Incorporating follow-up time in M-estimation for survival data

It has been approximately 30 years since D.R. Cox introduced the proportional hazards method to model the relationship between covariates and survival time. However, the proportional hazards model has limited value when the proportionality assumption is violated. Over the years, there have many been many alternative proposals to the proportional hazards regression model for the case of right censored survival data, but to date none have demonstrated widespread acceptance. In general, problems encountered in these methods include their computational algorithms or evaluation of their asymptotic properties. In this work, an estimating equation based on a U-statistic of degree 2 is proposed. It is easy to implement and the U-statistic framework provides a straightforward development of asymptotic inferential theory for the regression parameters.