 10 °C |
0.9 logs in 10 days 1.5 log in 15 days 2.4 log in 15 days |
0.197 0.074 0.049 |
5 5.4 7 |
Papageorgiou and Marth, 1989a | Blue cheese | 5 °C | Decreased during storage, 3 logs in 56 days | 0.000 | — |
Sulzer and Busse, 1993 | Camembert Camembert (surface growth) |
14 °C 7 °C 4 °C |
4.5 logs in 34 days — — |
0.022 — — |
7 (L. innocua surrogate) 6 4 |
Goat, Sheep, and Feta Cheeses | |||||
Papageorgiou and Marth, 1989b | Feta | 4 °C | survival > 90 days (Scott A 1.28 logs decrease, 3.07 logs in 90 days) |
0 | — |
Sarumehmetoglu and Kaymaz, 1994 | Turkish white Brined cheese | refrigerated | < 2 logs decrease 100 days | -0.015 | — |
Tham, 1988 | goat | — | 1 logs decrease in 13 wk | -0.008 | — |
Fresh Soft Cheeses | |||||
Glass et al., 1995 | queso blanco | 4 °C 20 °C |
1.4 logs in 14 days — |
0.142 — |
7.9 (Not used in risk assessment model) |
Heat-Treated Natural Cheeses and Processed Cheese | |||||
Genigeorgis et al., 1991 | cottage cheese (multiple brands) teleme cheese ricotta (3 company brands) cream cheese |
8 °C 4 °C 8 °C 4 °C 8 °C 4 °C 8 °C 4 °C |
0.59 logs in 18 days 1.87 decrease in 36 days 0.42 logs in 24 days 1.13 logs in 8 days 1.87 decrease in 8 days 0.39 logs in 24 days 0.34 logs in 24 days 0.41 logs in 16 days 0.94 logs in 36 days 1.87 logs decrease in 8 days 2.2 logs in 36 days 0.42 logs decrease in 36 days 2.11 logs in 8 days 1.75 logs in 6 days 1.88 logs in 8 days 1.53 logs in 30 days 3.58 logs in 36 days 1.97 logs in 22 days 2.0 logs decrease in 30 days 2.0 logs decrease in 36 days |
0.015 -0.024 0.007 0.064 -0.106 0.023 0.020 0.036 0.037 -0.333 0.028 -0.017 0.120 0.132 0.106 0.072 0.141 0.127 -0.030 -0.079 |
— — — — — — — — — — — — — — — — — — — — |
Cottin et al., 1990 | cream cheese | 4 °C | 2 logs in 2 days | 1.423 | 3 |
Papageorgiou et al., 1996 | ricotta (whey cheese) | 5 °C 12 °C |
16.2 – 20.2 hr in GT 5.1 – 5.8 hr in GT |
0.397 0.292 |
7 to 8 — |
Chen and Hotchkiss, 1993 | cottage cheese | 4 °C 7 °C |
2.0 logs in 40 days 2.4 logs in 10 days |
0.071 0.137 |
7.5 7.4 |
Fedio et al., 1994 | cottage cheese | 5 °C | 2 logs in 22 days | 0.091 | 6.0 |
El-Shenawy and Marth, 1990 | cottage cheese | refrigerated 6 °C |
0.5 to 1.5 logs decrease in 1 to 5 wk assume 1 log in 21 days |
— -0.035 |
— — |
Stecchini et al., 1995 | mozzarella | 5 °C | 4 logs in 21 days | 0.190 | — |
Aged Cheese | |||||
Northolt et al., 1988 | gouda | — | Survival 6 weeks | 0.000 | 2 to 4 |
Yousef and Marth, 1988 | colby | 4 °C | 1.5 logs decrease in 100 days (after 40 days) |
-0.053 | 3.5 to 4.5 |
Ryser and Marth, 1987a | cheddar | 13 °C | 2 logs decrease in 75 to 150 days | -0.003 | 3.7 |
Buazzi et al., 1992 | swiss | 7 °C | 4 logs decrease in 10 days (complete inactivation 66-80 days ripening at 24 °C) |
-0.228 | — |
