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

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.