# Dose Response Modeling R Code

**Dose Response Modeling**

**Dose Response Modeling**

**Author: Mark H. Weir Ph.D. - The Ohio State University**

**General overview**

Classical dose response modelling is most typically an exercise in optimization of the current dose response models. For more in-depth information regarding the development of the exponential and beta Poisson dose response models can be found in Haas *et al* (2014) ^{[1]}. Weir (2016) outlines the optimization and bootstrapping methodology with illustrative examples within the context of environmental and clinical pathogens ^{[2]}.

In essence the exponential dose response model is derived by assuming that the exposed dose to a host is Poisson distributed for the average of the bolus dose. This means that we assume the distribution of the average of the bolus dose is random in description. Then the probability that the pathogens will survive to initiate an infection is best described using a Binomial distribution. This means that either the pathogen survives or does not to initiate an infection. The beta Poisson dose response model is an expansion from the exponential dose response model. In this case rather than assuming the rate term in the binomial distribution is constant we allow it to vary based on a beta distribution. This allows for an increased level of realism in modeling the dose response relationship in the host.

### Reference

- ↑ Haas, C.N., Rose, J.B. and Gerba, C.P. 2014. Quantitative Microbial Risk Assessment. Second. J. Wiley and Sons. Wiley Link
- ↑ Weir, M.H. 2016. “Dose-Response Modeling and Use: Challenges and Uncertainties in Environmental Exposure.” In Manual of Environmental Microbiology, 4th ed., 3.5.3–1 – 3.5.3–17. ASM Press. Link to ASM book page