Expanded Fermi Solution to estimate health risks or benefits from interacting factors

Food related health risk/benefit factors might be additive or multiplicative, but some can be interrelated in ways that are neither or both. Since there is always inherent uncertainty concerning the magnitude of risk/benefit factors their contribution is better represented by a probable range than a single numerical value. With the Expanded Fermi Solution method, random values of the factors are generated within their respective ranges and used to calculate the combined risk or benefit based on the chosen mathematical model. In the case of additive or multiplicative independent factors, the combined risks/benefits so calculated have approximately normal or lognormal distribution, respectively, as anticipated from the Central Limit Theorem. The distribution's mode, i.e., the most frequent value, is considered the risk's best estimate. In interactive factors, the emergence of a specific parametric distribution is not guaranteed, but the histogram of the randomly generated combined risks or benefits can be used to identify the best estimate. This is demonstrated with three abstract interactive risk/benefit models of increasing number of parameters and complexity, whose calculation has been automated and posted on the Internet as freely downloadable interactive Wolfram Demonstration. Also given is a hypothetical but realistic example of dose-response based microbial risk assessment where uncertain bacterial growth parameters are involved, which can be implemented with a new Wolfram Demonstration. The methodology and software allow rapid examination of numerous combinations of interactive factors and evaluation of their potential effect on a food's or supplement's risk or benefit.