Bachmann and Spahr, 1995 | emmenthaler, tilster | — | no survival after 24 hours (initial level was 104 cfu/g) |
— | — |
Kaufmann, 1990 | emmenthaler, gruyere | — | no survival after 24 hours (initial level was 104 cfu/g) |
— | — |
Yousef and Marth, 1990 | parmesan | — | no survival after aging | 0.015 0.000 |
— |
Ryser and Marth, 1989a | Brick (surface ripened) tilsiter, trappist, havarti, limburger |
— 10 °C |
can get to high number during ripening < 1 logs in 20 wk |
— 0.015 |
— — |
Kovincic et al., 1991 | Trappist | — | Initial 1 log during ripening, stable 30 days, decrease for 90 days |
0.000 | — |
Fluid Milk, Pasteurized and Unpasteurized | |||||
Northolt et al, 1988 | unpasteurized milk | 5 °C 7 °C |
GT 3.5 in days GT 1.0 in days |
0.085 0.173 |
— — |
Northolt et al, 1988 | pasteurized milk | 4 °C 7 °C |
2 logs in 7 days 2 logs in 3 days |
0.407 0.380 |
— — |
Farber et al., 1990 | unpasteurized fluid milk | 4 °C 10 °C 15 °C |
GT in 25.3 hours GT in 10.8 hours GT in 7.4 hours |
0.404 0.204 0.142 |
7.1 7.1 7.1 |
Rajkowski et al., 1994 | uht milk | 12 °C | GT in 4.7 hours | 0.337 | — |
Rosenow and Marth, 1987 | skim, whole, chocolate milk | 4 °C 8 °C |
3.3 logs in 18 days 4 logs in 8 days |
0.261 0.227 |
7 (chocolate 8.5) 7.5 |
Ice Cream & Frozen Dairy Products | |||||
Berrang et al., 1988 | ice cream | — | No growth | — | — |
Dean and Zottola, 1996 | soft serve | — | No growth | — | — |
Miscellaneous Dairy Products | |||||
Rosenow and Marth, 1987 | cream | 4 °C 8 °C |
3.3 logs in 18 days 4 logs in 8 days |
0.261 0.227 |
7 8.0 |
Farrag et al., 1990 | sweetened condensed milk evaporated milk |
7 °C 7 °C |
decrease 1.2 logs in 42 days 4 logs in 14 days |
-0.016 0.163 |
— — |
Olsen et al., 1988 | butter | 4 to 6 °C 13 °C |
1.9 logs in 49 days 2.7 logs in 42 days |
0.039 0.012 |
5.5 6 |
Schaack and Marth, 1988 | buttermilk yogurt |
4 °C 4 °C |
decrease, survives 2.5-13 wk decrease, survived 4-12 days (~1 log decline detectable) |
-0.02 -0.18 |
— — |
Choi et al., 1988 | yogurt buttermilk |
4 °C 4 °C |
survives 21-24 days, most drop in first 8-12 days (~2 log decline detectable) survives 18-26 days |
-0.12 -0.12 |
— — |
Siragusa and Johnson, 1988b | yogurt | 5 °C | low level survived < 3 days high level survived 9 days (2 logs drop in 3-6 days) |
— -0.40 |
— — |
MEATS | |||||
Frankfurters | |||||
Glass and Doyle, 1989 | frankfurters | 4.4 °C | 2.3 logs in 6 weeks | 0.064 | — |
McKellar et al., 1994 | frankfurters | 5 °C | 3.5 logs in 21 days | 0.168 | — |
McKellar et al., 1994 | poultry wieners | 5 °C | 3.5 logs in 21 days | 0.090 | — |
Wederquist et al., 1994 | turkey | 4 °C | 7.0 logs in 55 days | 0.181 | — |
Dry/Semi-Dry Fermented Sausages | |||||
Farber and Peterkin, 1999 | various | — | No growth | — | — |
Deli Meats | |||||
Glass and Doyle, 1989 | bologna | 4.4 °C | 1 to 2 logs in 14 days | 0.131 | — |
