The Effect of Estimation Error on Risk-Adjusted Survival Time CUSUM Chart Performance

Research on risk‐adjusted control charts has gained great interest in healthcare settings. Based on monitored variables (binary outcome or survival times), risk‐adjusted cumulative sum (CUSUM) charts are divided into Bernoulli and survival time CUSUM charts. The effect of estimation error on control chart performance has been systematically studied for Bernoulli CUSUM but not for survival time CUSUM in continuous time. We investigate the effect of estimation error on the performance of risk‐adjusted survival time CUSUM scheme in continuous time with the cardiac surgery data. The impact is studied with the use of the median run lengths (medRLs) and the standard deviation (SD) of medRLs for different sample sizes, specified in‐control median run length, adverse event rate and patient variability. Results show that estimation error affects the performance of risk‐adjusted survival time CUSUM chart significantly and the performance is more sensitive to the specified in‐control median run length (medRL0) and adverse event rate. To take the estimation error into account, the practitioners can 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 alarms don't signal too slow. Moreover, additional event occurrences can be used to update the estimation but should be from in‐control process. Finally, non‐parametric bootstrap can be applied to reduce model misspecification error.