Robust Estimation in the Additive Hazards Model

ALVAREZ, E.E.; FERRARIO, JULIETA

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

TAYLOR & FRANCIS INC

Lugar: Londres; Año: 2013

0361-0926

In the Additive Hazards Model the hazard function of a survival variable T is modeled additively as l(t)=l0(t)+b´z, where l0(t) is a common nonparametric baseline hazard function and z is a vector of independent variables. For this model, the pioneering work of Lin and Ying (1994) develops a closed-form estimator for the regression parameter b from a new estimating equation. That Equation has a similar structure to the corresponding partial likelihood score function for the multiplicative model (Cox 1972) in that it exploits a martingale structure and it allows estimation of b separate from the baseline hazard function. Their estimator is asymptotically normal and highly efficient. However, a potential drawback is that it is very sensitive to outliers. In this paper we propose a family of robust alternatives for estimation of the parameter b in the Additive Hazards Model which is robust to outliers and still highly efficient and asymptotically normal. We prove Fisher-consistency, obtain the influence function and illustrate the estimators with simulated and real data. The latter corresponds to the time-honored Welsh Nickels Refiners dataset first introduced by Doll et.al. (1970) and subsequently analysed by Breslow and Day (1987) and Lin and Ying (1994), among others.