Grau and Vanderline, 1992 | corned beef | 4.8 °C | 0.13 | 0.130 | — |
Grau and Vanderline, 1992 | vacuum packed ham | 5 °C | 0.30 | 0.300 | — |
Glass and Doyle, 1989 | cooked ham | 4.4 °C | 2 to 3 logs in 28 days | 0.131 | — |
Beumer et al., 1996 | cooked ham | 7 °C | 6 logs in 35 days | 0.098 | — |
Grant et al., 1993 | roast beef | 5 °C 10 °C |
5 logs in 15 days 5 logs in 6 days |
0.333 0.254 |
7.9 8.7 |
Glass and Doyle, 1989 | chicken, sliced vacuum packed |
4.4 °C 4.4 °C |
4.15 logs in 14 days 5.90 logs in 14 days |
0.364 0.517 |
< 8.46@ spoilage < 8.34 @ spoilage |
Siragusa and Johnson, 1988a | chicken, homogenate | 4.0 °C | 5.2 logs in 20 days | 0.370 | 7.9 |
Siragusa and Johnson, 1988a | chicken fillets, breaded | 5.0 °C | 0.9 logs in 6 days | 0.150 | — |
Glass and Doyle, 1989 | turkey, sliced | 4.4 °C 4.4 °C 4.4 °C |
2.0 logs in 14 days 3.11 logs in 28 days 3.08 logs in 14 days |
0.175 0.136 0.270 |
6.15 pre-spoilage 3.73 pre-spoilage |
Glass and Doyle, 1989 | turkey, sliced vacuum packed |
4.4 °C 4.4 °C |
3.83 logs in 14 days 5.09 logs in 14 days |
0.336 0.446 |
< 8.28 @ spoilage < 8.32 @ spoilage |
Ingham and Tautorus, 1991 | turkey loaf, cooked, uncured, vacuum |
3 °C | 0.09 logs in 12 days | 0.016 | — |
Pâté and Meat Spreads | |||||
Farber et al., 1995 | pâté | 5 °C | 0.361 log in 1 day | 0.361 | 6 to 7 |
Hudson and Mott, 1993a | pâté | 4 °C | 4 logs in 680 hours | 0.143 | — |
COMBINATION FOODS | |||||
Deli Salads | |||||
No data found | |||||
aLogs = Log10 cfu/g bGT = Generation Time cEGR = Exponential Growth Rate |
Appendix 9. Table 1. Predicated Number of Cases of Listeriosis per Annum for each Food Category and Population | |||||||||
Food Category | Number of Cases of Listeriosis per Annum | ||||||||
Perinatal Percentiles | Elderly Percentiles | Intermediate-Age Percentiles | |||||||
Median | 5th | 95th | Median | 5th | 95th | Median | 5th | 95th | |
SEAFOOD | |||||||||
Smoked Seafood | 6.2 | 0.8 | 63.4 | 18.5 | 0.2 | 1,105.2 | 8.6 | 0.0 | 1,295.0 |
Raw Seafood | 0.1 | 0.0 | 1.5 | 0.0 | 0.0 | 0.3 | 0.1 | 0.0 | 32.7 |
Preserved Fish | 0.7 | 0.0 | 7.5 | 1.8 | 0.0 | 138.1 | 0.6 | 0.0 | 154.8 |
Cooked Ready-to-Eat Crustaceans | 3.8 | 0.4 | 37.1 | 8.4 | 0.0 | 498.6 | 5.6 | 0.0 | 878.9 |
PRODUCE | |||||||||
Vegetables | 3.2 | 0.0 | 495.5 | 7.4 | 0.0 | 3,809.1 | 3.9 | 0.0 | 3,006.6 |
Fruits | 0.5 | 0.0 | 45.1 | 1.3 | 0.0 | 484.9 | 0.4 | 0.0 | 370.2 |
DAIRY | |||||||||
Soft Mold-Ripened and Blue-Veined Cheese | 0.4 | 0.0 | 9.5 | 0.8 | 0.0 | 96.0 | 0.5 | 0.0 | 125.7 |
Goat, Sheep, and Feta Cheese | 0.0 | 0.0 | 1.1 | 0.0 | 0.0 | 10.0 | 0.0 | 0.0 | 8.1 |
Fresh Soft Cheeses | 7.0 | 1.1 | 50.0 | 4.3 | 0.1 | 188.3 | 7.5 | 0.0 | 964.3 |
Heat-Treated Natural Cheeses and Processed Cheese | 3.7 | 0.4 | 31.1 | 7.4 | 0.1 | 399.6 | 5.1 | 0.0 | 776.8 |
