Two Human Challenge Studies Confirm High Infectivity of Norwalk Virus

To the Editor—In a recently published article, Atmar et al [1] estimated the human infectious dose 50% (HID50) of Norwalk virus to be 1320–2800 genomic equivalents (gEq). The authors stated that this estimate is higher than the estimate reported by Teunis et al [2]. However, this apparent difference in HID50 is actually due to the different statistical approaches used to generate the estimates, rather than due to true biological differences. We compared the dose-response data from the studies by Atmar et al and Teunis et al in 3 steps. First, the data from each study were independently fitted to the dose-response model described by Teunis et al (an exact beta-Poisson model). The data from Atmar et al can be readily fitted to the published dose response model, assuming there is no inoculum aggregation (Figure 1; see the article by Teunis et al [2] for the same statistics from their data set). Second, the data from both studies were pooled and fitted by the same dose-response model (now including the correction for aggregation of the 8fIIa inoculum; Figure 1). Likelihood ratio tests for goodness of fit confirmed that the dose-response model can predict the outcomes in each data set, whether fitted independently or pooled. Finally, a likelihood ratio test that compared the independent models (fitted to the data set of Atmar et al or to the 8fIIa, 8fIIb data) to the pooled model supported the null hypothesis that the models do not yield statistically different results. This result indicates that the separate dose-response models (with 2 + 2 + 3 free parameters) do not provide a significantly better fit than the pooled model (with only 3 free parameters). Therefore, we conclude that the data from Atmar et al are completely consistent with the infectivity data published by Teunis et al [2]. Best fit (maximum likelihood) dose-response curves for Norwalk virus. Open circles, data points from the study by Atmar et al [1]. Upper line, exact beta-Poisson model fitted to the data from Atmar et al (α = .28, β = .58, minimum residual deviance = 1.63). Lower line, exact beta-Poisson model fitted to the pooled data from Atmar et al and Teunis et al [2] (α = .024, β = .017, µc = 517, minimum deviance = 15.71). HID studies are always subject to a high degree of statistical uncertainty in the outcomes. For norovirus studies, this uncertainty is due to small numbers of subjects, heterogeneity in susceptibility to infection, uncertainty in dose calculations, and, for some inocula, aggregation of the virus, which affects the amount of virus in a challenge dose. For small challenge groups, the confidence interval (CI) around the infected fraction at any given dose can be quite large. This wide CI explains the discrepancy in infection outcome discussed by Atmar et al. For the 3240 genomic equivalent copies (GEC) dose of 8fIIa, 3 of 9 subjects became infected, which may seem unexpected given the estimated HID50 of 1015 GEC. However, for a binomial fraction of 3 of 9, the 95% CI is .085–.651; thus, the number of infected subjects could range from 0 subjects to 5 of 9 subjects challenged and still be statistically consistent with the estimated HID50. Finally, Atmar et al state that Teunis et al “reported an HID50 estimate that ranged from 18 to 1015 gEq” [1, p. 1021]. This is an oversimplification of the results from the study by Teunis et al and has complicated the comparison of the studies. In fact, the HID50 for disaggregated virus, using the data from Teunis et al, is 18.2 GEC, with a 95% CI of 1.03–4350 GEC. Given this range and the natural variability in subject infectivity, it is clear that the results of these studies are similar. Careful statistical analysis of the dose-response data further supports this conclusion. It is reassuring that the findings of these 2 challenge studies, which use different Norwalk virus inocula, are in agreement and support the conclusion that this is a highly infectious virus, consistent with its epidemiologic characteristics [3]. Potential conflicts of interest. All authors: No reported conflicts. All authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest. Conflicts that the editors consider relevant to the content of the manuscript have been disclosed.