Mimicking Cox-Regression

Abstract

A class of objective functions, related to the Cox partial likelihood, that generates unbiased estimating equations is proposed. These equations allow for estimation of interest parameters when nuisance parameters are proportional to expectations. Examples of the objective functions are applied to binary data with a log-link in three situations: independent observations, independent groups of observations with common random intercept and discrete survival data. It is pointed out that the Peto–Breslow approximation to the partial likelihood with discrete failure times fits a conditional model with a log-link.

Keywords:

• Discrete survival data
• Log-linear models
• Matched sets
• Nuisance parameters
• Objective functions
• Proportional hazard model
• Unbiased estimating functions

Acknowledgments

This article was written while the author was visiting the Department of Biostatistics at Harvard School of Public Health. The author would like to thank the department for their hospitality and in particular Louise Ryan and Matt Wand for discussion that led to this work. The author also acknowledges support from The Norwegian Research Council and Johan and Mimi Wessmann's foundation.