SCR-CUSUM: An illness-death semi-Markov model-based risk-adjusted CUSUM for semi-competing risk data monitoring

Assessing the medical quality of hospitals based on control charts has received lots of attention. However, existing control charts produce delay and false alarms when applying to semi-competing risk (SCR) data, which widely exist in biomedical and clinical fields. Some studies have suggested that SCR data are important for investigating the healthcare quality of hospitals, but there are seldom targeted control charts for monitoring the medical quality implied by them. Therefore, in this paper, we propose a risk-adjusted cumulative sum control chart based on illness-death semi-Markov model, named SCR-CUSUM, to monitor the deterioration of hospitals' medical quality by detecting the shifts of non-terminal and terminal events simultaneously. The chart statistic of SCR-CUSUM shows good interpretability. By replacing the preset log-likelihood ratio with the generalized likelihood ratio, SCR-CUSUM become more sensitive and general. Meanwhile, we provide the theoretical control limit and verify its feasibility. Both of the results of simulation and case study prove that SCR-CUSUM works better than the comparison methods when applying to SCR data. In addition, we also analyze the causes of false and delay alarms for existing control charts using simulation data.