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.

中文翻译：

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删失了长度偏向数据的加性危害模型的估计方程

Aalen的加性危害模型在生存分析中起着非常重要的作用。在本文中，我们感兴趣的是在带有长度偏倚的数据被审查的情况下，估计附加危害模型中回归系数的问题。通过比例似然比模型的参数不变性和长度有偏数据的独特结构，我们提出了一个成对的伪似然估计方程，该方程仅依赖于删失的长度有偏数据的完整剩余寿命。另外，还考虑了两个组合的估计方程式来估计协变量系数。这些估计量被证明是一致的并且渐近正常。为了评估有限样本中建议的估计器的性能，进行了一些模拟。最后，还提供了一个真实的数据示例。