Enfoque Psicolingüístico: nivel inferencial

Generally, models are built using current prevailing knowledge. They are not always meant to reproduce every realistic scenario, but increase the understanding of the processes under evaluation and the factors influencing them. Sensitivity analyses of models are mathematical techniques designed to identify the parameters most influential to the model output and therefore the investigated processes (Anonymous 2004b). If a model is highly sensitive to a parameter in which there is some degree of concern about its accuracy, this indicates that more information is needed on the parameter to increase the model’s ro- bustness and practical value. Generally, knowledge of key inputs describing variability in the model can help identify efficient control measures, while knowledge of key inputs describing uncertainty highlights areas that require further data collection. Sensitivity analyses can therefore be of great assistance to risk managers, responsible for the devel- opment of targeted control strategies (Frey & Patil 2002). Furthermore, these analyses can play important roles in model verification (Fraedrich & Goldberg 2000, Saltelli & Scott 2000). Model verification ensures that the model is being executed as planned. Model validation, on the other hand, is the process whereby the model results are com- pared to independent observations obtained from the system being modelled. Complete validation may not always be possible in risk assessment studies due to data insufficiency (Frey & Patil 2002). This section provides a brief overview of three methods for conduct- ing sensitivity analyses in food-safety risk assessment models.

Methods for conducting sensitivity analyses can be classified as mathematical or sta- tistical. Mathematical analyses assess the model output with a range of variations of input values. These methods fail to address the variance in the output as a result of the variance in the input values. One example of this method is the nominal range sensitivity analysis.

Statistical methods incorporate simulations. Inputs are assigned probability distri- butions and the effect of the input variance on the output variance can be determined (Andersson et al. 2000, Neter et al. 1996). Statistical methods used for conducting sensi- tivity analyses include regression analysis and correlation analysis among others. Graph- ical illustrations, such as scatter-plots and tornado plots provide a visual indication of the effect of the input parameter on the output (Geldermann & Rentz 2001, Stiber et al. 1999). Frey & Patil (2002) discuss various statistical methods for conducting sensitivity analy- ses, however, with respect to quantitative microbial risk assessments, only correlation and scatterplots are widely used (Perez-Rodriguez et al. 2007).

The nominal range sensitivity analysis is a simple mathematical method, applicable to deterministic models, and therefore not for probabilistic analyses. Very few examples have been found in the literature where the technique has been employed in risk assess- ment. Dakins et al. (1994) used this technique when conducting an exposure assessment of flounder in a contaminated harbour. The effect of the predicted model output was assessed by varying the entire range of model inputs, one at a time. That is, one input was varied, while all others inputs kept fixed at their nominal values. The output of this sensitivity analysis was presented as the percentage change (both positive and negative) from the nominal solution. This technique is most appropriate in linear models (Frey & Patil 2002). Nonetheless, it is limited to deterministic linear models as it is unable to evaluate interactions between inputs (Cullen & Frey 1999).

Regression analysis as the name suggests, uses regression models to describe the re- lationship between variables and the predicted model output. If the regression coefficient of input values significantly differs from zero, then the model is sensitive to changes in the input value. The more significantly the coefficient of the input varies from zero, the greater the influence of the corresponding input value on the output value (Frey & Patil 2002). This method produces accurate results when the underlying assumptions of the regression model are met. For example, least squares regression assumes a straight line relationship between input and output variables, and also, that residuals are normally distributed. Regression analysis works well when there is independence of inputs (Neter et al. 1996). Mokhtari et al. (2006) used both correlation and regression techniques to conduct sensitivity analyses and compared these results with sensitivity analyses using classification and regression trees (CART) methodology. CART has previously been used

in the medical field for decision making analyses. Sensitivity analyses using the three techniques were conducted on a microbial food safety risk model of E. coli O157 in beef at a theoretical slaughter house. The results of the sensitivity analyses were different using each of the techniques, with CART showing results most similar to the regression analysis technique. The CART technique is available is some statistical software packages.

Correlation analysis is another type of statistical method employed in sensitivity analy- ses. Both partial rank correlation coefficients and Spearman’s rank correlation used by Blower & Dowlatabadi (1994) and Armstrong & Haas (2007) respectively, evaluate the contribution of model inputs with respect to variation in selected model outputs (Brikes & Dodge 1993). The results of these analyses have no units and range from -1 to 1. Weak predictive inputs produce values close to zero (Cassin et al. 1998) and correspondingly, results closer to -1 or 1 represent inputs with more influence on the output (Zwietering & van Gerwen 2000). Negative values represent inverse correlation (Vose 2000). The correlations measured are between the variability of the inputs and outputs. The rank order correlation technique is fast, easy to calculate and has been cited as the preferred method to multivariate stepwise regression by the Organisation International des Epi- zooties (Anonymous 2004b, Vose 2000). Armstrong & Haas (2007) used a rank order correlation coefficient to conduct a sensitivity analysis of the quantitative microbial risk assessment of Legionnaire’s disease at selected spa pools. Of the four spa pools assessed, inhalation rate of the pathogen was determined to have the greatest effect on the probabil- ity of having an outbreak of the disease.