  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.