Aged Cheeses | 0.0 | 0.0 | 69.1 | 0.0 | 0.0 | 305.4 | 0.0 | 0.0 | 348.1 |
Pasteurized Fluid Milk | 67.0 | 12.5 | 276.7 | 224.2 | 7.9 | 4,082.7 | 119.7 | 1.0 | 6,748.9 |
Unpasteurized Fluid Milk | 0.3 | 0.0 | 2.2 | 0.75 | 0.0 | 27.8 | 0.4 | 0.0 | 43.9 |
Ice Cream/Frozen Dairy Products | 0.0 | 0.0 | 198.5 | 0.0 | 0.0 | 1,083.6 | 0.0 | 0.0 | 676.6 |
Miscellaneous Dairy Products | 13.1 | 1.9 | 70.1 | 41.0 | 0.9 | 1,198.5 | 19.7 | 0.0 | 1,687.3 |
MEATS | |||||||||
Frankfurters | 22.8 | 2.4 | 201.5 | 32.0 | 0.3 | 1,552.0 | 34.9 | 0.0 | 4,570.3 |
Dry/Semi-Dry Fermented Sausages | 1.2 | 0.0 | 30.8 | 2.1 | 0.0 | 222.7 | 1.2 | 0.0 | 377.9 |
Deli Meats | 325.5 | 41.3 | 2,467.4 | 650.3 | 8.6 | 32,091.9 | 470.6 | 0.5 | 63,701.5 |
Pâté and Meat Spreads | 4.3 | 0.7 | 25.7 | 12.3 | 0.2 | 444.2 | 6.4 | 0.0 | 682.5 |
COMBINATION FOOD | |||||||||
Deli Salads | 41.1 | 6.8 | 356.8 | 142.2 | 3.4 | 5,923.7 | 199.4 | 0.7 | 22,302.4 |
Appendix 9. Table 2a: Certainty For a Specified Predicted Listeriosis per Serving by Food Category -
Intermediate Age Note: The Intermediate Age includes susceptible populations not captured as elderly or Perinatal, such as cancer, AIDS, and transplant patients, from whom there are insufficient data to consider as a separate population. |
|||||||||||||||||||||
Servings per 1 case of Listeriosis | Rate of Listeriosis per Serving | ||||||||||||||||||||
1012 | 1.0 x 10-12 | 0.98 | 0.92 | 0.92 | 0.97 | 0.80 | 0.67 | 0.95 | 0.78 | 0.99 | 0.93 | 0.44 | 0.98 | 0.95 | 0.41 | 0.96 | 0.96 | 0.90 | 0.98 | 0.99 | 0.98 |
1011 | 1.0 x 10-11 | 0.97 | 0.86 | 0.89 | 0.96 | 0.66 | 0.50 | 0.93 | 0.64 | 0.98 | 0.87 | 0.37 | 0.96 | 0.90 | 0.37 | 0.92 | 0.94 | 0.84 | 0.96 | 0.98 | 0.97 |
1010 | 1.0 x 10-10 | 0.94 | 0.73 | 0.80 | 0.92 | 0.38 | 0.31 | 0.85 | 0.45 | 0.96 | 0.70 | 0.23 | 0.89 | 0.77 | 0.31 | 0.82 | 0.89 | 0.70 | 0.94 | 0.96 | 0.94 |
109 | 1.0 x 10-9 | 0.89 | 0.42 | 0.67 | 0.82 | 0.15 | 0.14 | 0.64 | 0.21 | 0.91 | 0.31 | 0.09 | 0.60 | 0.51 | 0.26 | 0.47 | 0.75 | 0.48 | 0.87 | 0.92 | 0.86 |
108 | 1.0 x 10-8 | 0.76 | 0.16 | 0.47 | 0.53 | 0.10 | 0.05 | 0.26 | 0.08 | 0.78 | 0.13 | 0.06 | 0.19 | 0.20 | 0.13 | 0.15 | 0.40 | 0.24 | 0.67 | 0.80 | 0.56 |
107 | 1.0 x 10-7 | 0.38 | 0.08 | 0.14 | 0.18 | 0.01 | 0.00 | 0.13 | 0.02 | 0.40 | 0.01 | 0.01 | 0.05 | 0.06 | 0.05 | 0.03 | 0.14 | 0.09 | 0.26 | 0.42 | 0.18 |
106 | 1.0 x 10-6 | 0.14 | 0.00 | 0.08 | 0.09 | 0.00 | 0.00 | 0.02 | 0.00 | 0.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.04 | 0.03 | 0.13 | 0.14 | 0.09 |
105 | 1.0 x 10-5 | 0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
104 | 1.0 x 10-4 | 0.00 | 0.0 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
NOTE: All values are cumulative probabilities that give the likelihood that the listeriosis rate will be less than or equal to the indicated rate of listeriosis value (i.e. 10-12 to 10-4).
