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Cumulative sum (Cusum) charts are effective tools for monitoring processes. Daniel Gomon, Hein Putter and I have developed a new type of control chart for survival outcomes, and applied these to data of the Dutch Arthroplasty Register. In addition, I collaborated with organ transplantation surgeons to monitor outcomes related to liver transplantation and with maxillofacial surgeons to understand the learning curve of a new surgical approach.


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.


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 transplantation surgeon David Lam I investigated what type of Cusum chart is most useful to monitor the quality of organ procurement, and found only limited added benefit of adjusted Cusum charts compared to unadjusted Cusum charts. The upside of this finding is that there is a lot to be gained by implementing only a relatively simple unadjusted Cusum chart, which requires less historical data and assumptions than an adjusted chart.

With Luc Karssemakers I calculated a so-called 'learning curve Cusum' (LC-CUSUM) to understand the learning process of a new approach for condylectomy. Condylectomy is a treatment for unilateral condylar hyperplasia, which causes facial asymmetry. The LC-CUSUM was combined with a regular Cusum as well as other methods to understand the learning process. We found that after approximately 50 surgeries, a surgeon will have mastered the new approach.

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. Biostatistics, kxac041 [link]

Lam, H.D., Schaapherder, A.F., Alwayn, I.P., Nijboer, W.N., Tushuizen, M.E., Hemke, A.C., Baranski, A., van der Pas, S.L. (2023). Quality assessment of donor liver procurement surgery using an unadjusted CUSUM prediction model. A practical nationwide evaluation. Clinical Transplantation 37 (5), e14940. [link]

Karssemakers, L.H.E., de Winter, D.C.M., van der Pas, S.L., Nolte, J.W., Becking, A.G. (2023). The learning curve of transoral condylectomy; a retrospective analysis of 100 consecutive cases of unilateral condylar hyperplasia. Journal of Cranio-Maxillofacial Surgery, online preview. [link]

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