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Risk-adjusted monitoring of time to event

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Listed:
  • A. Gandy
  • J. T. Kvaløy
  • A. Bottle
  • F. Zhou

Abstract

Recently there has been interest in risk-adjusted cumulative sum charts, CUSUMs , to monitor the performance of e.g. hospitals, taking into account the heterogeneity of patients. Even though many outcomes involve time, only conventional regression models are commonly used. In this article we investigate how time to event models may be used for monitoring purposes. We consider monitoring using CUSUMs based on the partial likelihood ratio between an out-of-control state and an in-control state. We consider both proportional and non-proportional alternatives, as well as a head start. Against proportional alternatives, we present an analytic method of computing the expected number of observed events before stopping or the probability of stopping before a given observed number of events. In a stationary set-up, the former is roughly proportional to the average run length in calendar time. Adding a head start changes the threshold only slightly if the expected number of events until hitting is used as a criterion. However, it changes the threshold substantially if a false alarm probability is used. In simulation studies, charts based on survival analysis perform better than simpler monitoring schemes. We present one example from retail finance and one medical application. Copyright 2010, Oxford University Press.

Suggested Citation

  • A. Gandy & J. T. Kvaløy & A. Bottle & F. Zhou, 2010. "Risk-adjusted monitoring of time to event," Biometrika, Biometrika Trust, vol. 97(2), pages 375-388.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:375-388
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    File URL: http://hdl.handle.net/10.1093/biomet/asq004
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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. Athanasios Sachlas & Sotirios Bersimis & Stelios Psarakis, 2019. "Risk-Adjusted Control Charts: Theory, Methods, and Applications in Health," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 630-658, December.
    3. Gandy, Axel, 2012. "Performance monitoring of credit portfolios using survival analysis," International Journal of Forecasting, Elsevier, vol. 28(1), pages 139-144.
    4. Rena Jie Sun & John D. Kalbfleisch, 2013. "A Risk-Adjusted O–E CUSUM with Monitoring Bands for Monitoring Medical Outcomes," Biometrics, The International Biometric Society, vol. 69(1), pages 62-69, March.

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