A Bootstrap Goodness-of-Fit Test for Parametric Survival Models Under Random Censoring

Abstract

In many scientific disciplines, finding a suitable model compatible with real-world observations is the basis for statistical inference and prediction. In survival analysis, this task is further complicated by censoring. This dissertation introduces a new bootstrap approach to goodness-of-fit testing for parametric survival models, based on the Kaplan–Meier process with estimated parameters. The test statistic compares the nonparametric Kaplan–Meier estimator to a fitted parametric model, quantifying deviations from the null via functionals that yield Kolmogorov–Smirnov or Cramér–von Mises-type tests. We establish the asymptotic correctness of our method by showing that the original and bootstrap test statistics have the same weak limit under the null. The result is a consistent, easily implementable framework for assessing model fit in censored settings.