Practical considerations when analyzing discrete survival times using the grouped relative risk model
- 134 Downloads
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.
- Kosmidis I (2013) brglm: bias reduction in binomial-response generalized linear models. http://www.ucl.ac.uk/~ucakiko/software.html
- McKerracher LJ, Collard M, Altman RM, Sellen D, Nepomnaschy P (2016) Mode of cultural learning, not ecology, influences duration of exclusive breastfeeding in a sample of indigenous Maya women from Guatemala. Am J Hum Biol 28:287–287Google Scholar
- Peña EA, Garrison D (2002) Goodness-of-fit tests with right-censored discrete data. In: Third international conference on mathematical methods in reliability: methodology and practice (submitted paper). http://www.math.ntnu.no/mmr2002/