This paper presents a unified rank-based inferential procedure for fitting the accelerated failure time model to partially interval-censored data. A Gehan-type monotone estimating function is constructed based on the idea of the familiar weighted log-rank test, and an extension to a general class of rank-based estimating functions is suggested. The proposed estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal via standard empirical process theory. Unlike common maximum likelihood-based estimators for partially interval-censored regression models, our approach can directly provide a regression coefficient estimator without involving a complex nonparametric estimation of the underlying residual distribution function. An efficient variance estimation procedure for the regression coefficient estimator is considered. Moreover, we extend the proposed rank-based procedure to the linear regression analysis of multivariate clustered partially interval-censored data. The finite-sample operating characteristics of our approach are examined via simulation studies. Data example from a colorectal cancer study illustrates the practical usefulness of the method.

翻译：本文提出了一种统一的基于秩的推断方法，用于对部分区间删失数据拟合加速失效时间模型。基于常见的加权对数秩检验思想，构建了Gehan型单调估计函数，并进一步推广至更一般的秩估计函数族。所提出的估计量可通过线性规划求解，且利用标准经验过程理论证明其具有相合性和渐近正态性。与部分区间删失回归模型中基于极大似然的常见估计方法不同，本文方法无需对潜在残差分布函数进行复杂的非参数估计，即可直接获得回归系数估计量。同时，本文考虑了回归系数估计量的高效方差估计流程。此外，我们将所提出的基于秩的方法拓展至多元聚类部分区间删失数据的线性回归分析。通过模拟研究检验了该方法在有限样本下的操作特性，并结合结直肠癌研究的数据实例验证了该方法的实际应用价值。