Change point detection in risk adjusted control charts

Precise identification of the time when a change in a clinical process has occurred enables experts to identify a potential special cause more effectively. In this article, we develop change point estimation methods for a clinical dichotomous process in the presence of case mix. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the odds ratio and logit of risk of a Bernoulli process. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted CUSUM and EWMA control charts. In comparison with alternative EWMA and CUSUM estimators, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities enhance when probability quantification, flexibility and generaliability of the Bayesian change point detection model are also considered. The Deviance Information Criterion, as a model selection criterion in the Bayesian context, is applied to find the best change point model for a given dataset where there is no prior knowledge about the change type in the process.