Spatial modelling of infectious diseases with covariate measurement error

Abstract

Abstract In spatial infectious disease models, it is typical to assume that only the distance between susceptible and infectious individuals is important for modelling, but not the actual spatial locations of the individuals. Recently introduced geographically-dependent individual level models (GD-ILMs) can be used to also consider the effect of spatial locations of individuals and the distance between susceptible and infectious individuals for determining the risk of infection. In these models, it is assumed that the covariates used to predict the occurrence of disease are measured accurately. However, there are many applications in which covariates are prone to measurement error. For instance, to study risk factors for influenza, people with low socio-economic status (SES) are known to be more at risk compared to the rest of the population. However, SES is prone to measurement error. In this paper, we propose a GD-ILM which accounts for measurement error in both individual-level and area-level covariates. A Monte Carlo expectation conditional maximisation algorithm is used for inference. We use models fitted to data to predict areas with high average infectivity rates. We evaluate the performance of the proposed approach through simulation studies and by a real-data application on influenza data in Manitoba, Canada.