Statistical Inference Based on Accelerated Failure Time Models Under Model Misspecification and Small Samples

Abstract

Abstract–Accelerated failure time (AFT) models give an intuitive estimator for survival data analysis, but there is a risk of model misspecification. As a serious problem of model misspecification, the test size is likely to be far from the nominal level. Many researchers provided asymptotic corrections of various test statistics under model misspecification. However, their corrected statistics do not have good performance in small samples; in particular, they cause an inflation of test size. Although, the Bartlett adjustment is a popular approach for small-sample correction of the likelihood ratio statistic under the null hypothesis, it is impossible to derive the adjustment factor analytically under model misspecification. In this article, we proposed a robust test to model misspecification in small samples. Our proposed method is based on the Bartlett adjustment and we used the nonparametric bootstrap method to estimate the adjustment factor. We applied the proposed method to the AFT models when the error distribution and/or mean structure are misspecified in small samples. Our simulation results showed that the test size for the proposed method was close to the nominal level, although the existing methods resulted in substantial inflation of the test size. We illustrated our proposed method using two empirical examples.

Keywords:

• Bartlett adjustment
• Bootstrap method
• Likelihood ratio test
• Test size

Supplementary Materials

The supplementary materials contain simulation results for all the settings and Kaplan-Meier curves for datasets used in our case studies, as well as the sample R codes and its description.

Acknowledgments

We would like to thank the associate editor and two anonymous reviewers for their helpful comments.

Additional information

Funding

This research was supported by JSPS KAKENHI grant number 18K11187.