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An overview of risk‐adjusted charts

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  • O. Grigg
  • V. Farewell

Abstract

Summary. The paper provides an overview of risk‐adjusted charts, with examples based on two data sets: the first consisting of outcomes following cardiac surgery and patient factors contributing to the Parsonnet score; the second being age–sex‐adjusted death‐rates per year under a single general practitioner. Charts presented include the cumulative sum (CUSUM), resetting sequential probability ratio test, the sets method and Shewhart chart. Comparisons between the charts are made. Estimation of the process parameter and two‐sided charts are also discussed. The CUSUM is found to be the least efficient, under the average run length (ARL) criterion, of the resetting sequential probability ratio test class of charts, but the ARL criterion is thought not to be sensible for comparisons within that class. An empirical comparison of the sets method and CUSUM, for binary data, shows that the sets method is more efficient when the in‐control ARL is small and more efficient for a slightly larger range of in‐control ARLs when the change in parameter being tested for is larger. The Shewart p‐chart is found to be less efficient than the CUSUM even when the change in parameter being tested for is large.

Suggested Citation

  • O. Grigg & V. Farewell, 2004. "An overview of risk‐adjusted charts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 523-539, August.
    • Handle: RePEc:bla:jorssa:v:167:y:2004:i:3:p:523-539
    DOI: 10.1111/j.1467-985X.2004.0apm2.x
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    Cited by:

    1. Axel Gandy & Jan Terje Kvaløy, 2013. "Guaranteed Conditional Performance of Control Charts via Bootstrap Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 647-668, December.
    2. Hassan Assareh & Kerrie Mengersen, 2012. "Change Point Estimation in Monitoring Survival Time," PLOS ONE, Public Library of Science, vol. 7(3), pages 1-10, March.
    3. Jianbo Li & Jiancheng Jiang & Xuejun Jiang & Lin Liu, 2018. "Risk-adjusted monitoring of surgical performance," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-13, August.
    4. Nataliya Chukhrova & Arne Johannssen, 2020. "Monitoring of high-yield and periodical processes in health care," Health Care Management Science, Springer, vol. 23(4), pages 619-639, December.
    5. Y. Samimi & A. Aghaie, 2010. "Monitoring heterogeneous serially correlated usage behavior in subscription-based services," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(10), pages 1761-1777.
    6. Kolb, Aaron M., 2019. "Strategic real options," Journal of Economic Theory, Elsevier, vol. 183(C), pages 344-383.
    7. Isabel González & Ismael Sánchez, 2009. "On‐line evaluation of the stability of an inspection process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 719-736, November.
    8. Sotirios Bersimis & Athanasios Sachlas & Ross Sparks, 2017. "Performance Monitoring and Competence Assessment in Health Services," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1169-1190, December.

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