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