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We propose a set of goodness-of-fit tests for the semiparametric acceleratedfailure time (AFT) model, including an omnibus test, a link function test, anda functional form test. This set of tests is derived from a multi-parametercumulative sum process shown to follow asymptotically a zero-mean Gaussianprocess. Its evaluation is based on the asymptotically equivalent perturbedversion, which enables both graphical and numerical evaluations of the assumedAFT model. Empirical p-values are obtained using the Kolmogorov-type supremumtest, which provides a reliable approach for estimating the significance ofboth proposed un-standardized and standardized test statistics. The proposedprocedure is illustrated using the induced smoothed rank-based estimator but isdirectly applicable to other popular estimators such as non-smooth rank-basedestimator or least-squares estimator.Our proposed methods are rigorouslyevaluated using extensive simulation experiments that demonstrate theireffectiveness in maintaining a Type I error rate and detecting departures fromthe assumed AFT model in practical sample sizes and censoring rates.Furthermore, the proposed approach is applied to the analysis of the PrimaryBiliary Cirrhosis data, a widely studied dataset in survival analysis,providing further evidence of the practical usefulness of the proposed methodsin real-world scenarios. To make the proposed methods more accessible toresearchers, we have implemented them in the R package afttest, which ispublicly available on the Comprehensive R Archieve Network.

A general model-checking procedure for semiparametric accelerated failure time models