FDA/Center for Food Safety and Applied Nutrition
USDA/Food Safety and Inspection Service
Centers for Disease Control and Prevention
January 2001

Draft Assessment of the Relative Risk to Public Health from Foodborne Listeria monocytogenes Among Selected Categories of Ready-to-Eat Foods

Table of Contents

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

A. The Dose Frequency Curve-Fitting Program

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:

• No background parameter.
• Background Dose. A background dose specified by an extra model parameter is added to the nominal dose when predicting frequency.
• Background Frequency. A background frequency specified by an extra model parameter is added to the predicted frequency. The dose-frequency function is applied to the fraction of the population who would otherwise not respond.

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:

• Beta


• Cauchy


• Exponential


• Gamma


• Logistic


• Lognormal


• Normal


• Rectangular (Uniform)


• Triangular


• Weibull

Model Weighting Criteria

The frequency of use of each model is allocated according to it relative model weight which is calculated as follows:

Model Weight = (((1 + n / Pn) ^ O) * ((1 - gof) ^ H))

n = number of observations. This value reflects the number of data points to which the curve is fit. Values below the limit of detection (i.e. text values) are not counted for this purpose.

* = 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:

Gof = (predicted – Observed)² * n * concentration ^0.25

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.

B. MC2D

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:

bytes = 4 * Uncertainty Iterations * Variability Iterations * # of Output Cells

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