Summary Rapidly detecting problems in the quality of care is of utmost importance for the well-being of patients. Without proper inspection schemes, such problems can go undetected for years. Cumulative sum (CUSUM) charts have proven to be useful for quality control, yet available methodology for survival outcomes is limited. The few available continuous time inspection charts usually require the researcher to specify an expected increase in the failure rate in advance, thereby requiring prior knowledge about the problem at hand. Misspecifying parameters can lead to false positive alerts and large detection delays. To solve this problem, we take a more general approach to derive the new Continuous time Generalized Rapid response CUSUM (CGR-CUSUM) chart. We find an expression for the approximate average run length (average time to detection) and illustrate the possible gain in detection speed by using the CGR-CUSUM over other commonly used monitoring schemes on a real-life data set from the Dutch Arthroplasty Register as well as in simulation studies. Besides the inspection of medical procedures, the CGR-CUSUM can also be used for other real-time inspection schemes such as industrial production lines and quality control of services.
Background During the past 14 years, a clinical audit has been used in the Netherlands to provide hospitals with data on their performance in colorectal cancer care. Continuous feedback on the quality of care provided at each hospital is essential to improve patient outcomes. It is unclear which methods should be used to generate most informative output for the identification of potential quality issues. Our aim is to compare the commonly employed funnel plot with existing cumulative sum (CUSUM) methodology for the evaluation of postoperative survival and hospital stay outcomes of patients who underwent colorectal surgery in the Netherlands. Methods Data from the Dutch ColoRectal Audit on 25367 patients in the Netherlands who underwent surgical resection for colorectal cancer between 2019 and 2021 is used to compare four methods for the detection of deviations in the quality of care. Two methods based on binary outcomes (funnel plot, binary CUSUM) and two CUSUM charts based on survival outcomes (BK-CUSUM and CGR-CUSUM) are considered. A novel approach for determining hospital specific control limits for CUSUM charts is proposed. The ability to detect deviations as well as the time until detection are compared for the four methods. Charts were constructed for the inspection of both postoperative survival and hospital stay. Results Methods using survival outcomes always yielded faster detection times compared to approaches employing binary outcomes. Detections between methods mostly coincided for postoperative survival. For hospital stay detections varied strongly, with methods based on survival outcomes signalling over half the hospitals. Further pros and cons as well as pitfalls of all methods under consideration are discussed. Conclusions Methodology for the continuous inspection of the quality of care should be tailored to the specific outcome. Properly understanding how the mechanism of a control chart functions is crucial for the correct interpretation of results. This is particularly true for CUSUM charts, which require the choice of a parameter that greatly influences the results. When applying CUSUM charts, consideration of these issues is strongly recommended.
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