We propose a set of goodness-of-fit tests for the semiparametric accelerated failure time (AFT) model, including an omnibus test, a link function test, and a functional form test. This set of tests is derived from a multi-parameter cumulative sum process shown to follow asymptotically a zero-mean Gaussian process. Its evaluation is based on the asymptotically equivalent perturbed version, which enables both graphical and numerical evaluations of the assumed AFT model. Empirical p-values are obtained using the Kolmogorov-type supremum test, which provides a reliable approach for estimating the significance of both proposed un-standardized and standardized test statistics. The proposed procedure is illustrated using the induced smoothed rank-based estimator but is directly applicable to other popular estimators such as non-smooth rank-based estimator or least-squares estimator.Our proposed methods are rigorously evaluated using extensive simulation experiments that demonstrate their effectiveness in maintaining a Type I error rate and detecting departures from the assumed AFT model in practical sample sizes and censoring rates. Furthermore, the proposed approach is applied to the analysis of the Primary Biliary Cirrhosis data, a widely studied dataset in survival analysis, providing further evidence of the practical usefulness of the proposed methods in real-world scenarios. To make the proposed methods more accessible to researchers, we have implemented them in the R package afttest, which is publicly available on the Comprehensive R Archieve Network.

翻译：我们针对半参数加速失效时间（AFT）模型提出了一套拟合优度检验方法，包括综合检验、链接函数检验和函数形式检验。这套检验基于一个多参数累积和过程，该过程被证明渐近地服从零均值高斯过程。其评估基于渐近等价的扰动版本，从而能够对假定的AFT模型进行图形化和数值化评估。经验p值通过Kolmogorov型上确界检验获得，这为估计所提出的非标准化和标准化检验统计量的显著性提供了一种可靠方法。所提出的程序使用诱导平滑秩估计量进行说明，但可直接应用于其他流行的估计量，如非平滑秩估计量或最小二乘估计量。通过大量模拟实验对我们的方法进行了严格评估，结果表明其在维持第一类错误率方面效果显著，并且能够在实际样本量和删失率条件下检测出对假定AFT模型的偏离。此外，我们将所提出的方法应用于原发性胆汁性肝硬化数据的分析，这是生存分析领域广泛研究的数据集，进一步证明了该方法在实际场景中的实用性。为便于研究人员使用，我们已在R语言afttest包中实现了所提出方法，该包可在综合R档案网络上公开获取。