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Risk-Adjusted Cumulative Sum Charting Procedures

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Book cover Frontiers in Statistical Quality Control 10

Part of the book series: Frontiers in Statistical Quality Control ((FSQC,volume 10))

Abstract

Risk-adjusted charting procedures for monitoring the performances of a cardiac surgeon or a group of surgeons have recently gained prominence. Charting procedures developed for manufacturing processes are no longer appropriate because they do not take a patient’s risk into account. The first charting procedure, variable life-adjusted display (VLAD) that takes a patient’s risk into account was introduced in 1997. The VLAD plots the predicted mortality count minus the observed count cumulatively. The statistic plotted is intuitive and it has gained widespread attention and adoption. However, the run length performance of this chart is still not clearly understood because of the lack of a proper signalling rule. A risk-adjusted cumulative sum (RA-CUSUM) chart based on testing the odds ratio that a patient dies was proposed in 2000. In this paper, we developed and studied a general RA-CUSUM chart of which the RA-CUSUM chart based on odds ratio is a special case. The general RA-CUSUM chart allows testing to be done beyond just testing the odds ratio. One interesting note: although the VLAD and RA-CUSUM chart look seemingly different, we show that the RA-CUSUM chart and the RA-CUSUM chart based on the VLAD’s monitoring statistic are in fact the same chart.

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Acknowledgements

The first and third authors are supported by the Academic Research Fund Tier 1 (R-155-000-092-112), Ministry of Education, Singapore. We wish to thank Dr Alistair Hall for providing the data from the EMMACE-1 Study and the permission to use it here.

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Authors and Affiliations

  1. Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore, 117546, Singapore

    Fah F. Gan, Lin Lin & Chok K. Loke

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  1. Fah F. Gan
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  2. Lin Lin
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Correspondence to Fah F. Gan .

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Editors and Affiliations

  1. , Inst. Statistik und Ökonometrie, Freie Universität Berlin, Garystr. 21, Berlin, 14195, Berlin, Germany

    Hans-Joachim Lenz

  2. LS für Quantitative Methoden,, insbesondere Statistik, Europa-Universität Viadrina, Grosse Scharrnstr. 59, Frankfurt/Oder, 15230, Brandenburg, Germany

    Wolfgang Schmid

  3. , Inst. Statistik und Ökonometrie, Freie Universität Berlin, Garystr. 21, Berlin, 14195, Berlin, Germany

    Peter-Theodor Wilrich

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© 2012 Springer-Verlag Berlin Heidelberg

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Gan, F.F., Lin, L., Loke, C.K. (2012). Risk-Adjusted Cumulative Sum Charting Procedures. In: Lenz, HJ., Schmid, W., Wilrich, PT. (eds) Frontiers in Statistical Quality Control 10. Frontiers in Statistical Quality Control, vol 10. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2846-7_15

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