Statistical inference for infectious disease data of animals

Abstract

Efficient parameter estimation is increasingly recognised to be essential in fitting epidemic models to data. This thesis primarily explores parameter estimation methods as applied to data generated from an experimental infection with foot and mouth disease (FMD) virus in sheep. Data were generated from two ex¬ periments involving four groups of sheep, housed under restricted mixing, where sheep in the initial group were inoculated with type O FMD virus. The aim of the analysis is to investigate the presence of any trend in the infection rate with increased generation.The infection process of FMD virus in sheep can be modelled using chain binomial models and generalized linear models. However, application of these methods requires that the epidemic chain of infection pathways be known. The set of true pathways is an unobservable quantity and, in general, infectious disease data will be incomplete because the infection process is only partially observed. One proposed strategy is subjectively to assign an epidemic chain to the data and to analyse it on this basis. This approach is evaluated.An alternative to modelling the FMD infection process for individual sheep is to consider the transmission among groups of sheep, thus avoiding the need to make inference about individual infection pathways. Martingale methods and maximum likelihood estimation methods are used to estimate the typical infection rate /3 applying to groups of sheep where the aim is to investigate whether the infection rate changes across groups. The expected total infection exposure for each group is estimated. This entails knowledge of the time of infection, the latent period and the infectious period for each infected sheep. Parameters for the latent period and infectious period distributions are estimated from the data. A joint distribution of time to infection and latent period is formulated from which expected values for time to infection and the latent period for each infected sheep are estimated. The expected infectious period is estimated by fitting the infectious period distribution to the observed data. Estimates of these expectations and of j3 are calculated iteratively using an analogy of the Expectation Maximization (EM) algorithm until convergence occurs.Trends in estimates across groups are summarised using weighted linear regres¬ sion and their significance is tested using bootstrap methods. The power of the methodology is explored using simulated data from a Susceptible-LatentInfectious-Removed (SLIR) model that reflects the design of the experiments.In the final part of the thesis, the properties of the confidence interval based on asymptotic likelihood theory are compared with those of the percentile confidence interval generated by parametric and semi-parametric bootstrap methods. Boot¬ strap calibration is applied to each of these methods. Simulated data are used to explore the coverage properties of different confidence intervals for the basic reproduction ratio (Rq) of a SIR infection process.