This paper examines the accelerated failure time competing risks model with missing cause of failure using the monotone class rank-based estimating equations approach. We handle the non-smoothness of the rank-based estimating equations using a kernel smoothed estimation method, and estimate the unknown selection probability and the conditional expectation by non-parametric techniques. Under this setup, we propose three methods for estimating the unknown regression parameters based on 1) inverse probability weighting, 2) estimating equations imputation and 3) augmented inverse probability weighting. We also obtain the associated asymptotic theories of the proposed estimators and investigate the estimators' small sample behaviour in a simulation study. A direct plug-in method is suggested for estimating the asymptotic variances of the proposed estimators. A real data application based on a HIV vaccine efficacy trial study is considered.

中文翻译：

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失效原因缺失加速失效时间竞争风险模型的平滑秩回归

本文使用基于单调类秩的估计方程方法研究了具有丢失故障原因的加速故障时间竞争风险模型。我们使用核平滑估计方法处理基于秩的估计方程的非光滑性，并通过非参数技术估计未知选择概率和条件期望。在这种设置下，我们提出了三种估计未知回归参数的方法：1) 逆概率加权，2) 估计方程插补和 3) 增强逆概率加权。我们还获得了所提出的估计量的相关渐近理论，并在模拟研究中研究了估计量的小样本行为。建议使用直接插件方法来估计所提出估计量的渐近方差。考虑了基于 HIV 疫苗功效试验研究的真实数据应用。