Bayesian estimation of the time of a linear trend in risk-adjusted control charts

Abstract

Change point detection is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of disturbance in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in an in-control clinical dichotomous process in the presence of variable patient mix. To model the process and change point, a linear trend in the odds ratio of a Bernoulli process is formulated using hierarchical models in a Bayesian framework. We use Markov Chain Monte Carlo 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 riskadjusted CUSUM and EWMA control charts for different magnitude and direction of change scenarios. In comparison with alternative EWMA and CUSUM estimators, reasonably accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

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