A marginal moment matching approach for fitting endemic-epidemic models to underreported disease surveillance counts
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Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic-epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. We demonstrate that the reporting probability cannot be estimated from time series data alone and needs to be specified based on external information. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analysed. Notably, we show that this leads to a downward bias in model-based estimates of the effective reproductive number. The good performance of the proposed approach is demonstrated in simulation studies. An extension to time-varying parameters and reporting probabilities is discussed and applied in a case study on rotavirus gastroenteritis in Berlin, Germany.
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