Inference methods for First Few Hundred Studies

Abstract

Infectious diseases are a threat to the health of populations around the world. During the early stages of a novel infectious disease outbreak, intensive data collection may be conducted on the first few hundred symptomatic individuals in what is referred to as a First Few Hundred (FF100) Study. This data is used to assess the potential impact of a pandemic in terms of its transmissibility and clinical severity; these are used to inform a response that is proportionate to the level of risk posed by the disease. Transmissibility is not only determined by the infectiousness of a disease; it is also determined by how individuals interact with one another in a population. Household epidemic models allow for interactions at a household level and interactions at a population level. Hence, they account for some of the inherent structure in a population. Furthermore, data in FF100 studies are collected from all individuals within an infectious individuals' household, hence these models are appropriate when considering FF100 Study data. This thesis develops new statistical methods, based upon continuous-time Markov chain epidemic models, to estimate the transmissibility of a disease in a population of households. In particular, we use Bayesian inference to estimate posterior distributions for the rate of infection between households. The large state space of household models means that conventional methods for calculating likelihoods for Markov chain models are infeasible for this problem and hence motivates the development of the new methods presented in this thesis. These are based on the assumption that between household infections only occur between an infectious household and a household of susceptible individuals. This is a reasonable assumption for the beginning of an outbreak in a large population and allows us to consider the dynamics of infection within households, following the import of infection, independently of each other. Under the assumption of no secondary introductions into households, the force of infection of newly infected households and hence the likelihood for the number of newly infected households over a day can be calculated as a convolution of the force of infection within each household. Two types of methods for evaluating the likelihood are developed: the first method calculates the expected force of infection; and, the second method calculates the distribution of the force of infection. The expectation method utilises matrix exponential methods on the small, household process. The distribution method utilises recursive methods to calculate the Laplace transform of the force of infection within households, and then numerically inverts the Laplace transform of the distribution corresponding to the product of individual households forces of infection. These methods are compared for accuracy - in terms of point estimates and posterior distributions - and numerical efficiency.