An endemic-epidemic beta model for time series of infectious disease proportions

Abstract

Time series of proportions of infected patients or positive specimens are frequently encountered in disease control and prevention. Since proportions are bounded and often asymmetrically distributed, conventional Gaussian time series models only apply to suitably transformed proportions. Here we borrow both from beta regression and from the well-established HHH model for infectious disease counts to propose an endemic-epidemic beta model for proportion time series. It accommodates the asymmetric shape and heteroskedasticity of proportion distributions and is consistent for complementary proportions. Coefficients can be interpreted in terms of odds ratios. A multivariate formulation with spatial power-law weights enables the joint estimation of model parameters from multiple regions. In our application to a flu activity index in the USA, we find that the endemic-epidemic beta model provides a better fit than a seasonal ARIMA model for the logit-transformed proportions. Furthermore, a multivariate approach can improve regional forecasts and reduce model complexity in comparison to univariate beta models stratified by region.

Keywords: Multivariate time series; beta regression; epidemic modelling; influenza-like illness; seasonality.