Estimating equation for additive hazards model with censored length-biased data

Aalen’s additive hazards model plays a very important role in survival analysis. In this paper we are interested in the problem of estimating regression coefficients in the additive hazards model with censored length-biased data. Through both of the parametric invariance of the proportional likelihood ratio model and the unique structure of length-biased data, we propose a pairwise pseudo-likelihood estimating equation, which only relies on the complete residual lifetimes in censored length-biased data. In addition, two combined estimating equations are also considered to estimate covariate coefficients. These estimators are proved to be consistent and asymptotically normal. In order to evaluate the performance of the proposed estimators in a finite sample, some simulations are conducted. Finally, a real data example is also provided.