# **Box  4.2 Quantitative microbial risk analysis**

Quantitative microbial risk analysis (QMRA) determines a numerical value of the risk (i.e., probability) of disease and/or infection as a result of a person or a community being exposed to a specified number of a specified pathogen as a result of some activity—in this case the relevant activities are consuming wastewaterirrigated foods and working in wastewater-irrigated fields. QMRA can be used to estimate disease and infection risks for any pathogen as long as there are dose-response data available for it. The disease and/or infection risks can then be estimated by a dose-response equation (as shown in section A.3 of Annex A).

**Interpreting values of risk:** values of risk (probability) are in the range 0−1 and are expressed per person per exposure event or, more commonly in relation to wastewater use in agriculture, per person per year (pppy). For example, an infection risk of 0.01 (i.e., 1 × 10<sup>−2</sup> )  pppy means that each year an exposed individual has a 1% chance of becoming infected as a result of a given number of exposure events per year. Alternative ways of interpreting this infection risk of 0.01 pppy are (a) that the exposed individual will become infected once every 100 years (i.e., essentially once in his or her lifetime), or (b) that, for a community, an infection risk of 0.01 pppy means that every year 1% of the community will become infected.

Note that there is no such thing as a ‘zero risk’. A risk can be very small—for example, 1 × 10<sup>−</sup><sup>_x_</sup> pppy, where _x_ is very large—but it is not zero.

**Monte Carlo risk simulations:** many of the parameters used in QMRA risk determinations have ‘uncertain’ values—for example, it might be assumed that 10 mL of wastewater remains on 100 g of lettuce after irrigation, but this ‘fixed’ value of _exactly_ 10 mL may not always occur: the value could be anywhere in the range of 5−15 mL, for example.  To overcome, at least partially, the uncertainty of many of the parameters used in QMRA risk determinations, Monte Carlo risk simulations are used in which a _range of values_ is assigned to each parameter used in the calculations, rather than a _single fixed value_ , although a fixed value can be assigned to any given parameter if so desired. A computer program then selects at random a value for each parameter from the range of values specified for it and then determines the resulting annual risk.<sup>_a_</sup> The program repeats this process a large number of times (generally for a total of 1000 or 10,000 times) and determines the median and 95-percentile risks. This large number of repetitions removes some of the uncertainty associated with the parameter values and makes the results generated by multi-simulation QMRA-Monte Carlo risk analyses much more robust than those determined by simple QMRA calculations which use only ‘fixed’ parameter values, although of course they are still only as good as the assumptions made. Sections A.2−A.6 of Annex A illustrate the use of this ‘QMRA-MC’ approach to risk determination.

> _a_ See the Note at the end of Annex A concerning the availability of QMRA-MC computer programs.

36