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Practical considerations when analyzing discrete survival times using the grouped relative risk model

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  • Rachel MacKay Altman

    (Simon Fraser University)

  • Andrew Henrey

    (Simon Fraser University)

Abstract

The grouped relative risk model (GRRM) is a popular semi-parametric model for analyzing discrete survival time data. The maximum likelihood estimators (MLEs) of the regression coefficients in this model are often asymptotically efficient relative to those based on a more restrictive, parametric model. However, in settings with a small number of sampling units, the usual properties of the MLEs are not assured. In this paper, we discuss computational issues that can arise when fitting a GRRM to small samples, and describe conditions under which the MLEs can be ill-behaved. We find that, overall, estimators based on a penalized score function behave substantially better than the MLEs in this setting and, in particular, can be far more efficient. We also provide methods of assessing the fit of a GRRM to small samples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:3:d:10.1007_s10985-017-9410-7
    DOI: 10.1007/s10985-017-9410-7
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    References listed on IDEAS

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    1. 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.
    2. Kauermann G. & Carroll R.J., 2001. "A Note on the Efficiency of Sandwich Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1387-1396, December.
    3. Altman, Rachel MacKay, 2007. "Mixed Hidden Markov Models: An Extension of the Hidden Markov Model to the Longitudinal Data Setting," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 201-210, March.
    4. Ioannis Kosmidis & David Firth, 2009. "Bias reduction in exponential family nonlinear models," Biometrika, Biometrika Trust, vol. 96(4), pages 793-804.
    5. Amalia S. Meier & Barbra A. Richardson & James P. Hughes, 2003. "Discrete Proportional Hazards Models for Mismeasured Outcomes," Biometrics, The International Biometric Society, vol. 59(4), pages 947-954, December.
    6. Enrico A. Colosimo & Liciana V. A. S. Chalita & Clarice G. B. Demétrio, 2000. "Tests of Proportional Hazards and Proportional Odds Models for Grouped Survival Data," Biometrics, The International Biometric Society, vol. 56(4), pages 1233-1240, December.
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