Lifetime Data Analysis

, Volume 24, Issue 3, pp 532–547 | Cite as

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

  • Rachel MacKay AltmanEmail author
  • Andrew Henrey


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.


Bias reduction Discrete survival times Efficiency Grouped relative risk model Penalized score function Small samples 



This work was supported in part by a Discovery Grant (Grant Number RGPIN 293140) and an Undergraduate Student Research Award from the Natural Sciences and Engineering Research Council of Canada.

Supplementary material

10985_2017_9410_MOESM1_ESM.pdf (2.1 mb)
Web appendices and figures referenced in Sections 5 and 6 are available online. (PDF 2,104 KB)


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Statistics and Actuarial ScienceSimon Fraser UniversityBurnabyCanada

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