CUSUM control charts to monitor series of Negative Binomial count data

To detect outbreaks of diseases in public health, several control charts have been proposed in the literature. In this context, the usual generalized linear model may be fitted for counts under a Negative Binomial distribution with a logarithm link function and the population size included as offset to model hospitalization rates. Different statistics are used to build CUSUM control charts to monitor daily hospitalizations and their performances are compared in simulation studies. The main contribution of the current paper is to consider different statistics based on transformations and the deviance residual to build control charts to monitor counts with seasonality effects and evaluate all the assumptions of the monitored statistics. The monitoring of daily number of hospital admissions due to respiratory diseases for people aged over 65 years in the city São Paulo-Brazil is considered as an illustration of the current proposal.