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Checking the Grouped Data Version of the Cox Model for Interval‐grouped Survival Data

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  • CHRISTIAN B. PIPPER
  • CHRISTIAN RITZ

Abstract

. Epidemiology research often entails the analysis of failure times subject to grouping. In large cohorts interval grouping also offers a feasible choice of data reduction to actually facilitate an analysis of the data. Based on an underlying Cox proportional hazards model for the exact failure times one may deduce a grouped data version of this model which may then be used to analyse the data. The model bears a lot of resemblance to a generalized linear model, yet due to the nature of data one also needs to incorporate censoring. In the case of non‐trivial censoring this precludes model checking procedures based on ordinary residuals as calculation of these requires knowledge of the censoring distribution. In this paper, we represent interval grouped data in a dynamical way using a counting process approach. This enables us to identify martingale residuals which can be computed without knowledge of the censoring distribution. We use these residuals to construct graphical as well as numerical model checking procedures. An example from epidemiology is provided.

Suggested Citation

  • Christian B. Pipper & Christian Ritz, 2007. "Checking the Grouped Data Version of the Cox Model for Interval‐grouped Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 405-418, June.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:2:p:405-418
    DOI: 10.1111/j.1467-9469.2006.00537.x
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    Cited by:

    1. C. B. Pipper & C. Ritz & T. H. Scheike, 2011. "Explained Variation in a Fully Specified Model for Data-Grouped Survival Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1361-1368, December.
    2. Rachel MacKay Altman & Andrew Henrey, 2018. "Practical considerations when analyzing discrete survival times using the grouped relative risk model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 532-547, July.

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