A classical hypothesis test for assessing the homogeneity of disease transmission in stochastic epidemic models

This paper addresses the problem of assessing the homogeneity of the disease transmission process in stochastic epidemic models in populations that are partitioned into social groups. We develop a classical hypothesis test for completed epidemics which assesses whether or not there is significant within‐group transmission during an outbreak. The test is based on time‐ordered group labels of individuals. The null hypothesis is that of homogeneity of disease transmission among individuals, a hypothesis under which the discrete random vector of groups labels has a known sampling distribution that is independent of any model parameters. The test exhibits excellent performance when applied to various scenarios of simulated data and is also illustrated using two real‐life epidemic data sets. We develop some asymptotic theory including a central limit theorem. The test is practically very appealing, being computationally cheap and straightforward to implement, as well as being applicable to a wide range of real‐life outbreak settings and to related problems in other fields.