Seasonality of hospitalizations due to respiratory diseases: modelling serial correlation all we need is Poisson

The identification of seasonality and trend patterns of the weekly number of hospitalizations may be useful to plan the structure of health care and the vaccination calendar. A generalized additive model with the negative binomial distribution and a generalized additive model with autoregressive terms (GAMAR) and Poisson distribution are fitted including seasonal parameters and nonlinear trend using splines. The GAMAR includes autoregressive terms to take into account the serial correlation, yielding correct standard errors and reducing overdispersion. For the number of hospitalizations of people older than 60 years due to respiratory diseases in São Paulo city, both models present similar estimates but the Poisson-GAMAR presents uncorrelated residuals, no overdispersion and provides smaller confidence intervals for the weekly percentage changes. Forecasts for the next year based on both models are obtained by simulation and the Poisson-GAMAR presented better performance.