Statistical Analysis of Multivariate Infectious Disease Surveillance Time Series

To meet the threats of infectious diseases, many countries have established surveillance systems for the routine collection of infectious disease data. The analysis and modelling such notification data is essential in the attempt to control and prevent disease. In this thesis, statistical methodology for the analysis of multivariate time series of counts as collected in surveillance systems on notifiable diseases is developed. The aim is to provide a flexible model which is able to explain the temporal and spatio-temporal patterns in the data, as well as account for dependencies between different pathogens. The methodology is implemented in the open-source R-package ‘surveillance’ which facilitates its use in practice. A particular challenge is the modelling of outbreaks and irregularities in the data. Motivated by a branching process formulation, well-known in infectious disease epidemiology, the epidemic behavior is modelled via an autoregressive formulation. Possible dependencies between related diseases are analyzed by introducing disease-specific parameters. An analysis of weekly influenza and meningococcal disease counts shows empirical evidence that influenza infections predispose meningococcal disease. In a spatio-temporal context, we propose incorporating external data such as travel intensities between regions to better reflect the regional spread of a disease. The non-linear autoregressive model formulation is further extended to integrate regional heterogeneity in disease transmission and incidence for highly multivariate time series. Such differences may be due to age, sex, vaccination status or environmental conditions. Two approaches to address heterogeneity are developed, depending on whether or not suitable covariate information about such factors is available. In the first approach, uncorrelated and spatially correlated random effects are included in the model. The random effects may describe heterogeneity in disease incidence levels as well as in the autoregressive coefficients, relating disease incidence to past counts in the same or neighboring regions. Inference for this non-standard model is based on penalized likelihood methodology. Variance parameters are estimated using marginal likelihood. The estimation procedure is adapted to handle correlated random effects. As classical model choice criteria such as AIC or BIC can be problematic in the presence of random effects, model choice is performed using one-step-ahead predictions and proper scoring rules. As exemplified by two applications, the predictive performance improves if existing heterogeneity is accounted for via random effects. When heterogeneity is due to known and observable factors, this information can be directly related to for example the autoregressive parameters via a regression formulation. Such a formulation also permits the autoregressive parameter to vary over time, for instance to reflect public health interventions. In an application to German measles surveillance data, region-specific vaccination coverage levels are used to explain regional differences in the incidence pattern.