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Biostatistics Advance Access published online on February 27, 2008
Biostatistics, doi:10.1093/biostatistics/kxn003
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Regression models for infant mortality data in Norwegian siblings, using a compound Poisson frailty distribution with random scale

Tron Anders Moger* and Odd O. Aalen

Institute of Basic Medical Sciences, Department of Biostatistics, University of Oslo. PO Box 1122 Blindern, N-0317 Oslo, Norway tronmo{at}medisin.uio.no

* To whom correspondence should be addressed.

The power variance function distributions, which include the gamma and compound Poisson (CP) distributions among others, are commonly used in frailty models for family data. In a previous paper, we presented a frailty model constructed by randomizing the scale parameter in a CP distribution. When combined with a parametric baseline hazard, this yields a model with heterogeneity on both the individual and the family level and a subgroup with zero frailty, corresponding to people not experiencing the event. In this paper, we discuss covariates in the model. Depending on where the covariates are inserted in the model, one may have proportional hazards at the individual level, the family level, and a larger group level (for covariates shared by many families, e.g. ethnic groups) or get accelerated failure times. Each of these alternatives gives a specific interpretation of the covariate effects. An application to data infant mortality in siblings from the Medical Birth Registry of Norway is included. We compare the results for some of the different covariate modeling options.

Keywords: Family data; Frailty; Infant mortality; Relative risk; Survival analysis

Received March 2, 2007; revised January 14, 2008; accepted for publication January 22, 2008.


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