Example: Using smoked seafood, the values in the table can be interpreted to predict that for the Intermediate Age, there is an 98% probability that smoked seafood would be responsible for causing one case for every one trillion servings consumed, an 97% probability for one case for every one hundred billion servings consumed, a 94% probability of being responsible for one case for every ten billion servings, a 89% probability of being responsible for one case for every one billion servings, a 76% probability of being responsible for one case for every one hundred million servings, a 38% probability of being responsible for one case for every ten million servings, and a 14% probability of being responsible for one case for every one million servings. This manner of presentation provides estimates of both the risk associated with the various food groups and the uncertainty associated with those predictions.
Appendix 9. Table 2b: Certainty For a Specified Predicted Listeriosis per Serving by Food Category - Elderly Population | |||||||||||||||||||||
Servings per 1 case of Listeriosis | Rate of Listeriosis per Serving | ||||||||||||||||||||
1012 | 1.0 x 10-12 | 1.00 | 0.97 | 0.95 | 1.00 | 0.84 | 0.72 | 0.99 | 0.82 | 1.00 | 0.98 | 0.48 | 1.00 | 0.98 | 0.43 | 0.99 | 1.00 | 0.94 | 1.00 | 1.00 | 1.00 |
1011 | 1.0 x 10-11 | 1.00 | 0.93 | 0.93 | 0.99 | 0.73 | 0.56 | 0.97 | 0.70 | 1.00 | 0.94 | 0.40 | 0.99 | 0.95 | 0.38 | 0.97 | 0.98 | 0.89 | 1.00 | 1.00 | 1.00 |
1010 | 1.0 x 10-10 | 0.98 | 0.82 | 0.86 | 0.97 | 0.45 | 0.37 | 0.92 | 0.51 | 1.00 | 0.81 | 0.26 | 0.95 | 0.85 | 0.35 | 0.91 | 0.95 | 0.76 | 0.98 | 1.00 | 0.98 |
109 | 1.0 x 10-9 | 0.95 | 0.50 | 0.73 | 0.91 | 0.16 | 0.16 | 0.76 | 0.26 | 0.97 | 0.39 | 0.10 | 0.74 | 0.61 | 0.30 | 0.59 | 0.86 | 0.56 | 0.94 | 0.97 | 0.92 |
108 | 1.0 x 10-8 | 0.86 | 0.18 | 0.56 | 0.64 | 0.11 | 0.04 | 0.33 | 0.09 | 0.91 | 0.12 | 0.06 | 0.24 | 0.25 | 0.17 | 0.17 | 0.51 | 0.29 | 0.78 | 0.89 | 0.63 |
107 | 1.0 x 10-7 | 0.48 | 0.07 | 0.19 | 0.21 | 0.01 | 0.00 | 0.13 | 0.02 | 0.61 | 0.00 | 0.02 | 0.01 | 0.03 | 0.05 | 0.01 | 0.16 | 0.08 | 0.34 | 0.54 | 0.19 |
106 | 1.0 x 10-6 | 0.14 | 0.00 | 0.07 | 0.06 | 0.00 | 0.00 | 0.01 | 0.00 | 0.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.01 | 0.12 | 0.15 | 0.03 |
105 | 1.0 x 10-5 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
104 | 1.0 x 10-4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
NOTE: All values are cumulative probabilities that give the likelihood that the case rate attributable to listeriosis will be less than or equal to the indicated rate of listeriosis value (i.e. 10-12 to 10-4).
Example: Using smoked seafood, the values in the table can be interpreted to predict that, for the elderly, there is a 100% probability that smoked seafood would be responsible for causing one case for every one trillion servings consumed, a 100% probability for one case for every one hundred billion servings consumed, a 98% probability of being responsible for one case for every ten billion servings, a 95% probability of being responsible for one case for every one billion servings, a 86% probability of being responsible for one case for every one hundred million servings, a 48% probability of being responsible for one case for every ten million servings, an 14% probability of being responsible for one case for every one million servings, and a 1% probability of being responsible for one case for every hundred thousand servings. This manner of presentation provides estimates of both the risk associated with the various food groups and the uncertainty associated with those predictions.
