Monitoring therapeutic processes using risk-adjusted multivariate Tukey's CUSUM control chart

Using control charts for monitoring therapeutic processes has become popular lately. As the application of traditional control charts in the therapeutic processes may be misleading due to the inherent differences between patients, a multifactor correlated risk measure is considered in monitoring of these processes. Therefore, using risk-adjusted control charts for monitoring the therapeutic processes is of interest to practitioners. Furthermore, in health care monitoring, statistical models should account for abnormal distributions and outlier data to minimize misinterpretations of monitoring schemes. This study proposes a risk-adjusted multivariate Tukey's cumulative sum (RA-MTCUSUM) control chart. The proposed method is a combination of the accelerated failure time (AFT) regression model, the Tukey's control chart (TCC) featuring robustness against abnormality, and the multivariate cumulative sum (MCUSUM) control chart for monitoring multivariable process. Simulation experiments are performed to evaluate the performance of the proposed control chart using the average run length (ARL) measure. Results show that the RA-MTCUSUM control chart has better performance in comparison with traditional ones for monitoring various distributions (normal and non-normal). Based on the simulation results, outlier data do not disturb the proposed control chart's performance. Moreover, applying the RA-MTCUSUM control chart to a real-world dataset related to sepsis patients of a hospital located in Tehran, Iran indicates that the control chart has more reasonable performance than the traditional control charts in the real applications due to its robustness.