LMR-EWMA: A LASSO-based Multivariate Residual Control Chart for Monitoring Rare Health-Related Events

Monitoring rare health-related events using control charts is crucial for timely detecting potential changes in healthcare scenarios. For example, sequentially testing the level of changes in infectious disease patient numbers helps prepare before an epidemic. Unlike general health-related events, the observation of rare ones often involves an excess of zeros, making it more appropriate to use the zero-inflated Poisson (ZIP) distribution rather than the classical Poisson. Although residual-based charts have attracted significant attention in this field, few studies have explored how to appropriately select residuals with different advantages in the complex situations like healthcare scenarios. Therefore, in this paper, we propose LMR-EWMA, a least absolute shrinkage and selection operator (LASSO)-based multivariate residual exponentially weighted moving average (EWMA) control chart, to automatically select the optimal residuals for monitoring changes (i.e., shifts) in the number of rare health-related events. Additionally, we have innovatively designed a bi-directional moving mechanism to address the limitation of current research in distinguishing the practical significance of shifts. Experimental results on three simulation cases and two real datasets demonstrate that LMR-EWMA outperforms existing charts in monitoring performance.