Appendix 9. Table 2c: Certainty For a Specified Predicted Listeriosis per Serving by Food Category -
Perinatal Population Note: The Perinatal population is a susceptible population that includes fetuses and neonates. Exposure occurs most often in utero from contaminated food eaten by the pregnant woman. |
|||||||||||||||||||||
Servings per 1 case of Listeriosis | Rate of Listeriosis per Serving | ||||||||||||||||||||
1012 | 1.0 x 10-12 | 1.00 | 1.00 | 0.98 | 1.00 | 0.98 | 0.94 | 1.00 | 0.96 | 1.00 | 1.00 | 0.85 | 1.00 | 1.00 | 0.75 | 1.00 | 1.00 | 0.98 | 1.00 | 1.00 | 1.00 |
1011 | 1.0 x 10-11 | 1.00 | 1.00 | 0.98 | 1.00 | 0.97 | 0.91 | 1.00 | 0.93 | 1.00 | 1.00 | 0.71 | 1.00 | 1.00 | 0.66 | 1.00 | 1.00 | 0.97 | 1.00 | 1.00 | 1.00 |
1010 | 1.0 x 10-10 | 1.00 | 1.00 | 0.97 | 1.00 | 0.95 | 0.81 | 1.00 | 0.90 | 1.00 | 1.00 | 0.55 | 1.00 | 1.00 | 0.49 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 | 1.00 |
109 | 1.0 x 10-9 | 1.00 | 1.00 | 0.96 | 1.00 | 0.88 | 0.66 | 1.00 | 0.80 | 1.00 | 1.00 | 0.47 | 1.00 | 1.00 | 0.40 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 | 1.00 |
108 | 1.0 x 10-8 | 1.00 | 0.97 | 0.92 | 1.00 | 0.66 | 0.49 | 1.00 | 0.62 | 1.00 | 0.98 | 0.39 | 1.00 | 0.96 | 0.39 | 1.00 | 1.00 | 0.87 | 1.00 | 1.00 | 1.00 |
107 | 1.0 x 10-7 | 1.00 | 0.77 | 0.81 | 1.00 | 0.23 | 0.26 | 0.96 | 0.39 | 1.00 | 0.66 | 0.16 | 0.97 | 0.79 | 0.35 | 0.88 | 0.99 | 0.71 | 1.00 | 1.00 | 1.00 |
106 | 1.0 x 10-6 | 0.99 | 0.28 | 0.73 | 0.91 | 0.13 | 0.03 | 0.58 | 0.12 | 1.00 | 0.09 | 0.06 | 0.33 | 0.36 | 0.27 | 0.21 | 0.80 | 0.42 | 0.98 | 1.00 | 0.76 |
105 | 1.0 x 10-5 | 0.79 | 0.03 | 0.35 | 0.34 | 0.00 | 0.00 | 0.13 | 0.00 | 0.91 | 0.00 | 0.01 | 0.00 | 0.00 | 0.05 | 0.00 | 0.20 | 0.08 | 0.60 | 0.85 | 0.12 |
104 | 1.0 x 10-4 | 0.16 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.16 | 0.00 |
103 | 1.0 x 10-3 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
NOTE: All values are cumulative probabilities that give the likelihood that the case rate attributable to listeriosis will be less than or equal to the indicated rate of listeriosis value (i.e. 10-12 to 10-5).
Note: Based upon data collected by the California State Department of Health Services (Buchholz, pers.comm), prenatal cases numbered 1.5 times the number of neonatal cases. The cases presented in this table account for prenatal and neonatal cases.
Example: Using Smoked Seafood, the values in the table can be interpreted to predict that, for pregnant women and their fetuses and newborns, there is a 100% probability that smoked seafood would be responsible for causing one case for every one trillion servings consumed, a 100% probability for one case for every one hundred billion servings consumed, a 100% probability of being responsible for one case for every ten billion servings, a 100% probability of being responsible for one case for every one billion servings, a 100% probability of being responsible for one case for every one hundred million servings, a 100% probability of being responsible for one case for every ten million servings, a 99% probability of being responsible for one case for every one million servings, a 79% probability of being responsible for one case for every hundred thousand servings, and a 16% probability of being responsible for one case for every ten thousand servings. This manner of presentation provides estimates of both the risk associated with the various food groups and the uncertainty associated with those predictions.
