A Quantitative Risk Assessment Model for Campylobacter jejuni for chicken products -variability and uncertainty for input distributions

Helle M. Sommer*, Bjarke B. Christensen, Hanne Rosenquist and Niels L. NielsenDivision of Microbiological Safety, Institute of Food Safety and Toxicology, 2860 Søborg, Denmark. * Contact Helle M. Sommer at hms@fdir.dk

Introduction

In this presentation focus is on the impact of choosing a proper distribution as input distribution to represent a given set of data in a quantitative risk assessment model (QRA model). For a given input data set variability and uncertainty are separated using a variance component analysis. The impor-tance in separating variability and uncertainty is obviously when deciding whether to collect further samples to reduce the uncertainty and improve our estimate of the future. Variability is a function of the system and not reducible through further measurement, but may be reduced through changing the physical system. The ‘after bleeding’ data is here employed to illustrate the impact of choosing a proper input distribution and to illustrate the separation of variability and uncertainty.

During the 1990’s Denmark has, like many other countries, experienced an increase in the number of registered cases of human enteric infections caused by Campylobacter. The frequencies of Campylobacter found in e.g. beef and pork meat is low (<1%) where as the frequencies in poultry meat is somewhat higher (~40%). A (QRA) model was developed to describes the spread of Campylobacter from farm to fork focusing on whole chicken products. In order to create a mathematical model a number of steps that influence the risk estimate in the processing and handling of chicken products were taken into consideration. The objectives of the risk assessment were to gain a better understanding of chicken processing and handling operations and to identify important steps in the model, in other words, to generate a tool that can assist the decision making process in reducing the risk to the consumer. A software program, @RISK (Palisade Corporation, NY), based on Monte Carlo simulations was employed. It must be remembered, that the quality of the final risk estimates is merely as good as the quality of the model and the data within it.

Results

The impact of employing different probability distributions for one of the input data sets (the ‘after bleeding’ data) are shown in Fig. 4 and 5. Tree different input distributions were employed while the remaining input distributions in the QRA model were fixed :1) the triangle distribution (Fig. 2), 2) a normal distribution with a variance equal to the total variance (variability + uncertainty), and 3) a normal distribution with a variance equal to the variance component (variability) (Fig.3).

The estimated distribution of Campylobacter concentration at the exit of the slaughter plant is obviously affected by the choice of just this one distribution for the ‘after bleeding’ data. The triangle distribution results, as expected, in the most narrow output distribution simulated by use of the Monte Carlo technique (Fig. 4). Thus, employing the triangle distribution as shown above results in an underestimation of the tails.

The uncertainty was estimated to E2 = 0.57 and the variability to 0

2 = 1.08. If the total uncer-tainty is nearly all due to variability it is a waste of time to collect more measure-ments in the given area for which the variability and uncertainty was estimated. If the blue and the red curve in Fig. 3 and 5 are nearly identical the uncertainty is small compared to the variability and no further measurements should be carried out in the effort of improving the estimate of the Campylobacter concentration exiting the slaughter plant.

References(1) Oosterom J., Notermans S., Karman H. & Engels G.B. 1983. Jr of Food Prot. 46 : 339-344(2) Mead G.C., Hudson W.R., & Hinton M.H. 1995. Epidemiol. Infect. 115 : 495-500

There are often insufficient data available upon which to create a smooth histogram of the concentration to be used as input distribution to the model (see Fig. 1). Instead, the 17 data points of ‘after bleeding’ concentration are fit to a probability distribution. The triangle distribution is frequently employed because of it’s simplicity (Fig.2). However, due to the difficulties in estimating the absolute minimum and maximum values, the choice of fitting the triangle distribution to the data often result in an underestimation for the tails. If we assume that each of the 17 data points are normal distributed with the mean and standard deviation reported in the literature we can estimate a normal distribution that represent all 17 data points. This way not only the data points are made use of but also the knowledge of how well they are determined. A variance component analysis can then be carried out in order to obtain estimates of the uncertainty (E

2) and variability (02). The total variance is given by T

2 = E2 + 0

2.

Methods

Histogram of the 'after bleeding' data

2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4

Fig. 1. Concentration of Campylobacter [log10 cfu/g skin]

Normal distribution fit to data

-1 0 1 2 3 4 5 6 7 8

Fig. 3. Concentration of Campylobacter [log10 cfu/g skin]

Oosteromet al.

Mead et al.

Model w.variability

Model w.variability +uncertainty

Triangle distribution fit to data

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4

Fig. 2. Concentration of Campylobacter [log10 cfu/g skin]

Effects of a Triangel distribution as input

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 Fig. 4. Concentration of C. exiting the slaughter plant

[log cfu/g]

Effects of different input distributions (normal)

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

Fig. 5. Concentration of C . exiting the slaughter plant

variability +uncertainty

variability

[log cfu/g]