A risk-adjusted CUSUM for monitoring the surgical quality reflected by the time-to-event outcomes with a cured fraction

Time-to-event (TTE) data featuring a cured fraction is common in biomedical fields, especially in studies related to surgery where censoring rates are typically high. Considering the importance of surgical quality in ensuring patient safety, this paper focuses on constructing an effective control chart to monitor it when a cured fraction is present. Existing TTE charts potentially assume all patients will eventually experience the postoperative outcome of interest and therefore lack mechanisms for cure rate monitoring, limiting their detection capability and result reliability. Motivated by it, we propose a risk-adjusted CUSUM based on a semi-parametric mixture cure model, named RACure-CUSUM. By incorporating the relative risk and odds ratio, a unified chart statistic is constructed within the likelihood ratio test to simultaneously monitor changes in the cure rate and hazard. Then, numerical solutions for approximations of upper control limits are provided and validated through simulation data. Finally, we compare RACure-CUSUM and five existing charts in a simulation study with four scenarios, as well as a case study based on two real datasets with different censoring rates. The results of both studies demonstrate the RACure-CUSUM has the best overall monitoring performance when applied to the TTE data with a cured fraction.