Appendix 9. Table 3a: Certainty For a Specified Predicted Rate of Listerosis per Annum by Food
Category – Intermediate Age Population
Note: The Intermediate Age includes susceptible populations not captured as elderly or Perinatal, such as cancer, AIDS, and transplant patients, from whom there are insufficient data to consider as a separate population. |
||||||||||||||||||||
U.S. Annual Listeriosis Rate | ||||||||||||||||||||
0.01 | 0.95 | 0.78 | 0.79 | 0.95 | 0.86 | 0.74 | 0.88 | 0.51 | 0.96 | 0.94 | 0.45 | 0.99 | 0.86 | 0.41 | 0.97 | 0.95 | 0.86 | 0.98 | 0.96 | 0.99 |
0.10 | 0.91 | 0.51 | 0.66 | 0.90 | 0.79 | 0.60 | 0.74 | 0.28 | 0.92 | 0.89 | 0.38 | 0.97 | 0.68 | 0.37 | 0.94 | 0.93 | 0.73 | 0.97 | 0.92 | 0.97 |
1.00 | 0.81 | 0.20 | 0.44 | 0.76 | 0.66 | 0.43 | 0.38 | 0.10 | 0.81 | 0.76 | 0.24 | 0.95 | 0.37 | 0.32 | 0.87 | 0.87 | 0.53 | 0.94 | 0.79 | 0.94 |
10.00 | 0.47 | 0.11 | 0.13 | 0.39 | 0.38 | 0.23 | 0.14 | 0.04 | 0.45 | 0.38 | 0.10 | 0.87 | 0.12 | 0.27 | 0.62 | 0.70 | 0.28 | 0.89 | 0.42 | 0.88 |
100.00 | 0.15 | 0.00 | 0.08 | 0.14 | 0.15 | 0.09 | 0.07 | 0.00 | 0.14 | 0.14 | 0.06 | 0.54 | 0.01 | 0.15 | 0.22 | 0.31 | 0.11 | 0.75 | 0.14 | 0.63 |
1000.00 | 0.08 | 0.00 | 0.00 | 0.04 | 0.10 | 0.03 | 0.00 | 0.00 | 0.05 | 0.03 | 0.02 | 0.16 | 0.00 | 0.05 | 0.09 | 0.13 | 0.04 | 0.36 | 0.02 | 0.22 |
NOTE: All values are cumulative probabilities that give the likelihood that the listeriosis case rate will be less than or equal to the indicated value (i.e. 0.1,1,10, 100, or 1000). A case rate of 0.1 corresponds to 1 case every 10 years.
Example: Using Smoked Seafood as an example, the values in the table can be interpreted to predict that, in the Intermediate Age, there is a 91% probability that smoked seafood would be responsible for one case every 10 years, a 81% probability of 1 case per year, a 47% probability of 10 cases per year, a 15% probability of 100 cases per year and 0% probability. This manner of presentation provides estimates of both the risk associated with the various food groups and the uncertainty associated with those predictions.
