Fractional Poisson—A Simple Dose‐Response Model for Human Norovirus

Abstract

This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (<100), estimation error is small for the fractional Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures.

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“…Although most of these studies assumed linear relationships between these microbes, which could even be computationally incorrect, the variations in the ratios suggest that there is inadequate evidence to support one particular relationship. The other possible reason for the difference in risk estimates could be attributed to the fact that the WHO model used the Beta-poisson dose-response model on the direct norovirus dataset from Teunis et al [57], unlike the current study, which employed the fractional-poisson dose-response model [187].…”

“…The details of methods used to collect behavioural and microbiological exposure data have been presented elsewhere (Chapters 2, 3 & 4). Risk models for dose response assessments were based on peer-reviewed publications, but effort was made to adopt less complicated models which have been used on human challenge study data, and which was purposely designed to create dose-response models [57,187]. All fieldwork for observations, interviews, environmental and food sampling and laboratory analysis was done from October to December 2012 in the dry season, and from June to August 2013 in the rainy season.…”

“…The Fractional-Poisson model which is a modified version of the Beta-poisson model (β-Poisson) was used to model the infection risk of norovirus [187]. Building upon the dose-response model from Teunis et al, [57], the fractional-Poisson model considered two parameters, host susceptibility which it characterizes as either susceptible, or immune, and a second parameter which accounts for virus aggregation [187]. The pathogen infection risk is then estimated as the product of nonzero exposure (i.e.…”

“…probability that at least one virion is ingested) and the fraction of susceptible hosts; i.e. the single infection of the pathogen infection is given by the Equation below [187]:…”

“…Most of the input data for the current study originated from the same dataset, and from the same study area (Table 5.1), and hence less prone to uncertainties in the risk estimates compared to the use of models dominated by input parameters from different dataset, and also from different geographical areas with different exposure settings. The fractional poisson model adopted for the dose-response model was computationally simple, and has been validated to best describe data from the norovirus human challenge from which it was applied to [187]. The model uses lesser parameters compared to the beta-poisson which was originally used to describe the norovirus human challenge study data [57,187].…”