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Cusums

Cumulative sum (Cusum) charts are effective tools for monitoring processes. We have developed a new type of control chart for survival outcomes, and applied these to data of the Dutch Arthroplasty Register. In addition, with PhD student David Lam I investigate the utility of using Cusums to monitor outcomes related to organ transplantation.

Summary

Cumulative sum (Cusum) charts have proven to be useful in many applications, including detecting problems in the quality of care. Consider for example liver transplantation. A simple Cusum chart will go up if a liver transplantation fails within 1 year (= bad outcome) and down if the transplanted liver is still fine after 1 year (= good outcome). If there are many bad outcomes within a short span of time, the chart will keep increasing until it eventually passes some prespecified threshold, triggering an alarm.

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Many variations of Cusum exist. The amount they may go up or down can be made dependent on e.g. a patient's risk factors. With PhD student David Lam, I investigate what type of Cusum chart is most useful to monitor the quality of organ transplantations.

With Daniel Gomon, Hein Putter and Rob Nelissen, we designed a new type of control chart for survival outcomes. The few already 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 derived the Continuous time Generalized Rapid response CUSUM (CGR-CUSUM) chart. In addition to deriving theoretical properties of the CGR-CUSUM, we applied it to data from the Dutch Arthroplasty Register and published an open source R software package, available here. Daniel Gomon won the Best Thesis in Applied Math Award for his work on the CGR-CUSUM (news item).

Related papers

Gomon, D., Putter, H., Nelissen, R. G., & van der Pas, S. (2022). CGR-CUSUM: A Continuous time Generalized Rapid Response Cumulative Sum chart. arXiv preprint arXiv:2205.07618. [link]