Appendix 9. Table 3b: Certainty For a Specified Predicted Rate of Listerosis per Annum by Food Category - Elderly Population | ||||||||||||||||||||
U.S. Annual Listeriosis Rate | ||||||||||||||||||||
0.01 | 0.99 | 0.30 | 0.86 | 0.99 | 0.90 | 0.81 | 0.94 | 0.58 | 0.99 | 0.98 | 0.47 | 1.00 | 0.92 | 0.45 | 1.00 | 0.99 | 0.90 | 1.00 | 1.00 | 1.00 |
0.10 | 0.97 | 0.12 | 0.73 | 0.95 | 0.85 | 0.69 | 0.84 | 0.35 | 0.95 | 0.95 | 0.40 | 1.00 | 0.77 | 0.38 | 0.98 | 0.97 | 0.78 | 1.00 | 0.97 | 1.00 |
1.00 | 0.90 | 0.00 | 0.58 | 0.85 | 0.74 | 0.52 | 0.47 | 0.13 | 0.79 | 0.83 | 0.25 | 0.99 | 0.45 | 0.36 | 0.95 | 0.92 | 0.58 | 0.98 | 0.89 | 0.98 |
10.00 | 0.63 | 0.00 | 0.21 | 0.46 | 0.46 | 0.33 | 0.14 | 0.05 | 0.32 | 0.44 | 0.09 | 0.94 | 0.12 | 0.31 | 0.78 | 0.71 | 0.31 | 0.95 | 0.54 | 0.91 |
100.00 | 0.19 | 0.00 | 0.07 | 0.13 | 0.17 | 0.13 | 0.05 | 0.00 | 0.11 | 0.14 | 0.06 | 0.68 | 0.00 | 0.20 | 0.32 | 0.28 | 0.10 | 0.83 | 0.15 | 0.57 |
1000.00 | 0.06 | 0.00 | 0.00 | 0.01 | 0.11 | 0.03 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.19 | 0.00 | 0.05 | 0.06 | 0.09 | 0.02 | 0.41 | 0.00 | 0.16 |
NOTE: All values are cumulative probabilities that give the listeriosis case rate will be less than or equal to the indicated value (i.e. 0.1,1,10, 100, or 1000). A case rate of 0.1 corresponds to 1 case every 10 years.
Example: Using Smoked Seafood as an example, the values in the table can be interpreted to predict that, for the elderly, there is a 97% probability that smoked seafood would be responsible for one case every 10 years, a 90% probability of 1 case per year, a 63% probability of 10 cases per year, and a 19% probability of 100 cases per year. This manner of presentation provides estimates of both the risk associated with the various food groups and the uncertainty associated with those predictions.
Appendix 9. Table 3c: Certainty For a Specified Predicted Rate of Listerosis per Annum by Food
Category - Perinatal Population
Note: The Perinatal population is a susceptible population that includes fetuses and neonates. Exposure occurs most often in utero from contaminated food eaten by the pregnant woman. |
||||||||||||||||||||
U.S. Annual Listeriosis Rate | ||||||||||||||||||||
0.01 | 1.00 | 0.88 | 0.82 | 1.00 | 0.95 | 0.79 | 0.99 | 0.51 | 1.00 | 1.00 | 0.48 | 1.00 | 0.93 | 0.41 | 1.00 | 1.00 | 0.91 | 1.00 | 1.00 | 1.00 |
0.10 | 1.00 | 0.43 | 0.74 | 1.00 | 0.90 | 0.63 | 0.84 | 0.24 | 1.00 | 0.99 | 0.42 | 1.00 | 0.72 | 0.39 | 1.00 | 1.00 | 0.77 | 1.00 | 1.00 | 1.00 |
1.00 | 0.93 | 0.09 | 0.41 | 0.84 | 0.70 | 0.45 | 0.24 | 0.06 | 0.96 | 0.84 | 0.21 | 1.00 | 0.19 | 0.35 | 0.98 | 0.99 | 0.53 | 1.00 | 0.91 | 1.00 |
10.00 | 0.35 | 0.00 | 0.03 | 0.22 | 0.28 | 0.20 | 0.04 | 0.00 | 0.38 | 0.23 | 0.06 | 0.97 | 0.00 | 0.31 | 0.59 | 0.74 | 0.22 | 1.00 | 0.23 | 0.90 |
100.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.13 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.33 | 0.00 | 0.09 | 0.02 | 0.15 | 0.01 | 0.83 | 0.00 | 0.24 |
1000.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 | 0.00 |
NOTE: All values are cumulative probabilities that give the likelihood that the case rate attributable to listeriosis will be less than or equal to the indicated value (i.e. 0.1,1,10, 100, or 1000). A case rate of 0.1 corresponds to 1 case every 10 years.
Note: Based upon data collected by the California State Department of Health Services (Buchholz, pers.comm), prenatal cases numbered 1.5 times the number of neonatal cases. The cases presented in this table account for prenatal and neonatal cases.
Example: Using Smoked Seafood as an example, the values in the table can be interpreted to predict that, for pregnant women and their fetuses and newborns, there is a 100% probability that smoked seafood would be responsible for one case every 10 years, a 93% probability of 1 case per year, and a 35% probability of 10 cases per year. This manner of presentation provides estimates of both the risk associated with the various food groups and the uncertainty associated with those predictions.
Hypertext updated by dav/cjm/dms 2001-JAN-19