Conditional and marginal estimates in case-control family data – extensions and sensitivity analyses

Abstract

This work considers two specific estimation techniques for the family-specific proportional hazards model and for the population-averaged proportional hazards model. So far, these two estimation procedures were presented and studied under the gamma frailty distribution mainly because of its simple interpretation and mathematical tractability. Modifications of both procedures for other frailty distributions, such as the inverse Gaussian, positive stable and a specific case of discrete distribution, are presented. By extensive simulations, it is shown that under the family-specific proportional hazards model, the gamma frailty model appears to be robust to frailty distribution mis-specification in both bias and efficiency loss in the marginal parameters. The population-averaged proportional hazards model, is found to be robust under the gamma frailty model mis-specification only under moderate or weak dependency within cluster members.

Keywords:

• case-control family study
• clustered survival data
• frailty model
• marginalized hazard function

Acknowledgements

This work is supported in part by grants from the USA – Israel Binational Science Foundation (BSF) (grant number 2006412) and from the National Institute of Health (RO1 AG14358 and P01 CA53996).