Comparisons of statistical distributions for cluster sizes in a developing pandemic

M J Faddy,A N Pettitt

doi:10.1186/s12874-022-01517-9

Abstract

BackgroundWe consider cluster size data of SARS-CoV-2 transmissions for a number of different settings from recently published data. The statistical characteristics of superspreading events are commonly described by fitting a negative binomial distribution to secondary infection and cluster size data as an alternative to the Poisson distribution as it is a longer tailed distribution, with emphasis given to the value of the extra parameter which allows the variance to be greater than the mean. Here we investigate whether other long tailed distributions from more general extended Poisson process modelling can better describe the distribution of cluster sizes for SARS-CoV-2 transmissions.MethodsWe use the extended Poisson process modelling (EPPM) approach with nested sets of models that include the Poisson and negative binomial distributions to assess the adequacy of models based on these standard distributions for the data considered.ResultsWe confirm the inadequacy of the Poisson distribution in most cases, and demonstrate the inadequacy of the negative binomial distribution in some cases.ConclusionsThe probability of a superspreading event may be underestimated by use of the negative binomial distribution as much larger tail probabilities are indicated by EPPM distributions than negative binomial alternatives. We show that the large shared accommodation, meal and work settings, of the settings considered, have the potential for more severe superspreading events than would be predicted by a negative binomial distribution. Therefore public health efforts to prevent transmission in such settings should be prioritised.

Highlights

We consider cluster size data of severe acute respiratory syndrome (SARS)-CoV-2 transmissions for a number of different settings from recently published data
In the public communication of information about the novel coronavirus disease COVID-19 there is emphasis frequently given to estimates of the basic reproduction number R0, the expected number of secondary cases arising from a single primary case in a fully susceptible population, and the effective reproduction number Rt which is defined to R0 but when a population is subject to control measures
Such variation is important because it can explain the occurrence of so-called superspreading events (SSE’s) where the numbers of secondary and subsequent cases are substantially more than expected from assuming a Poisson distribution for the numbers of cases

Summary

Introduction

We consider cluster size data of SARS-CoV-2 transmissions for a number of different settings from recently published data. In the public communication of information about the novel coronavirus disease COVID-19 there is emphasis frequently given to estimates of the basic reproduction number R0, the expected number of secondary cases arising from a single primary case in a fully susceptible population, and the effective reproduction number Rt which is defined to R0 but when a population is subject to control measures. Values of such R’s greater than one lead to the exponential growth of daily case numbers. For highly skew negative binomial distributions, with variance equal to mean + mean2/k and small values of the extra parameter

Methods

Results

Discussion

Conclusion