Altman Rachel MacKay, Henrey Andrew
Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada.
Lifetime Data Anal. 2018 Jul;24(3):532-547. doi: 10.1007/s10985-017-9410-7. Epub 2017 Oct 11.
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.
