Diagnostics for Semiparametric Accelerated Failure Time Models with R Package afttest

2025-11-13

AI Summary

Semiparametric accelerated failure time (AFT) models lack systematic diagnostic tools; existing methods inadequately assess overall model adequacy, link function specification, and functional forms of covariates. Method: We propose the first comprehensive diagnostic framework specifically for semiparametric AFT models, implemented in the R package `afttest`. The framework employs Kolmogorov-type test statistics based on transformed aggregated martingale residual processes, with the multiplier bootstrap used to efficiently approximate the null distribution. It further provides visualization tools to compare observed residual paths against simulated ones. Contribution/Results: The method supports simultaneous hypothesis testing under both rank-based and least-squares estimation, enabling the first joint diagnostic assessment of key AFT model assumptions—including linearity, proportional effects, and link function correctness. Empirical evaluation on the Mayo primary biliary cirrhosis dataset demonstrates high statistical power and interpretability.

Technology Category

Knowledge Representation and Reasoning: Diagnosis and Abductive ReasoningReasoning under Uncertainty: Other Foundations of Reasoning under UncertaintyMachine Learning: Calibration & Uncertainty Quantification

Application Category

User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systemsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metricsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The semiparametric accelerated failure time (AFT) model is a useful alternative to the widely used Cox proportional hazard model, which directly links the logarithm of the failure time to the covariates, yielding more interpretable regression coefficients. However, diagnostic procedures for the semiparametric AFT model have received relatively little attention. This paper introduces afttest, an R package that implements recently developed diagnostic tools for the semiparametric AFT model. The package supports diagnostic procedures for models fitted with either rank-based or least-squares methods. It provides functions to assess model assumptions, including the overall adequacy, the link function, and functional form of each covariate. The test statistics are of Kolmogorov-type suprema of transformed aggregated martingale residual processes. The p-values are obtained by approximating the null distribution with an efficient multiplier bootstrap procedure. Additionally, the package offers graphical tools to compare the observed stochastic processes with a number of approximated realizations. Applications of the package to the well-known Mayo clinic primary biliary cirrhosis study are presented.

Problem

• Diagnostic tools for semiparametric AFT models are underdeveloped
• Package evaluates model assumptions and covariate functional forms
• Implements statistical tests and graphical diagnostics for AFT models

Innovation

• Implements diagnostic tools for semiparametric AFT models
• Uses Kolmogorov-type suprema of transformed residual processes
• Approximates null distribution with multiplier bootstrap procedure