Examining secular trends and seasonality in count data using dynamic generalized linear modelling: a new methodological approach illustrated with hospital discharge data on myocardial infarction

Time series of incidence counts often show secular trends and seasonal patterns. We present a model for incidence counts capable of handling a possible gradual change in growth rates and seasonal patterns, serial correlation, and overdispersion. The model resembles an ordinary time series regression model for Poisson counts. It differs in allowing the regression coefficients to vary gradually over time in a random fashion. During the 1983–1999 period, 17,989 incidents of acute myocardial infarction were recorded in the Hospital Discharge Registry for the county of North Jutland, Denmark. Records were updated daily. A dynamic model with a seasonal pattern and an approximately linear trend was fitted to the data, and diagnostic plots indicated a good model fit. The analysis conducted with the dynamic model revealed peaks coinciding with above-average influenza A activity. On average the dynamic model estimated a higher peak-to-trough ratio than traditional models, and showed gradual changes in seasonal patterns. Analyses conducted with this model provide insights not available from more traditional approaches.