Effect Of Estimation Error On The Performance Of Risk-adjusted Charts

Recently,more and more researchers have introduced quality control charts into healthcare environment.Risk-adjusted control chart is based on traditional control chart and developed by considering individual’s heterogeneity.General monitored variables include patients’ survival state and survival time.Survival state contains living and death which are indicated by 0 and 1 respectively,while survival time is continuous data type.The CUSUM charts can be separated into Bernoulli CUSUM and survival time CUSUM corresponding to the binary data and continuous data.Bernoulli CUSUM and the effect of estimation error on chart performance have been systematically studied,while for survival time CUSUM chart,especially in continuous time scale,the effect of estimation error hasn’t been investigated.Through real case combined with simulation,we study the effect of estimation error on the performance of risk-adjusted survival time CUSUM chart in continuous time.Considering the characteristic of the chart,the median run lengths(medRLs)and standard deviation(SD)are applied to measure the chart performance.The effect of sample sizes,specified in-control median run length(medRL0),adverse event rate and patient variability is also investigated on chart performance.The results show that estimation error affects the performance of risk-adjusted survival time CUSUM chart significantly and the performance is most sensitive to the specified in-control median run length(medRL0)and adverse event rate.Analyzing the results,it is recommended that the practitioners should take the estimation error into account and bootstrap many samples from Phase I data,and then determine the threshold that can guarantee at least a medRL0 with certain probability under which false alarms occur less frequently and meanwhile out-of-control monitoring efficiency is ensured.It is also recommended that additional event occurrences can be used to update the estimation but should be from in-control process.Finally,non-parametric bootstrap is advised to reduce model misspecification error.