Accurate prediction of flu activity enables health officials to plan disease prevention and allocate treatment resources. A promising forecasting approach is to adapt the well-established endemic-epidemic modeling framework to time series of infectious disease proportions. Using U.S. influenza-like illness surveillance data over 18 seasons, we assessed probabilistic forecasts of this new beta autoregressive model with proper scoring rules. Other readily available forecasting tools were used for comparison, including Prophet, (S)ARIMA and kernel conditional density estimation (KCDE). Short-term flu activity was equally well predicted up to four weeks ahead by the beta model with four autoregressive lags and by KCDE; however, the beta model runs much faster. Non-dynamic Prophet scored worst. Relative performance differed for seasonal peak prediction. Prophet produced the best peak intensity forecasts in seasons with standard epidemic curves; otherwise, KCDE outperformed all other methods. Peak timing was best predicted by SARIMA, KCDE or the beta model, depending on the season. The best overall performance when predicting peak timing and intensity was achieved by KCDE. Only KCDE and naive historical forecasts consistently outperformed the equal-bin reference approach for all test seasons. We conclude that the endemic-epidemic beta model is a performant and easy-to-implement tool to forecast flu activity a few weeks ahead. Real-time forecasting of the seasonal peak, however, should consider outputs of multiple models simultaneously, weighing their usefulness as the season progresses.
Count data with an excess of zeros are often encountered when modeling infectious disease occurrence. The degree of zero inflation can vary over time due to nonepidemic periods as well as by age group or region. A well‐established approach to analyze multivariate incidence time series is the endemic–epidemic modeling framework, also known as the HHH approach. However, it assumes Poisson or negative binomial distributions and is thus not tailored to surveillance data with excess zeros. Here, we propose a multivariate zero‐inflated endemic–epidemic model with random effects that extends HHH. Parameters of both the zero‐inflation probability and the HHH part of this mixture model can be estimated jointly and efficiently via (penalized) maximum likelihood inference using analytical derivatives. We found proper convergence and good coverage of confidence intervals in simulation studies. An application to measles counts in the 16 German states, 2005–2018, showed that zero inflation is more pronounced in the Eastern states characterized by a higher vaccination coverage. Probabilistic forecasts of measles cases improved when accounting for zero inflation. We anticipate zero‐inflated HHH models to be a useful extension also for other applications and provide an implementation in an R package.
Contents 1 HHS regions 2 Weighted influenza-like illness (wILI) by HHS region 3 One-week-ahead forecasts of model M5 4 Results with first-order adjacency weights
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