Risk‐Adjusted CUSUM Chart With Dynamic Probability Control Limits for Monitoring Multistage Healthcare Processes Based on Ordinal Response Variables

ABSTRACT Healthcare processes are often characterized by a multistage structure in which the output of each stage is the input of the subsequent stage. A modeling of these processes is based on the relation between the patient risks at each stage and outcomes of the prior stage. Most of the monitoring schemes of multistage healthcare processes have been designed when patient outcomes are binary, while it is more reasonable to consider different grades of recovery as ordinal. For this purpose, we use a risk‐adjusted (RA) control chart with dynamic probability control limits to monitor a multistage healthcare process when the patient outcomes are ordinal at each stage. To calculate the probability that a patient's outcome falls into a certain category, we have used an ordinal state‐space model on the basis of proportional odds logistic regression models, and it is shown that the fit of the logistic regression model with ordinal responses is superior to that of the regression model with binary responses. In this model, in addition to Parsonnet scores, the other categorical operational covariates and latent risks are considered as the patient's risks. Finally, we demonstrate the performance of the proposed chart through comprehensive simulations based on the average run‐length criterion and a real‐world case study in healthcare settings, and results disclose that the proposed RA cumulative sum control chart for multistage healthcare processes with ordinal responses performs satisfactorily when the process is in‐control and out‐of‐control.