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.

Comparison of Splitting Methods on Survival Tree

We compare splitting methods for constructing survival trees that are used as a model of survival time based on covariates. A number of splitting criteria on the classification and regression tree (CART) have been proposed by various authors, and we compare nine criteria through simulations. Comparative studies have been restricted to criteria that suppose the survival model for each terminal node in the final tree as a non-parametric model. As the main results, the criteria using the exponential log-likelihood loss, log-rank test statistics, the deviance residual under the proportional hazard model, or square error of martingale residual are recommended when it appears that the data have constant hazard with the passage of time. On the other hand, when the data are thought to have decreasing hazard with passage of time, the criterion using the two-sample test statistic, or square error of deviance residual would be optimal. Moreover, when the data are thought to have increasing hazard with the passage of time, the criterion using the exponential log-likelihood loss, or impurity that combines observed times and the proportion of censored observations would be the best. We also present the results of an actual medical research to show the utility of survival trees.